Microworld particles, their origin, properties and application in research and technology

AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy Physics and nuclear medicine

1. Nuclear and radiation physics
1.0. Physics - fundamental natural science
1.1. Atoms and atomic nuclei
1.2. Radioactivity
1.3. Nuclear reactions, nuclear energy
1.4. Radionuclides
1.5. Elementary particles and accelerators

1.6. Ionizing radiation

1.5. Elementary particles and accelerators

In interpreting the properties of atoms in Chapter 1.1, we have learned that neither an atom, nor even its nucleus, are elementary building blocks of matter, but are composed of even smaller particles - electrons, protons, neutrons. In the study of radioactivity, we also recognized some other particles - positrons, neutrinos. Are these subatomic particles really already internally "monolitic" - elementary and fundamental? Or do they have their internal structure, composed of "even smaller" particles? (A more detailed discussion is below in the section "Are elementary particles really elementary?").
  In this chapter we will try a brief but systematic trip to the varied and wonderful world of elementary particles. We will proceed inductively in the interpretation. After introductory passages on the common properties of particles, their classification and patterns of interactions, we will move from basic, known and widespread particles and their simple properties (straight from experiments), through "more exotic" particles and more complex mechanisms of interactions, to unitary symmetries and attempts to clarify the internal structure of particles. We will also mention hypothetical and model particles, some of which have not yet been directly discovered, or their role in nature is not yet fully understood.
  We will first outline the systematics of elementary particles and then analyze the properties and interactions of individual specific types of particles, including the formation of particles in high-energy interactions. And also antiparticles - their origin and annihilation, their role in nature, possibilities of use. We will also think about what the individual particles have in common and how we have progressed towards a unified understanding of particle and field physics - unitary field theory. Finally, we describe how we investigate the interactions of particles at high energies on particle accelerators.
  Behind all this knowledge about elementary particles is hidden the enormous effort and colossal volume of work of thousands of physicists, technicians and workers - designers of complex acceleration systems and detection apparatus.
  But before that, let's make a few general remarks and discussions about particles as such :
Terminological note - elementary ? :
The name "elementary" or "basic" should mean that it is a further indivisible object, without internal structure; it is thus the simplest material object acting as a separate physical entity. However, in the course of the scientific knowledge of the microworld, it has been shown several times that particles previously considered to be basic (elementary) have an internal structure and consist of even "smaller", more basic or "more elementary" particles. According to earlier opinions "indivisible atom" (hence its name), has a complex structure of the electron shell and the atomic nucleus. Protons and neutrons in atomic nuclei have also been considered indivisible, but next research (in a standard particle model) has shown that they consist of quarks (as do other hadrons). Opinions on the "elementality" of particles can thus vary depending on the current state of physical knowledge
(a more detailed discussion is in the passage below "Are elementary particles really elementary? ').
  Therefore, since many particles are "folded", the "elementary" may be misleading. However, this is the established name, like the name "atom", which has long been not "indivisible". In recent years, often the word "elementary"omits and speaks only of "particles".

Are there any elementary particles at all? "Ball" model.
Our idea of existence - that "something exists" - is based on our daily experience of observing the macroworld of the surrounding nature. There are, for example, stones - we can see, touch and weigh by hands, or throw them. There are different species of plants and animals with specific looks and properties. There are cells in organisms that can be observed under a microscope, including their internal structure
(see eg 5.2., Section "Cells - basic units of living organisms") and study their biochemical manifestations. However, in a microworld of subatomic or even subnuclear dimensions, it is more complicated.
  Particles of the microworld we can't see even with the strongest microscope - they are much smaller than the wavelength of visible light. Even if we reduced ourselves in the imagined sci-fi concept to "dwarfs" the size of a picometers and observed with radiation of much shorter wavelengths, we would not see any localized particles. Quantum uncertainty relations "blur" the velocity determination with accurate position measurement, and the particle velocity measurement in turn blurs its position. We would perhaps only see blurred tufts of fluctuating fields. From this usual point of view, we could make a "heretical" claim that "elementary particles do not exist "!
  However, in more detailed physical research, we come to the realization that there is a "something" hidden that carries physical forces, such as an electric charge, something that transmits energy trought space, that causes mutually influences - interactions - of material bodies. In classical physics it is a physical field, in quantum physics the quantum of fields. We call this "something" the elementary particles
(the word "elementary" discussed above). We can not imagine it in any concrete way and that is why model them as small spheres (small balls) - eg. electrons draw a red protons as blue, neutrons as gray spheres, neutrinos as perhaps green; it is a matter of convention. These bullets, having a certain mass, charge and other physical characteristics, are, according to the usual laws of (relativistic) mechanics move through space at a certain speed and the associated kinetic energy. With a certain probability (see "Effective cross-section" below), they can "collide" - interact - with other spheres (particles), while other spheres - particles of the same or different properties - fly out of this place. However, during the actual internal course of the interaction, the "ball model" cannot be used, there are often quite complex quantum-field processes (see "Feynman diagrams" below).
  The ball model is very successful - in co-production with physical mechanisms of electromagnetic, strong and weak interactions can explain or represent practically all phenomena with particles of the microworld in atomic, nuclear, radiation and particle physics. This "ball illustration", possible supplemented by the wave nature, therefore we draw in most of the pictures of our treatise "Nuclear Physics and the Physics of Ionizing Radiation".
Who ordered the "exotic" particles ?
To understand the structure of matter around us, we will suffice with the few particles mentioned above (1.1 and 1.2) - photons, electrons, protons, neutrons (in mor complex phenomena also neutrinos, mesons, quarks u and d ). Nevertheless, in the interactions of particles (whether artificially induced or in cosmic rays) we encounter many other particles, which - at is seem - they have no role to play in building of matter. Nothing of them are composed, they are not able to create bound structures, they usually disintegrate immediately after their formation. The metaphorical question arises "who ordered them?" - what is the meaning and role in the functioning of our world?
(This question was first raised by I.I.Rabi in connection with the discovery of the muon). The answer to this question is trying to find a unitary field theories and particle physics in co-production with astrophysics and cosmology.
  Unitary field theories attempt to find laws and mechanisms that allow or imply the existence of these particles - as a quantum of excited fields or geometric structures (B.6 "
Unification of fundamental interactions. Supergravity. Superstrings."). Astrophysics and cosmology show, that all these particles were probably once in the earliest stages in the universe, they already played their role in the "cooking" of matter and then disappeared (see eg 5.5 "Microphysics and cosmology. Inflationary universe." of the mentioned books); without them the universe would not be as it is, perhaps there would be no mass at all..?.. Some of these particles perhaps still form a mysterious "dark matter" in space (see eg 5.6 "The Future of the Universe. The Arrow of Time. Dart matter, Dark energy."). And we are now trying to re-create and explore these particles in order to understand the early universe and be able to answer the questions more surely, how matter was formed and what is its internal properties ...

Indistinguishability of elementary particles
Bodies and particles in classical mechanics do not lose their "individuality" during their motion, even if they are the same particles with the same physical properties (from a macroscopic point of view). Such particles forming a given physical system can be "marked" or "numbered" at a certain initial time and then, while monitoring their movement, we can, at least in principle, identify each of the particles in the system at any time - the particles are distinguishable here.
  In the analysis of motion and behavior of particles in quantum mechanics the situation is completely different in this respect. Due to corpuscular-wave dualism and the uncertainty principle, particles, such as electrons, have no trajectories in the sense of classical kinematics. If we determine the position of a particle at a given moment, its momentum becomes indeterminate; then in the following moments it is not possible to determine any specific values of the particle coordinates. Therefore, if we try to locate electrons at a certain moment and imaginarily "number" them, then at another point in time when locating an electron at a certain point in space, we can no longer determine which of the considered electrons got to this point. In quantum mechanics, there is no possibility to continuously monitor the motion of individual particles and thus distinguish them. Microparticles are manifested only by their interactions with other particles. Thus, in quantum mechanics, the same particles completely lose their individuality - their physical properties are identical, they are indistinguishable from each other.

Spin, symetry of wave function and statistical behavior of particles 
The quantum-mechanical behavior of sets consisting of the same type of particles is based on this principle of indistinguishability of particles. Since the particles are the same and indistinguishable, the physical states of the system obtained by exchange (swapping, transposition) the two particles "1" and "2" must be equivalent; from a quantum point of view, the probability density
y 2 of this system must remain the same when the particles are interchanged: y ("1", "2" y ("2", "1") 2 , ie either y ("1", "2") = y ("2", "1"), or y ("1", "2") = - y ("2", "1") - the wave function of the system can only change by a sign. Thus, there are two possibilities: 1. The wave function is either symmetrical and does not change with any permutation of particles; 2. Or, the wave function of the system is antisymmetric - it changes sign when each pair of particles is transposed. Which of these options is realized depends on the type of particles - it is related to their spin (1.1, passage "Spin"). Below, according to this criterion, we divide particles into bosons with a symmetric wave function (integer spin) and fermions with an antisymmetric wave function (half-number spin) - passage "Fermions-Bosons". By analyzing the wave functions of a system of the same particles, it can be shown that in a set of identical fermions, two particles (or more particles) cannot be in the same quantum state - the so-called Pauli exclusion principle applies. While in a set of bosons there may be an unlimited number of particles in the same quantum state.
  The analysis of the relationship between the spin of particles and their statistical behavior in a set of particles decays into three sub-problems :
1. Relationship between the spin and symetry of the wave function
Spin is an intrinsic angular momentum of particles, analogous to the rotational angular momentum of a particle during its rotation around its axis (but it cannot be explained quantitatively in this way!), rather related to symmetries with respect to spatial rotation (within quantum mechanics, spin is described in 1.1., passage "Spin"). From the point of view of quantum field theory (secondary quantization), a spin field is interpreted as a measure of symmetry in the plane wave of the field: a field has spin s (spin number s), if its plane wave is invariant to rotation by an angle of 2p/s around the propagation direction. Thus, the spin of a particle indicates the rotational symmetry of the wave function relative to the rotation in space. For particles with integer spin, most often s=1, the wave functions are invariant to rotation by an angle of 360o; the wave functions are symmetric with respect to the transposition. ..., the particles behave like bosons. For particles with a half-numbered spin 1/2, the wave functions are antisymmetric. ....... ......, the particles behave like fermions.
Note: This is just a brief heuristic outline of the relationship between the particle's spin and the symmetry of the wave function. In a more detailed derivation, analysis using relativistic quantum field theory is used.
2. Relationship between symetry of wave function and occupancy of quantum states
Consider two identical particles a, b with the wave functions y(....... y(........ ......; the wave function for a system composed of these two particles will then be Y(....... = ..... If the functions y(....... y(..... are antisymmetric with respect to the transposition of particles y(....... = - y(...., the resulting wave function Y(...... a pair of particles located in the same quantum state will be equal to zero - the probability is zero here. Two particles with an antisymmetric wave function cannot be in the same quantum state, applies to them so-called Pauli's exclusion principle. For particles with a symmetric wave function with respect to transposition, all combinations of state functions will have positive signs, so the resulting wave function y will also be positive and non-zero - any number of particles of this kind can be in the same quantum state.
3. Own statistic behavior of particle sets
By statistical behavior (abbreviated as "statistics") of particles we mean the average distribution of their states - according to velocities, kinetic energies - in a large set of these particles. This analysis is dealt with by a special field of statistical physics, in practice mostly in conjunction with thermodynamics. In the simplest case of a sufficiently large set of non-interacting particles in thermodynamic equilibrium, behaving according to the laws of classical (non-quantum) physics, analysis by methods of statistical mechanics shows that the average (expected) number of particles <N (E)> with energy E is given by Maxwell- Boltzmann distribution <N (E)> = 1 / e-E/kB.T, where T is the absolute temperature [oK] and kB is the Boltzmann constant (giving the conversion coefficient between the average kinetic energy of the particles in the gas and the thermodynamic temperature of the gas kB = 1.38064910-23 J/oK).
  In the case of the above-mentioned quantum properties (point 2.), the distribution function N(E) will depend on the occupation rules of quantum states. In quantum statistical physics, the distribution function according to the occupancy possibilities of quantum states of particles is specified to the form :
           < N(E) >  =  1 / (e-E/kB.T 1)   ,
where in the denominator the positive sign "+" applies to fermions - Fermi-Dirac statistical distribution and the negative sign "-" to bosons - Bose-Einstein distribution.
Note: In the thermodynamics of gases formed by atoms or molecules with a certain chemical composition, the denominator of distribution functions also has the so-called chemical potential m : e-(E-m)/kB.T, expressing energetic changes in chemical reactions that may occur during atomic collisions. For elementary particles, an analogy of this situation could arise if the particles had sufficient kinetic energy to interact with transmutations and the formation of new particles.
  In the Fermi-Dirac distribution of particles that satisfy Pauli's exclusion principle, there are also situations where the same energy corresponds to some different states - the so-called degeneration of energy levels occurs. In the numerator of the distribution law, instead of "1", there is a degeneration factor g, which indicates the number of different states corresponding to a certain same energy level: <N(E)> = g / (e-E/kB.T + 1). Degeneration of energy levels occurs mainly due to some kind of symmetry in the system, such as motion in a centrally symmetric field.
  An important property of the Fermi-Dirac distribution of particles in a set of fermions is the possibility of the formation of so-called degenerated matter or degenerated gas. In a set of non-interacting fermions - the ideal Fermi gas - particles enclosed in a finite volume can acquire only discrete energy values (quantum states). Pauli's exclusion principle prevents identical fermions from occupying the same quantum states. At high densities of matter, all energy levels of fermions are occupied up to a certain maximum energy, which corresponds to a certain maximum momentum; this condition is called degeneration, it is a degenerate fermion gas. Each additional fermion in a given volume must occupy a new higher energy level and thus have a higher momentum. The pressure here therefore increases significantly faster than corresponds to the equation of state of an ideal gas.
  The statistical behavior of electrons, protons and neutrons according to the Fermi-Dirac distribution, with degeneration, is of great importance in stellar astrophysics, where it co-determines the equilibrium state of stars against gravity, disturbance of this equilibrium and collapse of stars on white dwarf and neutron star (4.1 "The role of gravity in the formation and evolution of stars" and 4.2 "The final stages of stellar evolution. Gravitational collapse. The formation of a black hole." in the monography "Gravity, black holes and space-time physics").
  The outlined analysis of the relationships between spin, symmetry of wave functions and statistical behavior of sets of particles, can be summarized in the resulting theorem :

Spin => wave function symetry => statistical behavior of particles
Particles with half-numbered spin (s = 1/2, 2/3, ....) have a wave function antisymmetric with respect to the transposition of particles, in the same quantum state there can be at most one of these particles (Pauli exclusion principle) and in a set of particles is controlled by Fermi-Dirac statistics - they are fermions.
Particles with integer spin (s = 0, 1, 2, ....) have a wave function symmetric with respect to the transposition of particles, in the same quantum state there can be an unlimited number of these particles and in the set of particles they follow Bose-Einstein statistics - they are bosons.

Physical parameters of particles; quantum numbers
The properties of elementary particles are characterized by suitable physical parameters, some of which are also known from classical physics, others are purely quantum and have no classical analogy. These parameters of elementary particles, which are mostly quantized, ie take on discrete values, are called quantum numbers.
Rest mass, lifetime
These are the basic unquantized characteristics of particles. Rest mass of particles is rarely expressed in grams, but most often in energy units electron volts eV, keV, MeV *) - in connection with Einstein's relation E = m.c
2 equivalence of mass and energy. It is sometimes given in multiples of the electron mass. Life time, resp. the half-life of particles is expressed in seconds and their decimal fractions (10 -xx sec.); for stable particles it is considered to be .
*) More precisely, the energy expression of mass is in MeV/c2, but c2 is often omitted.
Size, dimensions and shape of elementary particles? - problematic!
In everyday life and in the physics of macroscopic phenomena, the spatial size of bodies, their shape and individual dimensions are of great importance. In the microworld, however, this is problematic. In the case of particles of the microworld, due to the wave nature and quantum relations of uncertainty, the concept of spatial "size" loses its meaning - it cannot be defined and measured. These particles are not some tiny "material bodies" with a solid surface, as we know from our usual experience from the macroworld, but rather spatially distributed "densities of fields" of a wave nature. They have no specific boundaries. Only some of them can be defined some "effective size" of particles in interactions - using the range of forces and the so-called effective cross section
(see below "Interactions of elementary particles", section "Effective cross section of particle interactions"). From scattering experiments in particle bombardment - in determining how "close to each other" particles penetrated. However, such an "effective size" may be different for the same particle in various types of interactions. These problems with particle size are circumvented by a physical agreement that elementary microworld particles will in principle be considered to be zero-sized points, while effective cross-sections being considered for interactions...
Physical efforts to determine the size of elementary particles 
In the early days of the study of the microworld, atomic and nuclear physicists worked hard to determine the size ("radius") of newly discovered particles - the electron and the proton.
For an electron with mass m e and elementary charge e, three very different values were reached in the analysis from different points of view :
- The classical (non-quantum) or Thomson radius of the electron is based on the model that the electron is a sphere on whose surface the electric charge of value e is uniformly distributed. The radius of electron r e is taken to be the radius of the sphere such that the electrostatic potential energy of this charge corresponds to the rest mass of the electron me according to the relativistic relation of the equivalence of mass and energy E = me. c2. Comes out: re = e2/4peo me c2 = 2.818x10-13 cm. It's such a radius that all resting electron mass me had an electrical origin (was formed by electrostatic potential energy; this approach is also analyzed in 1.6, passage "Nonlinear Electrodynamics" monograph "The gravity, black holes and spacetime physics").
- Bohr radius of the electron comes from the fact that the majority of electrons bound in atoms, so the size of the electron would be natural to deduce from the dimensions of the atom. According to Bohr's quantum model (1.1 , part "Bohr model of the atom") has the lowest (basic, unexcited) orbit of an electron in a hydrogen atom radius r1 =4peo h/m e e2 = 0.529 x10 -8 cm. This value is considered here as the radius of the electron re .
- The Compton wavelength of an electron is the smallest distance to which an electron can be constrained ("compressed") according to quantum uncertainty relations: lc ~ h / me c 10-9 cm. If we try to compress the electron to a smaller size, then according to the uncertainty principle, its momentum becomes so large that its kinetic energy exceeds the rest energy of the electron me c2. In this case, there will be enough energy to form a new electron-positron pair. Compton length is therefore the smallest distance, on which two electrons can penetrate without the formation of new particles ...
  From the current point of view, these values are only of model and historical significance and are not considered "real" dimensions of the electron. For electrons, in the end, no plausible value of "size" could be determined, the higher the kinetic energy, the deeper they approach each other during the interaction - as if they were points with zero size (<10-16 cm)..?.. Similar to that expected for other leptons *). From the point of view of corpuscular-wave dualism, the effective size of an electron, its "wavelength", would depend on its velocity (1.1, passage "Particle-wave dualism").
*) At neutrinos, which show only a weak interaction, the effective "size" is assumed to be significantly lower than for electrons, about 10-16 cm. No direct measurements are feasible here.
  For protons and neutrons, their effective "size" for strong interactions was set at about 1.6x10-13 cm, according to the measured range of these nuclear forces (see 1.1, passage "Strong nuclear interaction"), as a "residual" manifestation of a strong interaction between quarks inside protons and neutrons. Similarly for other hadrons (pions, kaons, hyperons). For electromagnetic interactionthe "size" of a proton is measured by the scattering of accelerated electrons. Another method is hydrogen spectrometry: accurate measurement of energy levels (difference in energies between 2S1/2 and 2S1/2 orbitals - hyperfine structure caused by Lamb shift due to quantum fluctuations of virtual electron-positron pairs in the electric field of a proton); this method resulted in a value of 0.88x10-13 cm. These measurements were modified in a new experiment where hydrogen atoms were exposed to a beam of low-energy muons, whereas some of the muons were captured, replacing electrons in the hydrogen atom. Such a muon due to its higher weight (it is about 200 times heavier than an electron) orbits significantly closer to a proton, so differences in energy levels are "more sensitive" to the structure of the proton. Here a slightly lower value of the proton radius of 0.84x10-13 cm was reached. Protons, like other hadrons, are not "elementary" particles, but are composed of quarks, so the so-called quantum chromodynamics (see "Imprisoned quarks" below) has something to say about their structure and "size", at the fundamental level then unitary field theory ("Unification of fundamental interactions. Supergravity. Superstrings." in the monograph "Gravity, black holes and space-time physics").
  For photons, as quanta of electromagnetic waves, their effective "magnitude" depends on the wavelength of the radiation. Photons of gamma radiation are effective only picometres dimensions, visible light photons hundreds of nanometers, in the case of radio waves we could absurdly imagine the many-meter dimensions of "photons" - here, however, photons can not prove at all ...
Electric charge
An extremely important parameter of particles is their electric charge, which is quantized and therefore, instead of in coulombs, is expressed in multiples of the magnitude of the elementary charge of the electron |e| with the sign *) - the electron then has a charge -1, proton +1, hyperon
W charge -2, neutron and other uncharged particles of course 0. Antiparticles to charged particles have charges of opposite sign (and the same absolute size). In all known interactions, the law of conservation of electric charge is strictly fulfilled: the sum of the charges of the particles before the interaction is the same as the sum of the charges of the particles flying out after the interaction.
*) Below we will also encouter the charge 1/3 e or 2/3 e in quarks.
Spin, magnetic moment
Another important quantum characteristic of particles is their spin or spin number s, expressing the own angular momentum of a particle in multiples of the Planck constant h. Except to the zero spin s=0 (occurring in the mesons
p and K), the smallest possible spin is the value s = 1/2 (electrons, protons, neutrons, neutrinos, muons have such a spin). Spin s = 1 have photons, s = 3/2 heavy hyperons W, spin s = 2 at gravitons. Closely related to the spin of corpuscular particles is their magnetic moment, given in multiples of the elementary Bohr magneton e.h/4p me , resp. nuclear magneton e.h/4p mp (discussed in more detail in 1.1, passage "Quantum momentum, spin, magnetic moment"). The spin number of the particles further determines the quantum-mechanical statistical behavior in the sets of particles - see "Bosons - Fermions" below.
Note: Spin - rotation ?
According to classical mechanics, the spin of particles is usually interpreted as their rotational momentum. However, this property of elementary particles has a specific quantum nature and cannot be satisfactorily explained by classical mechanical concepts
(spin cannot be quantitatively explained, for example, by the rotation of a particle around its own axis!) .
is the quantum number, characterizing the behavior of the wave function of quantum mechanical object - nuclei or elementary particles - relative to a spatial mirror reflection, i.e. the coordinate transformation x
-x, y -y, z -z, t t. If the while doing so the wave function describing the state of the particle does not change, the parity is positive: P = 1, or "+". If the wave function of the system changes sign during this transformation, the parity is negative: P = -1, or "-". It can be shown that the parity of a system with an orbital momentum l is (-1) l. Analysis of elementary particle interactions shows that the parity of the proton and neutron is positive, while the parity of photons and mesons p+, -, o is negative. The parity is sometimes given as the index at the top right of the quantum momentum J of the system, such as the nucleus, JP: either J+ or J-. For elementary particles then as an index for the spin number: sP - eg 0-, (1/2)+ and so on.
  Overall, parity P is not a very important quantum number. However, parity has its theoretical significance in connection with symmetry properties and conservation laws in particle interactions - see below the section "
CPT symmetry of interactions" in the section "Four types of interactions". Parity is maintained at a strong and electromagnetic interactions, but with weak interactions are not conserved (discussion and experimental verification see below "CPT symmetry interactions"; the hypothesis of the so-called mirror matter, discussed below in the section "Hypothetical model particles", passage "Shadow Mirror Matter - Cathoptrons?" is based on the failure to preserve parity).
Lepton and baryon number
In order to classify elementary particles, particles are assigned a lepton number L, which for leptons is L =
1 (depending on whether it is a particle or an antiparticle), for other particles L = 0, and the baryon number B, which for baryons is B = 1 (again "+" for particles, "-" for antiparticles) and for particles other than baryons is B = 0. The lepton and baryon number is preserved for practically all types of interactions *) - the sum of leptons and baryons (respecting the signs) before and after the interaction is the same.
*) The only exception is with the gravitational interaction involving black holes: when particles are absorbed below the horizon of a black hole, all their individual characteristics are lost except mass, electric charge and orbital momentum ("black hole has no hair"); the particle seems to "dissolve" in the total gravitational field of the black hole - see 4.5 "Theorem "black hole has no hair"", in "Gravity, black holes and spacetime physics". Lepton and baryon number is not preserved even during the quantum evaporation of black holes - 4.7 "Quantum radiation and the thermodynamics of black holes" in the same monograph.
Another quantum numbers isospin, strangeness, and hypercharge will be introduced below in connection with mesons K, hyperons, and unitary symmetries of elementary particles - see the passage "Unitary symmetries and multiplets of particles".

Intermediate and virtual particles
According to the ideas of quantum field theory, the mutual force action of two particles takes place in such a way that these particles exchange (transmit and receive) so-called intermediate particles, which are quantums of the respective field. Each particle subject to interaction is surrounded by a "cloud" of respective intermediate particles, which remain virtual, until there is an act of interaction.
  To explain the mechanisms of interactions and mutual transformations of elementary particles, not only observed "real" particles entering into interactions or radiated as a result of the interaction are used, but often also certain "auxiliary" particles mediating certain stages of interaction, that are not directly observed. Such virtual particles *) "exist" only for a very short time, which is shorter than the time required to measure their energy according to uncertainty relations. Commonly known and proven particles, such as photons, can serve as virtual particles, but often hitherto unknown and unproven particles are often used - model and hypothetical particles (they are mentioned below). Virtual particles cannot be directly detected, but can manifest themselves in real measurable phenomena because they interact with real particles and fields; such latent interactions can cause, for example, spontaneous emission of real particles or anomalies depending on the effective cross sections of the interactions on energy. Interactions using intermediate particles are represented by so-called
Feynman diagrams.
*) Virtual = imaginary, apparent, unreal, potential, physically absent. It originally comes from lat. virtus = man, masculinity, virtue, but has undergone a significant etymological change.

The "temperature" of the particles ?
In the science of heat - kinetic theory of heat, thermals, thermodynamics - temperature is closely related to the velocity or energy of particles. The temperature of a normal substance environment is given by the speed of oscillating or chaotic movement of particles of which a substance is composed - atoms and molecules. Root-mean-square speed v
k2 of the motion of particles is related to the thermodynamic temperature T [oK] the relation
/2 mo vk2  =  3/2 kB.T   ,
where k
B = 1.38.10-23 J . K-1 is Boltzmann's constant and mo is the rest mass of particules of matter (in the simplest case of an ideal monoatomic gas). Thus the temperature is proportional to the mean kinetic energy of the particles Ek = (1/2) . mo vk 2 .
  This kinetic concept of temperature is generalized from the material environment to the environment composed of particles other than molecules and atoms - to the physical sets of various microparticles and their bound combinations *). The kinetic energy of the particles E
k is then measured here in electron-volts [eV] and the Boltzmann constant has the value kB= 8.617.10-5 eV.K-1 (the carrier of kinetic energy in ionized matter and sets of particles are mostly electrons). In principle, therefore, we can equivalently measure the energy state of particle sets either by the mean kinetic energy Ek of the particles in [electron volts], or by the thermodynamic temperature T in [degrees of Kelvin].
*) It would certainly be misleading to say that "the particle has a temperature of xxx K"; the particles have no "temperature" quantity. More precise is the formulation "a given set of particles has a thermodynamic temperature of xxx K". The temperature in such a collection of particles has obviously not be measured by conventional thermometer inserted into the system (with the attainment of thermal equilibrium), but on the basis of the radiation emission or directly by measuring the energy particles by means of detectors.
  Room temperature T = cca 300 oK corresponds to the kinetic energy of the electrons Ek = about 26 millielectronvolts. The high-temperature plasma required for efficient thermonuclear fusion of deuterium and tritium must be heated to about 150 million degrees (regardless of Kelvin or Celsius), which represents a kinetic energy of particles of about 12 keV (see 1.3, section "Atomic fusion"). nuclei "). And in quark-gluon plasma a huge thermodynamic temperature higher than 1012 degrees is reached for a short moment (see the passage "Quark-gluon plasma -"5th state of matter" " below), the kinetic energy of the particles reaches the order of TeV.

Classification of elementary particles
Elementary particles are sorted and divided into groups according to their significant properties, expressed by physical parameters and quantum numbers. The most fundamental characteristic of each subject *), and therefore also the elementary particle, is its weight - more precisely the resting mass m
  According to the special theory of relativity, the actual mass m (inertial mass, characterizing according to 2. Newton's law F = m.a the resistance of the body to acceleration) depends on the speed of motion of the body v : m = mo/(1-v2/c2), where mo is the rest mass, determined in the inertial frame of reference in which the body is at rest. The resulting mass m is greater the faster the particle moves; for v c grows above all limits. Therefore, no particle whose rest mass is non-zero can move at the speed of light (or superlight speed). According to a special theory of relativity, the total energy of a particle (the sum of rest and kinetic energy) is equal to E = (mo/(1-v2/c2)).c2 = m.c2 - Einstein's equation expressing the equivalence of mass and energy.
*) Another basic characteristic of objects in the macroworld - spatial size (dimensions, volume), has no significance for elementary particles ! Due to corpuscular-wave dualism and the uncertainty principle, no certain size can be assigned to particles in the microworld
(discussed in more detail above in the section "Size, dimensions and shape of elementary particles? - problematic!"). In the model ideas, however, we can consider some "effective" particle sizes, given by the interaction properties of these particles (eg the proton has a dimension of 1.6.10-13 cm in terms of strong interaction). On this ideas based the so-called effective cross section of particle interaction (see below).
  According to the rest mass, we divide the particles into four groups :

The origin of particle rest masses
The above-mentioned diametrically different rest masses of different types of particles used to be a purely empirical matter in the past. Now the standard particle model tries to explain them by basically two mechanisms :
1. For basic, elementary structureless particles - photons, leptons, neutrinos, quarks, intermediate bosons - their mass depends on the values of the coupling constants of the interaction of the respective fields with the ubiquitous Higgs-Kibble scalar field (whose quanta are Higgs bosons). For fermions, this interaction is also called the Yukawa coupling (it is modeled by the Yukawa potential with an exponential dependence).We can imagine it in a simplified way, that a particle "draggs" with it a certain part of the energy-momentum of the Higgs field (according to the size of the coupling constant), which effectively makes it appear more massive (according to Newton's 2nd law), puts up a greater resistance to acceleration, and carries a higher kinetic energy at the same speed.
  Photons and gluons do not interact with the Higgs field at all, so they have zero rest mass. "Ordinary" electrons interact with the Higgs field only relatively weakly (coupling constant g ~ 3.10
-6), they have a rest mass of 511keV. Their related leptons, muons ("heavy electrons") interact more strongly (coupling constant ~ 6.10-4) and have a rest mass 200 times greater, 105.6 MeV. And tauons ("super-heavy electrons") interact with the Higgs field very strongly (coupling constant ~ 1.10-2) and therefore have a rest mass of 1777 MeV, more than 3000 times greater than electrons! Quarks "d" with a coupling constant ~ 2.6.10-5 have a mass of 4.6 MeV, "s" quarks with a coupling constant ~ 5.10-4 have a mass of 94.6 MeV, "b" quarks with a coupling constant ~ 5.10-2 have a mass of 4.3 GeV. The bosons W+,-, Z0, causing a weak interaction, have a particularly strong interaction with the Higgs field (coupling constant g ~ 1), which leads to their high masses of 80-90 GeV and a very short range of the weak interaction.
Note: Even this approach remains basically phenomenological: the empirically measured masses of M particles are only transformed into values of the coupling constant g with the Higgs field according to the simple formula M = g .Vv/21/2, where Vv is the "expected" value of the Higgs vacuum potential Vv = (21/2. GF)-1/2 ~ 246 GeV (GF is the reduced Fermi constant of the weak interaction). The standard model cannot yet predict specific values of masses or binding constants.
  This mechanism is often associated with the rather unintuitive concept of "spontaneous symmetry breaking" - it is discussed in more detail in B.6 "Unification of fundamental interactions. Supergravity. Superstrings.", passage "Symmetry in physics and their breaking" of the book "Black hole gravity and the physics of spacetime".
2. For "composite" particles, hadrons - protons, neutrons, hyperons, pions, kaons, ... - the rest mass of their structural components - quarks - is only a small part of the total mass, around 1%. Most of a hadron's mass comes from the kinetic energy of the internal motion of its quark components. E.g. proton has a mass of 938MeV, while the rest mass of the "u" quark is 2MeV and the "d" quark is 5MeV.

The spectrum of rest masses of particles - is it limited or infinite ?
The rest masses of various types of particles are very different, their values form a wide "spectrum". From photons with zero or neutrinos with a slight rest mass, through light electrons (about 0.5 MeV), mesons (around 140-500 MeV), to heavy baryons with rest masses of 1-1.7 GeV. The heaviest known particles are bosons W
+,-, Zo of weak interactions weighing about 80-90 GeV and Higgs bosons with rest mass 120 GeV approx. The question arises as to whether the mass spectrum is already ending here, or are there even heavier particles? In the 1960s and 1970s, the so-called Hagedorn hypothesis was discussed of existence an infinite number of particles of ever higher masses that could gradually appear as ever more powerful accelerators were constructed. Current particle physics is rather skeptical about this, it could possibly only be excited states of quark-gluon combinations..?.. - only future experiments can decide.

According to the way of interaction between elementary particles, a special group is singled out :

According to lifetime, we can divide elementary particles into :

Fermions - Bosons
In the passage "Indistinguishability of particles" - "Spin, symmetry of the wave function and statistical behavior of particles" we have shown how the spin of particles determines the statistical behavior of sets of particles.
Thus, according to spin, and consequently also according to quantum-mechanical statistical behavior in sets of particles, elementary particles are divided into two large groups :

Fermions in the role of bosons; Superconductivity
Under certain circumstances, even a set of fermions, such as electrons, can effectively behave like bosons. If we reduce the temperature of a conductive substance containing free electrons in the form of an "electron gas", at temperatures around 4 K, electrons combine into pairs - so-called Cooper pairs, in which the half-number spins of electrons in the opposite direction add up to zero spins (singlet pairing), ie integer. The bond between the electrons of a Cooper pair is mediated by their interaction with an oscillating crystal lattice. Such pairs then behave like bosons, which at low temperature tend to occupy the lowest energy state (Pauli's exclusion principle does not forbid them, because it does not apply to bosons). The so-called boson condensate is formedin the basic energy state, in which the paired electrons move through the crystal lattice completely freely without resistance - electrical superconductivity is created.


Superconductivity is thus a quantum-electric phenomenon in which the material does not put any ohmic resistance to the passage of an electric current and no heat is released in the material. It was discovered in 1911 by the Dutch physicist H.K.Onnes, who liquefied helium on a device of his own design and measured the electrical resistance of metals at low temperatures in further experiments. With decreasing temperature, the resistivity of metals generally decreases
(with slower oscillating atoms of the crystal lattice, electrons precipitate less often, they pass more easily). By extrapolating this slight almost linear decrease in resistance with temperature to absolute zero, a certain small residual value of resistance can be expected *).
*) From the classical point of view, the opposite situation could be expected: when stopping their thermal movements, electrons could combine with ions of the crystal lattice, "freeze" and stop moving - the conductor would become an insulator that does not transmit electric current.
  When Onnes measured the temperature dependence of the resistance on a sample of high-purity mercury, he was surprised to find a sudden drop in the mercury resistance to zero
(unmeasurably small) at temperatures around 4.2 K. Superconductivity was then found for lead, tin and many other materials and alloys. Microscopic theory of low-temperature superconductivity developed in 1957 by J.Bardeen, L.Cooper and J.R.Schriffer (BCS theory) - according to it, the bond between electrons and oscillations of the crystal lattice (phonons) can effectively lead to an attractive interaction between pairs of electrons: the electron as it passes through the crystal lattice creates a positive "hole" through which the second electron is attracted. This dynamic bond creates effectively bound Cooper pairs of two electrons, which form a boson condensate with a high degree of correlated electron arrangement. The temperature at which a substance transitions from a normal to a superconducting state is called the critical temperature. Intensive research on superconductivity has revealed a number of materials with this property, which can be divided into two groups :
- Type I superconductors are some metals that achieve superconductivity at low temperatures (critical temperature lower than 30 K) and lose superconducting properties in stronger magnetic fields (Meissner-Ochsenfeld effect). This superconductivity is explained by BCS theory.
- Type II superconductors are some alloys of metals (especially copper) and non-metallic admixtures (ceramic oxides), which achieve superconductivity even at higher critical temperatures and retain this property even in strong magnetic fields. Particularly interesting materials of this kind are composite compounds of yttrium, barium, copper and oxygen Y1Ba2Cu3O7, or analogously lanthanum. This is where superconductivity occurs at a critical temperature of 90-100 K - high - temperature superconductivity, which allows the use of liquid nitrogen for cooling. A complete microscopic theory of high-temperature superconductivity has not yet been developed, but research to date has shown the mechanism of electron binding to Cooper pairs by electron-spin interactions of electrons with excitations of spin (anti) ferromagnetic structures in a crystal lattice that has a "flake" structure.

Left: The superconducting electromagnet consists of a coil wound from a superconducting material, placed in a cryostat with liquid helium (short-circuiting bifilar line is used to turn on and off the current in strong persistent electromagnets - see "Electromagnets in accelerators") .
Right: Temperature dependence of the ohmic resistance of the Nb-Ti superconducting material (for 1m of wire 0.3 mm) .

Superconductivity is already finding significant application in many areas of science, technology and medicine. They are mainly superconducting electromagnets: a coil wound into a large number of turns of suitable superconducting material is placed in a Dewar vessel with a cooling medium (so far mostly liquid helium), a strong current (hundreds and thousands of amperes) is excited in it and both ends are connected. The current then flows indefinitely without consuming electricity and excites a strong magnetic field - units up to tens of Tesla - see below "Electromagnets in accelerators", section "Superconducting electromagnets". The condition of the function is, of course, continuous cooling to a temperature lower than critical *). Such superconducting electromagnets are preferably used in a number of areas - nuclear magnetic resonance , circular accelerators , thermonuclear tokamaks.
*) This continuous cooling of the superconducting coil must be carefully monitored ! If, due to evaporation, the coolant level dropped so much that part of the winding warmed above the critical temperature, the superconductivity would suddenly disappear. At this point in the winding, an ohmic resistance would arise, the current through the winding would decrease rapidly, and the magnetic field would disappear. This would result in an electromagnetic induction of a large electromotive force in the winding. The considerable energy stored in the magnetic field would be quickly converted into induced current by the winding, which would be strongly heated by the ohmic resistance, the rest of the cooling medium would be brought to a boiling boil and the winding could be burned!
   The temperature transition from the normal to the superconducting state in the vicinity of the critical temperature T
c is very steep - there is an almost perpendicular transition edge of the superconductivity at this point on the resistance-temperature curve. This phenomenon is used in very sensitive bolometers working on the edge of superconductivityTES (Transition Edge Sensor) - 2.5, section "Microcalorimetric detectors".
   If a really high-temperature superconductivity could be achieved - to develop materials that would be superconducting even at room temperature, it would probably lead to a revolution in low- and high-current electronics. Superconducting wires could conduct electricity without losses, without the need for high voltage transformation. It would be possible to store-accumulate electrical energy in superconducting electromagnets. Superconducting levitation is being used in industrial applications, in which the interaction of induced eddy currents leads to a force which allows the magnet to float above the superconductor or "hang" in the magnetic field. It is mainly considered for magnetic suspension instead of bearings and for use in magnetically levitating high-speed trains.
Similarly, atoms composed of fermions can effectively behave like bosons if their total spin is integer (or zero), resp. when there is a singlet or triplet pairing of atoms with a half-digit spin to the resulting integer spin (0 or 1). Here, too, boson condensate can form at low temperatures, the particles of which (or quasi-particles) can move freely in the environment without frictional resistance. On this principle is founded superfluidity some liquefied gases (especially helium) at low temperatures. It is interesting that helium does not have a solid phase, it remains liquid up to practically absolute zero. Below 2.17 K, it becomes superfluid - flows without internal and surface friction and has a very high thermal conductivity.

In relation to certain "strange" asymmetries in the production and decay of certain particles (see below), a special group is distinguished :

Antiparticles, antimatter, "anti-worlds"
In the world of elementary particles in general for each particle there is its "opposite" or "associated" partner - an antiparticle that has certain physical characteristics identical to a given elementary particle, but some other physical characteristics have the opposite sign or direction. The antiparticle has the same mass, spin number, lifetime and isospin as the particle, but its charge and magnetic moment are opposite (same in size but of opposite sign); the opposite sign is also attributed to the lepton number, the baryon number, and the isospin projection. In the case of neutral particles without electromagnetic properties, they can either be associated either to semselves (photon,
po, graviton), so actually they do not have antiparticles, or they may have particles and antiparticles different from each other (eg antineutron, antineutrino). In the case of fermions, particles and antiparticles are formed in pairs and also disappear in pairs.
   In our nature (composed of matter), antimatter, resp. antiparticles, occur where there is interactions of the particles with high energies - higher than twice the rest mass of an electron or positron 2
x 511 = 1.022 MeV; then positrons are formed. Positrons are also emitted during beta+ -radioactivity (see 1.2, section "Radioactivity b+"), where they form during the transmutation of quarks "u"-->"d" inside protons due to weak interactions (Fig.1.2.5 below). Heavier antiparticles (antiprotons, antineutrons, antihyperons) can then be formed only at very high energies, 3 GeV and higher. This is the domain of large accelerators (in very low intensity also cosmic radiation).
Note 1 - Antiworld
In many places in our treatise on nuclear and radiation physics, we use the term "antiworld "
- in an allegorical sense. Antiparticles formed during interactions and radioactivity in laboratories are, of course, part of "our" world. "Anti-worlds" are sometimes thought of in astronomy as those (hypothetical) formations or parts of the universe that are composed of antimatter (cf. also the passage "Antiatoms" below). The difficult question is, why do we observe incomparably fewer antiparticles than particles that are "normal and ordinary" to us? It attempts to answer cosmological theories in co-production with particle physics - see the link below in the note to the passage "Antiatoms, Antiworlds".
2 - Antiparticle => Negative energy? Time inversion? - No !
In the early days of the development of quantum physics, antiparticles (such as the positron) were considered to be "negative energy" particles, or particles moving "back in time"
(formal coordinate transformations in Dirac's equation allow this). At one time, these concepts played an important heuristic role in the development of particle physics. Now these misguided ideas are abandoned and particles and antiparticles have an "equal" place in the standard model, in applications, as well as in unitarization schemes.
Dirac particles and Majoran particles
According to their antiparticles, elementary particles are sometimes divided into two groups :

Dirac particles have different antiparticles. This includes in particular all electrically charged particles, but also some neutral particles such as neutrons or neutral K-mesons.
Majorana particles have identical particles and antiparticles. In addition to the photon, this includes neutral p- mesons (pion po); some hypotheses even consider neutrinos, it has not been decided yet.
  Some significant antiparticles have their own name or designation - antiparticle to electron e- is called positron e+, charge-associated antiparticles are denoted by opposite signs of charges, eg muons m-, m+, analogously pions p-, p+ and other particles. However, a number of antiparticles are simply denoted by the prefix "anti" and the wavy line "~" above the particle symbol *) - eg antiproton p, antineutron n.
*) Unfortunately, in the fonts available in the "html" format, characters with a wavy line at the top are not available, so in our texts we denote antiparticles by a comma ( ) at the top right.
Annihilation of antiparticles with particles
When antiparticles interact with their corresponding "counterparts", particles, these pairs can disappear from each other *) - annihilate - to form other (lighter) particles or antiparticles. These are often photons
(positrons annihilate with electrons to produce two gamma photons flying out in opposite directions, at an angle of 180, which is advantageously used in gammagraphic imaging by the positron emission tomography method in nuclear medicine after the application of a positron beta+-radionuclide, e.g. 18F - 4.3, part " Positron Emission Tomography PET"). The laws of conservation of energy and quantum numbers are met (opposite quantum numbers are "reset"). There is a complete conversion of the rest mass (+ kinetic energy) into the rest mass and energies of other particles and fields, while the original particles disappear. Specific annihilation processes will be described below for each particle type.
*) Annihilation of particles does not mean their destruction, nor the transformation of matter into "pure energy" !
There are still some almost mystical ideas about the process of annihilation of antiparticles with particles. They come from a time when these processes were just discovered and seemed so unusual to physicists that they attributed special philosophical significance to them. We now know two interrelated facts :

During the annihilation of particles, despite the name (Latin nihil = nothing ; annihilation = destruction, disappearance ), they are not destroyed, extinct or disappear from this world "without a trace", but their transformed into other particles of the microworld, when all the usual conservation laws (energy, momentum, charge and other quantum characteristics). Nothing was lost or gained.
Annihilation is not the conversion of matter into energy, or matter into "pure energy," as is sometimes stated. In annihilation (as in any known natural process) the law of conservation of energy is fulfilled - but the total, relativistically understood energy, including the rest energy of particles .So it's just about the transformation of one form of matter into another.
  After all, the conversion of "mass particles" into a field (with zero rest mass quantities) occurs in conventional particles only by annihilation of an electron with a positron. Antiprotons or antineutrons "annihilate" to form other massive particles (pions - see below), so the "transformation of matter into pure energy" cannot be spoken of at all ..!..
The largest annihilation in the history of our universe
took place at the beginning of its evolution more than 13 billion years, at a time of about 10
-4 s. after the Big Bang, at the transition between the hadron and lepton eras, when baryons and antibaryons anihilated each other, and immediately after, at the end of the lepton era (approx. 10 s.), when positrons with electrons anihilated. The result was radiation (now observed as relict) and remained a small excess of mass (1:109) from baryon asymmetry.
These grandiose events are discussed in more detail in 5.4 "Standard cosmological model. Big Bang" passage "Baryon asymmetry of the Universe" in book "Gravity, black holes and spacetime physics" (see also below passage "Why is our world of matter and not antimatter?").
"Antiatoms", "antiworlds"
Antiparticles have exactly the same properties *) of their interactions as particles, so that a positron can orbit around the antiproton and thus form an "antihydrogen" atom. Similarly, antiprotons and antineutrons can form atomic "antinucleus
- ", around which positrons+ in shells of the same energies and according to the same selection rules as we know from our atomic physics can orbit. Such "antiatoms" will then have exactly the same chemical and spectroscopic properties as the atoms of our matter - they will create elements or compounds of antimatter with the same properties as we know from our matter.
Is antimatter exactly the same as matter ? 
Matter and antimatter appear to us in practically all experiments to be the same - except for the opposite signs of el. charges and some other quantum numbers have the same properties. Nevertheless, antimatter differs slightly from matter in behavior - asymmetric production and decay of some "exotic" particles and antiparticles
(it was found experimentally mainly in K and B mesons). This hidden difference between matter and antimatter, generated in the earliest stages of the separation of basic interactions in the formation of the universe, may have eventually cooperate in the hadron era to give rise to the baryonic asymmetry (5.4 "Standard Cosmological Model. The Big Bang.", passage "Baryon Asymmetry of the Universe") in book "Gravity, black holes and spacetime physics"). That's why there is matter and we are here too..!..
  Arises naturally question whether somewhere in the universe is the antimatter? In order to exist in the long term, it must find antimatter separated from matter, otherwise there would be a massive annihilation. So the question is: are there "anti-worlds" somewhere? We do not know this remotely using conventional spectrometric methods - light from "anti-stars" or "anti-galaxies" would have exactly the same spectra as we know from our stars and galaxies due to the identical properties of "antiatoms".
  However, there are two compelling indications that there is no free antimatter in the available part of the universe :
1. In primary cosmic rays from outer space there are only protons, not antiprotons (a small proportion of about 10-4 antiprotons observed in cosmic rays are secondary antiprotons; they form when high-energy protons interact with the interstellar medium - with particles and photons of relic radiation; similarly positrons). No more complex "anti-nuclei" of helium or heavier elements (which would be composed of antiprotons and antineutrons) have been registered in cosmic rays so far *). Such "anti-nucleus" would have to be emitted in large quantities into space with each explosion of a possible "anti-star" as a supernova, in an (anti)stellar wind, as well as in jets from antimatter accretion disks around black holes. If cosmic rays contained more antiprotons or more complex "antinucleus", we could think of them as a kind of "envoy" of anti-stars and antigalaxies. In reality, however, we observe very few of antiprotons, just as many as are created by the interactions of ordinary high-energy protons of cosmic rays with ordinary matter.
*) A possible detection of more complex "antinucleus" would be strong evidence of the existence of a large amount of antimatter - "anti-stars", "antigalaxies" - somewhere in space. Such more complex "anti-cores" cannot be formed secondarily by any high-energy particle interactions, but could only originate in primary formation in a large amount of antimatter - in the thermonuclear synthesis of antiparticles in "anti-stars". Therefore, satellite "antimatter detectors", such as the AMS (Alpha Magnetic Spectrometer), are capable of detecting "antihelium" (anti-alpha particles), are important.
2. If some stars, galaxies or clouds of gas were made of antimatter, intense annihilation would occur at the interface of matter and antimatter, producing hard radiation g of energy 511keV. No measurements have yet recorded such annihilation radiation.
  In the universe, therefore, there is either no appreciable amount of antimatter, or the "antiworlds" are so far away from us --> the radiation is extremely weak that we are unable to register any of its manifestations with our devices.

Why is our world made of matter and not antimatter ?
(or why isn't it just from radiation?)
The interesting question is, why do we observe almost exclusively "ordinary" matter and almost no antimatter in the universe today? Or even why is there any matter at all and not just radiation? To answer these questions, we would have to go back to the very beginnings of the universe. According to current physical ideas, the same amount of matter and antimatter should initially be formed at the beginning of the universe. All experiments in nuclear physics show that in all particle interactions there is always a associeted - equal production of particles and antiparticles, in a ratio of 1:1.
  Due to certain specific phenomena - violation of the symmetry of interactions in the initial moments of the evolution of the universe - the amount of matter slightly prevailed over antimatter
(ca. 1:109), there was a slight baryon asymmetry of universe. A more or less random quantum fluctuation caused the victory of matter over antimatter in our very early universe. In hypothetical other universes, the opposite could have been the case, quantum fluctuation occurred at the appropriate moment occured on the opposite direction, and such a universe would be of antimatter ...  

  This slight excess of 1:109 caused this matter to remain for the further development of the universe *), while all the other matter and antimatter had already anihiladed each other during the hadron and lepton eras and eventually transformed into radiation (now observed as relic radiation). If there were no baryon asymmetry at the beginning of the universe, all particles would anihilate each other and the universe would consist only of radiation (in such dull univers could not have forme any stars, planets, life...). The questions of antimatter and baryon symmetry or asymmetry of the universe from astrophysical aspects are discussed in 5.4 "Standard cosmological model. Big Bang.", passage "Baryon asymmetry of the universe" and 5.5 "Microphysics and cosmology. Inflationary Universe." of book "Gravity, Black Holes and the physics of spacetime".
*) The terminology of antimatter is relative. What remains and what our surrounding world is, we simply called matter - "ordinary" matter, sometimes called koino-matter (Greek koinos = usual, ordinary ). And a hypothetical substance composed of opposite particles is antimatter to us. In the imaginary universe, where baryon asymmetry would prevail on the opposite side, the inhabitants there would have the opposite terminology, for them ordinary matter would be what we call antimatter.
Combined particle-antiparticle systems
Interactions of antiparticles with particles result in annihilation processes, but this annihilation may not occur immediately. If the particles and antiparticles have opposite signs of electric charge (+ and
-), they can form a bound particle-antiparticle system after sufficient deceleration just before annihilation. The best known bound system of this species is the positronium - a bounded system of electron and positron, which according to the model idea revolves around a common center of gravity to balance the centrifugal force of circulation and the electric attractive force (see below "Interactions of the most important elementary particles", passage "Positronium"). Similarly, an antiproton can be trapped in orbit around an atomic nucleus to load an electron - an antiproton atom is formed. The simplest antiproton atom is protonium, which is formed as a bound system of proton and antiproton orbiting a common center of gravity. Both positronium and protonium are unstable, in a short time (depending, among other things, on spin orientations) the antiparticle with the particle eventually annihilates. Thus, positronium and antiprotonium are of no general importance (except in special cases and applications).
  However, bound combinations of positrons and antiprotons (+ possibly also antineutrons), creating antiatoms, are important. Only this it can be real antimatter... From the point of view of nuclear physics, the properties of these antiatoms are important. Primarily spectrometric properties
(briefly mentioned in the passage "Artificial production of antimatter. Antihydrogen.") and also gravitational properties :
Antimatter: gravity or antigravity ?
The most difficult is the measurement of the gravitational properties of antimatter. Although we know that particles and antiparticles have the same (rest) mass, it remains to be verified whether the anti-hydrogen "falls" in gravity in exactly the same way as hydrogen? For ordinary matter composed of atoms formed by electrons, protons and neutrons, Newton's law of general gravitation
("Newton's law of gravitation") applies. In the general theory of relativity - the physics of gravity and curved spacetime - the very precisely proven principle of equivalence ("Universality - the basic property and the key to understanding the nature of gravity") applies, with the result that gravity does not depend on the composition and structure of matter. The gravitational interaction between matter and antimatter should be identical. An object made of antimatter will thus fall in the gravitational field of the Earth with the same acceleration as a body made of matter (here on the surface of the Earth its fall will take place with a known value of the gravitational acceleration of 9.81 m/s2) .
  Logically, we conclude that this also applies to individual elementary particles - common (electrons, protons, neutrons), and probably also exotic (neutrinos, mesons, hyperons, ...). However, direct experimental verification of the gravitational properties of individual isolated particles is practically impossible, because these particles move at high speeds and show electromagnetic
(and possibly strong) interactions with the environment, much stronger than gravitational - this completely "overpowers" a slight gravitational force. In general, however, it can be said that ordinary (koino) matter gravitates, showing universal attractive forces.
  However, as is the case with antiparticles (positrons, antiprotons, antineutrons), "antiatoms" composed of them, and antimatter in general? We know from experiments on accelerators that particles and antiparticles have the same inertial mass. But will antimatter gravitate or antigravity ? - does attractive or repulsive gravity act between matter and antimatter? However, some unsubstantiated hypotheses, as well as laymen's opinions suggested by the name "anti
-", hold the opinion of antigravity of antimatter.
  The analysis of the probabilities of short-term existence of virtual electron-positron, proton-antiproton and other particle pairs ("vacuum polarization") shows that the results of Etvs, Dicke and Braginski measurements confirm the validity of the principle of equivalence for common antiparticles (such as positron and antiproton) with accuracy ~10
-5 to 10-6. Therefore, "antigravity" can certenaily not be expected with antimatter - no "falling upward"! Antimatter will normally gravitate (only the strength of this gravitational interaction could theoretically be slightly different - a brief discussion is in 2.2, section "Principle of equivalence" of the book "Gravity, black holes and space-time physics").
  How does an antiproton "fall" in a gravitational field, compared to a normal proton? It is not possible to measure the gravitational effects directly on the basic particles of antimatter - positrons and antiprotons - because they are charged and the electrical action with the environment many times exceeds the investigated force of gravitational
(it is the same as discussed above for particles of ordinary matter ). For this purpose, it is necessary to prepare an electrically neutral antimatter composed of antiatoms. It would be optimal to create macroscopic bodies from antimatter-antiatoms. We would then release them downwards in the earth's gravitational field - as G. Galileo did historically (perhaps from the Leaning Tower of Pisa...). These bodies would be initially at rest and their instantaneous velocity would be determined only by the acceleration due to gravity. Alternatively, we would launch them horizontally with a defined initial speed and track their movement along a parabola.
  However, we cannot do anything like that with individual atoms. We are only able to create a gas composed of hydrogen antiatoms, in which the individual atoms move chaotically at different speeds in different directions, with a distribution of speeds according to the "temperature" that we would try to minimize. These atoms are not initially at rest, but have different initial velocities in different directions. In the gravitational field, they then fall along parabolic paths, whose instantaneous velocities in the vertical and longitudinal directions would add up to the initial velocities of the antihydrogen atoms.
  However, experiments are being prepared that would be able to eliminate or correct these effects and precisely measure the gravitational effects directly on the antihydrogen atoms - as discussed in the "Artificial Antimatter Production", section "Experimental Measurement of Antihydrogen Atoms" - AEGIS :
 Artificial production of antimatter. Antihydrogen.
When antimatter does not exist in the available part of the universe
(we do not have any "mining mines" for antimatter), would it be possible to "make" it artificially? In accelerators, we produce large amounts of positrons and amounts!), so it would seem that nothing stands in the way of artificially (more difficultly) antiprotons and antineutrons (but these are only submicroscopic "folding" these particles into "antiatoms". In reality, however, the artificial creation of antimatter is difficult !
extremely   The particles produced in accelerators move at high velocities close to the speed of light - they have high kinetic energies, many orders of magnitude exceeding the binding energies of atoms. If we aimed such fast antiprotons and positrons at each other, they would fly past each other "without noticing" - almost without interaction - and no antihydrogen atoms would be formed. In order for the antiproton and positron to electrically combine into an antihydrogen atom, they must be slowed down a million times!
  Therefore, in order for an anti-hydrogen atom to form, positrons and antiprotons from the original energies of the order of MeV must be slowed down to a sufficiently low mutual speed, that the antiproton can capture and hold the positron. This is not easy at all, so only recently (1995) on the LEAR accelerator in the CERN laboratory managed to create only 9 atoms of anti-hydrogen
(now it has managed to produce many thousands of antihyxdrogen atoms).
  Antiprotons were allowed to fly through the xenon, which slowed them down and the interaction also created pairs of electrons and positrons. In these several cases, the positron was subsequently captured by a flying antiproton to form an anti-hydrogen atom. During the order of 10-11 sec. then, during his flight through the environment, he annihilated with normal matter, and a flash of annihilating radiation proved its brief existence. With such a short period of existence, no properties of antiatoms can be measured.
  For more efficient "antimatter production", resp. anti-hydrogen atoms, has now been constructed at CERN electromagnetic antiproton decelerator. In the electromagnetic field
(generated by a high-frequency resonator), the antiprotons in the beam from the accelerator decelerate from the original energy of about 100 MeV to MeV units. This is still too high an energy for efficient production of antihydrogen atoms and for further experiments. Antiprotons are further slowed down by passing through thin aluminum degradation foils to approx. 5 keV (the yield here is very low, only approx. 0.1%). However, the last effective deceleration stage ELENA (Extra Low ENergy Antiproton ring), consisting of a 30 m hexagonal ring with radio frequency cavities and electron cooling, is in the preparation stage. Here, the antiprotons received from the antiproton decelerator are further slowed down from 5MeV to 100keV. Only a minor slowing down with degradation foils to ~5 keV is then sufficient, with significantly lower losses than with the use of only degradation foils; double the number of antiprotons is achieved. This leads to significantly more efficient production of a larger number of antihydrogen atoms.
  The slowed particles are then led to a cooled magnetic trap, where a cloud of antiprotons is trapped in a magnetic field and further "cooled" in it
(the kinetic energy of their movement decreases). Positrons are simply obtained from beta+ -radioactivity, most often the radioisotope 22 Na, or also by reactions using a linear accelerator. After basic deceleration in a thin film, they are led to a magnetic trap where they slow down further ("cool" similar to antiprotons) and then slow antiprotons and positrons are simultaneously injected into a reaction chamber with a magnetic trap, where positrons are trapped by antiprotons to form antihydrogen atoms. When decelerated and trapped in a magnetic trap, both particles have enough time to bind to each other in anti-hydrogen atoms. This method succeeded in detecting 80 antiatomic hydrogen atoms in the first phase, but after further improvement - the ALPHA device (Antihydrogen Laser PHysics Apparatus) - it is possible to produce tens of thousands of anti-hydrogen atoms for experiments, eg to compare electromagnetic spectra of anti-hydrogen and hydrogen atoms.
  For the production of anti-hydrogen atoms, it is advantageous to use positrons in the form of positronium - the electrically bound state of the electron and positron (see "Electrons and positrons"). Positrons from beta+-radioactivities are passed through a porous target of siliceous material, in which they capture electrons and form positronium e--e+. Using laser beams, the positronium is then excited to a higher quantum state (up to n = 25) and directed to the antiprotons. Highly excited positronium can relatively easily transmit a positron to an antiproton - there is a "charge exchange" in which the antiproton assumes the position of an electron in the positronium: (e--e+)* + p- -> H~* + e-, to form an excited antihydrogen atom H~*. This process has a relatively high effective cross section (depends on the 4th power of the quantum number n of positronium). Another advantage is the lower kinetic energy of the formed anti-hydrogen atom. Antihydrogen atoms are created here in a highly excited (Rydberg) state, so they are sensitive to gradients of electric and magnetic fields, which makes it possible to manipulate them in experiments.
  In addition to the production of the antiatoms themselves, another very difficult problem is their isolation from the surrounding mass in order to prevent immediate annihilation with the materials of the reaction vessel. A magnetic field is commonly used to keep charged particles (e.g. in tokamaks - see 1.3, section "Tokamak", or in the above-mentioned magnetic traps). However, the hydrogen atoms are electrically neutral on the outside. However, they have a magnetic moment, so they react to the magnetic field (albeit weakly). With the help of strong superconducting electromagnets, a "magnetic trap" can be created, which is able to keep anti-hydrogen atoms in the magnetic field inside the reaction vessel for some time. The magnetic field is specially shaped so that it is strongest at the edges and decreases towards the center. The atoms are drawn into the "magnetic well" in the middle, where they can remain trapped for some time. If this time is long enough, antiatoms have time to return to a ground state in which their physical properties can be measured, paving the way for accurate testing of the presumed symmetry of matter and antimatter (some minor differences are discussed below in the passage "CPT symmetry of interactions"). Revealing possibly small differences could help to explain why our universe is made up only of matter (cf. "Baryon's asymmetry of the universe").
 Experimental measurement of anti-hydrogen atoms - AEGIS, GBAR
The AEGIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) project is being developed at CERN for the precise measurement of the physical properties of antihydrogen atoms. It consists of several basic follow-up steps :
1. Production of antiprotons p- in the proton synchrotron. A beam of protons p+ accelerated to an energy of 25 GeV hits an iridium target, where, thanks to the high energy, showers of many secondary particles, including proton-antiproton pairs, are created. The antiprotons p- are separated using a magnetic field. They have high energies, velocities close to c, wide energy spectrum. They are not directly applicable for the creation of antiatoms, they must be slowed down :
2. The antiproton decelerator, which applies a strong electric radio-frequency field of opposite polarity, on a circular track in a magnetic field (created by electromagnets), it works "oppositely" to a synchrotron. It has an oval shape (diameter 60 m, in the diagram below it is drawn as a circle for simplicity), along its perimeter there are four short straight sections with radiofrequency electrodes, where antiproton braking takes place. In AEGIS, there is a slowdown to 5.3 MeV, which corresponds to about 10% of the speed of light. Antiprotons are further slowed down by passing through thin aluminum degradation foils to approx. 5 keV (the yield here is very low, only approx. 0.1%; not drawn on the diagram).
3. Capture and accumulation of antiprotons in an electromagnetic trap (the so-called Penning-Malmberg trap), a chamber with a magnetic field and a set of circular electrodes. Another slowing down of antiprotons by collisions in the electron cloud is also carried out here.
4. Production of positrons e+ using the beta+ radionuclide 22Na. ....
5. Creating positronium Ps by passing positrons through a nanoporous material. Ortho-positronium is used, which has a longer lifetime of 142 ns (compared to para-positronium which has a lifetime 1000 times shorter). Excitation of positronium to the Rydberg state Ps* with n=~25 using UV and IR lasers.
6. Creation of antihydrogen atoms H~ using the charge exchange reaction of an antiproton with an excited positronium Ps*. The slow antihydrogen atoms created in this way (with a speed of ~ 25-80 m/s, corresponding to a temperature of the order of 100 mK) are then already led to experiments to measure their properties.
7. For AEGIS, the creation of a pulsed horizontal beam of H*~ antihydrogen atoms with a constant speed of around 400 m/s. The effect of the inhomogeneous electric field on the highly Rydberg excited H*~ atoms is used here (it makes it possible to manipulate them using the Stark effect). It is important for further analysis of the parabolic motion of H~ atoms in the gravitational field.

Framework simplified scheme of experimental study of physical properties of anti-hydrogen atoms - AEGIS and GBAR.

In a gravitational experiment  at AEGIS, the horizontal stream of antihydrogen atoms is led from there into a system of two separation slits (grids) *) with a grid period of 80 mm, which create parallel bundles of antihydrogens. Subsequently, at the end of the L- path, these anti-hydrogens are annihilated by a silicon position-sensitive detector with a spatial resolution of 10 mm. The structure of the grating is analyzed, which is displayed on the position-sensitive detector as a series of maxima and minima at different heights when detecting a larger number of antiprotons. Their vertical positions depend on the decrease (deflection) of anti-hydrogen atoms in the Earth's gravitational field (approx. 20mm). It correlates with the arrival times of anti-hydrogen atoms on the detector (which correspond to their horizontal velocities v ). It is evaluated to what extent the height decrease h of antihydrogen at distance L corresponds to the law of horizontal velocity throw in the gravitational field of the Earth with gravitational acceleration g~ : h = 1/2 .g~. (L/v)2. This is a direct laboratory test of the validity of the weak principle of equivalence in the general theory of relativity (see 1.2, passage "Principle of equivalence" in the book "Gravity, black holes ...") which says that the trajectory of motion (here fall) of a material body depends only on its initial position and velocity, not on its structure and other properties - does it also apply exactly to antimatter..?... The accuracy of the determination of g~ in the AEGIS experiment is expected to be approximately Dg~/g~ ~1%.
*) This arrangement of two or three grids equidistantly placed in a row is called a moir deflectometer in optics (French moir = fabric, fine structure, grid). The last third grating is replaced by a position-sensitive detector. It is not used here in the interferometric mode as in optics, but serves to precisely define the horizontal parallel trajectories of anti-hydrogen atoms. The annihilating anti-hydrogen atoms will create bands on the detector - patterns of grid slits, by analyzing which it is possible to determine how much H~ dropped when moving along the parabola from the second grid to the impact on the detector.
  In addition to AEGIS, the gravitational measurement of antihydrogen is dealt with by the alternative experiment GBAR (Gravitational Behavior of Antihydrogen at Rest), operated at the same antiproton decelerator at CERN. To measure the gravitational acceleration of anti-hydrogen atoms, it does not use horizontal movement with evaluation using a moir-deflectometer, but the vertical free fall of anti-hydrogen atoms in the measuring chamber, with the evaluation of the exact time of annihilation when the anti-atoms hit the bottom of the chamber from above. The trajectory - the height h of freely falling H~ atoms - is related to time by the relation h = 1/2.g~.(t2-t1)2, where t1 is the time of entry of the atom into the upper detector of the chamber and t2 is the time of impact and annihilation of the antihydrogen atom on the bottom of the chamber. In the GBAR experiment, additional stages of slowing down antiproons (ELENA) and "cooling" of the p- beam will be used, eventually down to an energy of 1 keV. Antihydrogen atoms are prepared by further reaction with positronium in the form of positive antihydrogen ions H~+- one antiproton and two positrons (this requires a higher flux of positrons, which are generated here using a 9MeV linear accelerator). These H~+ are then cooled using Be+ ions to a temperature of around 10mK. Using a laser pulse, the outermost positron is then removed just before the measurement and a neutral antihydrogen atom H~ is created, whose free fall time is measured in a vertical chamber with detectors. Thanks to the measurement of the fall of very slowed down antihydrogen atoms (with almost zero initial velocity, ~0.5m/s), one can expect an improved accuracy of the determination of g~ about Dg~/g~ ~10-3.
  In anti-hydrogen atomic spectrometry, a slow beam of anti-hydrogen is led to another magnetic trap, where it is excited and the radiation emitted or absorbed during the jumps between the individual energy levels is measured. The energy levels in an atom depend on the inertial mass and the charge of an electron in a hydrogen atom or a positron in an antihydrogen. By comparing the energy of the electron transitions between the excited and ground levels of hydrogen and antihydrogen, we can verify whether the inertial masses and charges of the particles and antiparticles are exactly the same, or there is a slight difference. If the inertia mass of the particles and antiparticles differ, it could possibly be measure a slight difference by this spectrometry.
Production of more and heavier antimatter ?
Despite all the partial successes in the above-consuming experiments is unfortunately necessary to admit, that the creation of large quantities of antimatter, or more complex antiatoms than hydrogen *), yet there is no hope in the near future ...

*) The targeted "production" heavier antinuclei really is not hope for the foreseeable future. However, in small numbers (with negligible probability) they may arise randomly in high-energy interactions. Heavy nuclei collisions produce more antiprotons and antineutrons. If several co-produced antiprotons and antineutrons coincidentally fly in the same direction and at approximately the same speed, they can "bind" to the heavier antinucleus - nucleus anti-deuterium, anti-helium - by nuclear forces. Because this process is very unlikely, many billions of trillions of nuclear collisions to make any such heavier anti-nuclear accidental to formation. In 2011, at the RHIC heavy ion accelerator in Brookhaven, 18 nuclei of anti-helium-4 were identified in this way
(during several months of collisions), other successful experiments of this kind are taking place at CERN. The formation of even heavier antinuclides in this way, due to the almost zero probability, will probably not be proven....
Antimatter - a possible source of energy ?
In the popular science and sci-fi literature, it is often stated that annihilation of matter with antimatter results in a 100% conversion of matter into energy, in accordance with Einstein's relation E = m.c
2. Thus, in the distant future, antimatter could be an inexhaustible source of energy, or to power interstellar ships (photon rockets - see below) at speeds close to the speed of light? Unfortunately, this is not true, the problem is much more complicated, there are obstacles not only of a technical, but also of a fundamental physical nature.
  When annihilation an electron with a positron, in fact all the rest mass of both particles changes into electromagnetic radiation: e
+ + e- 2 g. However, it is not light, but hard gamma radiation, which would not be reflected by the mirror of the photon rocket, but absorbed. However, the annihilation of protons and neutrons with antiprotons and antineutrons does not produce electromagnetic radiation (at least not directly), but p- mesons, eg p~+ p 2 p+ +2 p- + po ; they then decay into muons and neutrinos, eg: p- m- + n'm , p+ m+ + nm . This is followed by the decay of muons, eg m- e- + n'e + nm , m+ e+ + ne + n'm , and only then could annihilation of electrons with positrons e+ + e- 2 g ( all these interactions are discussed in more detail below). Thus, in the hypothetical "annihilation reactor" of the future, would therefore need to achieve not only the efficient energy utilization of hard radiation g, but also the closure of proton, pion, muon and electron (+antiparticles) high-energy "plasma" so that secondary particles can effectively annihilate together. So far there is no known physical mechanism that would alow this. And it is absolutely impossible to use the energy carried away by neutrinos...
  The energy utilization of annihilation of matter with antimatter is also hindered by technical difficulties. If, for example, we want to combine two macroscopic bodies, one of matter and the other of antimatter, with the aim of complete annihilation, it would not be very successful in practice due to the emergence of the so - called Leidenfrost insulating barrier*). When the surfaces of both bodies touch, a powerful flow of energy (radiation and particles) is created, which repels, delays and insulates the next mass of the bodies from each other so that effective volume annihilation does not occur; the reaction is planar rather than massive volumetric. One possibility would perhaps be to collide the two bodies at high speed so that the kinetic energy overcomes the pressure of the generated radiation. Or even better, perform the annihilation sequentially in a stream of particles of matter and antimatter (the aforementioned "annihilation reactor"). None of this is feasible in the foreseeable future ...
*) A similar phenomenon can be observed in everyday life when we drip water on a hot stove. Water droplets usually do not evaporate immediately (explosively), but "jump" for a while on a hot plate: when the droplet comes into contact with the plate, steam is created, which for a while creates a gaseous "cushion" isolating the droplet from the plate.
Photon rocket ?
The collimated source of electromagnetic radiation shows the effect of a "rocket thrust"
(it is the inverse effect to the light pressure, which Lebedev first observed with light). This is a consequence of the law of conservation of momentum, or the law of action and reaction: electromagnetic radiation has a flow of momentum, which in clasical electrodynamics is describes by the Poynting vector and from a quantum point of view is given by the momentum of photons (each photon of the wave frequency f has energy E = h.f and momentum p = h.f /c). During radiation, this momentum is transmitted to the source in the opposite direction, the transmitted momentum per unit time indicating the applied "pull" force. In order for this "rocket effect" to be noticeable, an extremely high flux of radiation is required, which is not achievable by existing technical means. The photon rocket project envisages an annihilation reaction, or with a thermonuclear reaction that would take place in the focus of a large hemispherical or parabolic mirror that would reflect the resulting photons and collimate them "backwards". As already outlined above, the radiation generated by an annihilation or thermonuclear reaction is not light, but high-energy gamma and corpuscular radiation for which the law of reflection does not apply; a mirror of any known material would not reflect this radiation, but would mostly absorb it, leading to its thermal destruction.
Note: Instead of a "photon rocket", the name "quantum rocket" can be used , as the desired effect is created not only by the emission of photons, but also by other quantum particles carrying momentum. However, for photons, the most favorable ratio is [transmitted momentum thrust] / [required emitted mass and energy].
 Antimatter and antiworlds in sci-fi
The mysterious
impresion of the term "antimatter" led in the science fiction literature to the idea of "antiworlds", in which everything is "opposite" and in which possibly our "doubles" - "anti-people" may live. This sci-fi idea has no astronomical justification (as discussed above in the section "Antiatoms, Anti-Worlds") , it is rather a game for our imagination :
  Consider, therefore, the hypothetical situation that somewhere in the distant universe there is indeed a large region of antimatter, where (anti)galaxies and (anti)stars formed, including the (anti)Sun with the planetary system orbiting and the (anti)Earth, on which it evolved exactly the same life as here, including anti-people :

  Imagine, for example, in a sci-fi experiment, that would "girl made of matter" here on Earth via communications by electromagnetic signal, colluded with "antimatter boy" somewhere from a distant galaxy, a meeting - "dating" - at a certain point in space about halfway of path, without they would know they are composed mutually from antimatter. They would park in rockets near each other, get out into the open, and go to greet each other - "Hello!"; nothing special would happen yet. However, the moment they shook hands, there would be a massive annihilation of matter and antimatter *) and both partners would be destroyed in a massive atomic-particle explosion.  
*) Due to the formation of the above-mentioned Leidenfrost insulating barrier, there will be no total annihilation of both bodies, but only the surface parts of the palms of the hands. Even that would be enough to doom and destruction for both partners!
  If they were far-sighted, they could remotely test whether they were of the same nature. The easiest way is to send a weak beam of electrons against each other and measure whether annihilation gamma radiation of 511 keV is produced after their impact. If so, they should not approach each other (not a step!) - they would have to run away from each other quickly so that they do not perish ..!..

We do not deal here with the ideas of antimatter and antiworlds based on errors and misunderstandings, where the prefix "anti" is mistakenly attributed to other meanings, such as philosophical, reverse flow of time, etc. ..!..

Interaction of elementary particles - general properties
Mutual actions - interaction - the various objects are the basis of all events in nature. Interactions transfer energy, momentum, angular momentum, and charges between bodies. Physics has come to knowledge, that the essence of all interactions and forces in nature is the interactions between elementary particles of matter. In principle, we describe the interaction of particles in three ways :
-> Mechanical force action
Bodies and particles when approaching and contacting each other simply "act with a force" (the origin and microscopic nature of which we are not interested here), and we investigate the "mechanical" consequences of this force action (basically according to Newton's 3 laws of mechanics). With this immediate mechanical force action we have the greatest experience of everyday life. This is how physics proceeds in classical mechanics.

-> Physical field - acting at a distance
One particle in the space around it creates a field that exerts a force on another particle located in it. This very successful description is the basis of classical electrodynamics and gravitation.

We assign a corresponding field to each type of interaction - a space in which certain forces act on particles. The magnitude of the field action at each point in space is expressed by the field intensity (force acting on the "unit test particle") or by its potential (work associated with the transfer of particles to a given place). In classical physics, it is an electric, magnetic, gravitational field. The changes - "commotion" - in this field propagate at a finite speed from place to place, which is accompanied by the transfer of energy, momentum, and other physical quantities.
  From the point of view of classical physics, quantities such as energy and momentum are transmitted continuously during field changes. In quantum physics, it turns out that during changes (disturbances) in the field, physical quantities are transmitted discontinuously over certain "portions" - by quantum. Quantum field theory assigns certain particles to these quantums as carriers of the interaction, which leads to the following process :
-> Exchange of particles in quantum physics
Particles transmit and receive certain
quantum of fields, which causes their interaction. We imagine this exchange quantum as a particle - a carrier of interactions. This description is characteristic of quantum field theory (basic principles are outlined in 1.1, passage "Quantum field theory").
  In the standard particle model, interactions are mediated by the exchange of intermediate bosons, which are in a virtual state during this exchange - they exist so short that we cannot directly observe them due to the quantum principle of uncertainty. However, if the virtual particle gains sufficient energy during the interaction, it can be released and become a real particle; this is commonly observed for photons, in accelerator experiments it is also possible to indirectly observe heavy bosons W
+, - and Z0.

Spatial reach of interactions
In everyday life and in the surrounding nature, we encounter two types of interactions: electromagnetic and gravitational. They have an infinite reach - the field intensity E(r) at a distance r is given by the inverse square law E(r) ~ k/r
2 and the potential f(r) ~ k/r. The inverse square law has a geometric origin: a spherical surface of radius r has a surface S=4pr2. Coulomb's law of electrostatics and Newton's law of classical gravity have this dependence.
  In the microworld, we encounter two other types of forces, which, however, have a short reach: the so-called strong nuclear interactions
(1.1, passage "Strong nuclear interaction") and weak interactions (1.2, passage "Mechanism beta. Weak interaction."). If the field-interaction has a short range, the dependence of its potential f(r) on the distance r is modeled by an additional exponential factor e-m.m.r: f(r) ~ k.e-m.m.r/r, where m is the mass of the intermediate particle, m is the scaling constant. Such dependence is called the Yukawa potential (H.Yukawa introduced it in 1935 for strong nuclear interactions; however, here it later turned out differently...). The value r ~ 1/(m.m) is the effective reach of the interaction (the distance at which the interaction drops to a value of 1/e).
  The spatial reach of interactions in the concept of particle exchange is closely related to the rest mass m
o (or rest energy Eo=mo.c2) of exchange intermediate particles. It can be shown most simply using the quantum uncertainty relation DE.Dt h, from which it follows that for an mediated virtual particle that perturbs the energy by the value DE (equal to its rest energy Eo=mo.c2), the maximum time of this perturbation can be Dt h/DE = h/Eo. During that time, this particle can travel the path hu Ds= c.Dt c.h/Eo at the speed of light, which represents the maximum or effective range of the interaction mediated by this mediated particle.
  Electromagnetic interaction has an infinite range, the mediating particle is a photon with zero rest mass
(photons can therefore transmit almost zero energy in the limit, so according to the uncertainty relations they can exist virtually for an almost infinite time and reach an infinite distance also). Gravitational interaction also has an infinite range, it is mediated by gravitons with zero rest mass (so far hypothetical or model particles that we cannot observe in any way).
  On the other hand, weak interactions are mediated by heavy intermediate bosons W
+,- and Z0 with rest energies of 80 and 91 GeV/c2, so their reach is very small, on the order of 10-15cm (see the passage "Bosons W+,-, Z0" below). Therefore, even on subnuclear scales, this interaction is very weak (on even smaller scales, however, it is not weaker than the electromagnetic one).
  The situation is more complicated for strong interaction. In atomic nuclei (and in general between hadrons) we observe a very short range of the strong nuclear interaction of about 1,210
-13 cm. This fact was previously (provisionally, incorrectly...) explained using the exchange of intermediate p-mesons with a rest mass of approx. 135 and 140 MeV/c2. However, after the clarification of the quark structure of hadrons, this concept was abandoned. The strong interaction is known to act primarily between quarks inside hadrons and is mediated by gluons of zero rest mass, so its range should be infinite. Now, the nuclear forces between nucleons are understood as a residual manifestation of the strong interaction between quarks (discussed in more detail below in the section "Quark structure of hadrons" and "Four types of interactions in nature", also in 1.1, section "Strong nuclear interaction").

Scatering experiments
The basis of studying the structure of the microworld are the so-called scattering experiments *). They consist in firing the studied object with suitable particles - electrons, protons,
a -particles, etc., and we study the products of collision (or close convergence) of the arriving particle with the target object (resp. with the second particle). These are either the original particles dispersed (that is, at lower energies) or other secondary particles, emitted during interaction (this occurs at higher energies). By analyzing the energies, momentum, charges, angles of flying away and other parameters of secondary particles, we can obtain important information about the structure of the investigated micro-objects and the mechanisms of interactions of the respective particles. Particle interactions are important in the study of the structure of matter, and they play a key role in the formation of matter in universe. All the matter that is here (and of which we are composed ourselves) was formed during the interactions of particles in the initial stages of the universe, or inside the stars.
*) We simply do not have another option to study microstructures so small that they are not directly observable (after all, even ordinary visual observation is to some extent a kind of "scattering experiment" with visible light photons...). The first important scattering experiment was carried out as early as 1911 by E.Rutheford together with H.Geiger and E.Marsden - it led to the discovery of the atomic nucleus (see 1.1, section "Structure of atoms", Fig.1.1.4) .
  By interactions of elementary particles we understand the processes of mutual collisions of two particles, or collisions of a particle with an atomic nucleus
(here the problem is partly intertwined with the nuclear reactions discussed in 1.3 "Nuclear reactions and nuclear energy"). The simplest two - particle interaction of primary particles a and b can be symbolically written as: a + b c + d - Fig.1.5.1.A. The resulting secondary particles c and d after the interaction can be either the same as a and b, or different particles. However, the interaction often results in different particles than the original and also a different number of particles - especially at high energies, a higher number of secondary particles is usually formed (see below). Primary particles a and b, entering the reaction, are already known "in advance" (they were purposefully created in the "ion source" and accelerated in the accelerator, or one of them prepared in the target - see "Accelerators" below). Flying-out particles c , d , or other new secondary particles, we detect and measure their properties using detectors. The processes of itself interaction (collisions) take place in a spatial area with micro-dimensions of the order of 10-8 -10-15 cm, so they are not available for direct observation. Based on reconstructions of the interaction, we create certain model ideas and theories about their mechanisms, which explain the transition from the initial state (a + b) to the final state (c + d + /or other particles).
  During the interactions of particles between them, there are three basic types of forces (physical fields) *) :

*) The gravitational interaction of elementary particles is completely negligible and has never been observed se far. It could perhaps only manifest itself at extremely high energies (1019 GeV), many orders of magnitude higher than we can now achieve. However, this would not be a commonly known gravitational attraction, but gravity would be part of the unitary field (see B.6 "Unification of fundamental interactions. Supergravity. Superstrings" in the book "Gravity, Black Holes and the Physics of Spacetime").

  In the interactions of particles, the principle is generally applied: "what is allowed is also realized" - all kinds of processes *) occur, which are compatible with the laws of conservation of energy, momentum, angular momentum, electric charge, lepton number. If enough energy is available, a number of processes take place during particle collisions, but with different probabilities. This probability is given by the internal mechanisms of interaction of the respective fields and the relationship between the respective initial and final state configurations. The probabilities of individual processes ("channels" of interaction) are determined by quantum field theory using so-called matrix elements (elements of the scattering matrix S, see also below "Feynman diagrams").
*) As if all quantum of all fields were potentially, covertly and implicitly - virtually - present everywhere in space, in a "vacuum". From this "unitary" field, by supply of energy - excitation of the field - then releases the relevant particles, whether virtual or real.
  The course and result of the interaction of particles depends mainly on two circumstances :
On the type of interacting particles.
On the kinetic energy with which the particles collide (determined here by the energy in the center of gravity of both particles).
Even with collisions of the same particles and with the same energy, however, the interaction usually takes place in a slightly different way each time - through different "channels" of the reaction. We can explain this by the fact that on the one hand the collision can take place "frontally" or "peripherally" (ie with different impact factor and mutual angular momentum of both particles), and on the other hand due to stochastic laws of quantum physics the individual possible configuration states are realized with different probabilities.

Feynman diagrams
The so-called Feynman diagrams are often used for a clear graphical representation of the mechanisms of particle interactions (R.Feynman first introduced them in 1948). They come out from an exchange description of particle interactions. The trajectories of "matter" particles, fermions (electron, proton, ...) are marked by straight solid lines with arrows - particles have an arrow pointing to the right, antiparticles to the left. Exchangeable intermediate particles (photons, W-bosons, gluons ...) are marked with dashed lines or wavy lines. In the horizontal direction there is a time orientation
(other conventions are also used) - however, only symbolic, these diagrams do not serve to concretely express the time course of interactions, but only to "topologically" represent their mechanisms; are a kind of analogy of spacetime diagrams used in relativistic physics. The basic Feynman diagram of the general unspecified interaction of two particles a + b c + d is shown in Fig.1.5.1.A. The primary particles a and b arrive into close proximity to each other - the interaction area, the actual processes of interaction take place inside, after which the resulting particles c and d fly out of this area. The upper part of Figure 1.5.1.A shows the usual spatial drawing of the collision of both particles, the lower part of the figure shows Feynman's presentation of this interaction.
  Feynman's own diagrams then specify and illustrate possible processes within the interaction region for specific types of incoming and outgoing particles. Again, they consist of outer lines with "free ends", showing the particles entering and leaving the interaction. The actual interaction processes are drawn by the so-called interaction vertices - points at which wave or dashed lines connect to the initial outer line of the particle, corresponding to exchangeable intermediate particles mediating the interaction *). The laws of conservation of energy, momentum, electric charge, lepton number are fulfilled in the interaction vertices . The inner lines between the interaction vertices of the outer lines correspond to the virtual particles which do not leave the interaction area and are not present between the incoming or the resulting "physical" particles in the initial or final state; however, in their own interaction, they act and contribute to the result. Lines with a second free end can also emerge from some interaction peaks: these correspond to real particles (photons, W-bosons, fermions) emitted during the process.
*) In quantum field theory, these lines correspond to the so-called propagations - functions indicating the amplitude of probability (amplitude of "wave propagation") when moving a particle with a certain energy and momentum. These are fermion (eg electron) and boson(eg photon) propagator. Propagators can be expressed using the so-called Green's functions , which are solutions of the wave equations of the respective particles (either inhomogeneous Dirac equations with d -function of coordinates and time, or dAlembert's equation for electromagnetic field potentials). The actual interaction peaks correspond to the operators of creation and annihilation of the respective particles.
  We will give examples of Feynman diagrams for some specific typical interactions of particles - Fig.1.5.1. From the point of view of nuclear, radiation and particle physics, these interactions are discussed in more detail in other relevant places (1.2, 1.3, 1.5, 1.6) of our treatise. Let's start with low energy interactions. The simplest process with particles is the interaction of two electrons under the influence of electromagnetic force. According to the concept of quantum electrodynamics, the basic mechanism operating in the interaction region is the exchange of photons between the two electrons - in the Feynman diagram, the electron lines in their interaction vertices are connected by a photon line (Fig.1.5.1.B) - one electron emits a virtual photon
g*, the other absorbs it, whereby both electrons scatter in their orbits (elastic scattering). The resulting state is again two electrons. However, this is only one of the possible processes and, moreover, only in the first approximation. It is already known from classical electrodynamics, that with each accelerated movement of electric charges, electromagnetic waves are emitted. Photon emission of braking radiation occurs even when electrons are scattered. At higher energies, interaction peaks with energetic particles can also be realized, which can generate real particles - lines with free ends corresponding to secondary leptons; at the highest energies also the production of heavy particles (see below).
  Another simple process of electromagnetic interaction is the scattering of a photon on an electron - Compton scattering (is described in 1.6 "Ionizing radiation", part "Interaction of gamma and X-rays", Fig.1.6.3). In the Feynman diagram in the upper part of Fig.1.5.1.C we see a solid electron line and a wavy photon in the input region. In the interaction vertice, a virtual electron e* (which seems to "absorb" the energy of the photon) is formed, which in the second vertice changes again into a flying away electron and a photon. The interaction of the positron with the electron can take place again at low energies either as a Coulomb elastic scattering (Feynman diagram is completely analogous to Fig.1.5.1.B), or as a process of annihilation with the formation of gamma photons - lower part fig.1.5.1.C. At higher energies, there are again more possibilities in both of these processes with the formation of additional secondary particles.
  At the highest energies, there are many possibilities for the production of heavy particles, including Higgs bosons. Two such possibilities of "electro-weak production" of the Higgs boson are shown in Fig.1.5.1.D: direct interaction of e+ + e- Z* Z + H ( H-emission ) and combined production of W or Z and their subsequent fusion to H. Higgs bosons are highly unstable particles and immediately decay into either two high-energy photons or four leptons (via intermediate W or Z bosons), or other ways (the properties of Higgs bosons are described below in the section "Hypothetical and model particles").

Fig.1.5.1. Examples of Feynman diagrams of some significant particle interactions.

Note: Symbolic images of protons, neutrons and
p- mesons are not part of standard Feynman diagrams; they are drawn here for illustration only.

  Weak interactions are mediated by exchangeable intermediate bosons W (or Z). In Fig.1.5.1.F is a diagram of an important process of transmutation of the d to u quark in the b--radioactive conversion of a neutron to a proton, an electron and an (anti)neutrino: no p+ + e- + n'e . This process, as well as the analogous b+ process, corresponds to Figure 1.2.5 in 1.2 "Radioactivity", section "Radioactivity beta". Other important processes, taking place due to weak (or electroweak) interaction, are decays of pions into muons and neutrinos, eg p- m- + n'm (the decay of p+ takes place analogously) and muons into electrons and neutrinos, eg m- e- + n'e + nm (analogously for m+) - this is shown by the Feynman diagrams in Fig.1.5.1.G.
  Strong interactions are mediated by "exchange" gluons between quarks contained inside hadrons - mesons (especially p and K) and baryons (protons, neutrons, hyperons). The nonlinearity of quantum chromodynamics of strong interaction together with the idea of asymptotic freedom (see below "Inprisoned Quarks", or "Unification of Fundamental Interactions. Supergravity. Superstrings.") allows Feynman diagrams (and the perturbation approach) to be used only in processes where high momentum is passed to quarks. The "quiescent" interactions of quarks in hadrons, the strong interaction of nucleons in nuclei, and the "hadronization" of quark-gluon plasma cannot be analyzed in this way. However, high-energy interactions between hadrons can be well described. Fig.1.5.1.E shows a Feynman diagram of pion production in the collison of twoo protons p+pp+p+po; it is one of the possible processes, alternatively a proton, a neutron and a p+ can be formed , or two neutrons and a p-.
  In high-energy interactions (see below), when enough energy is available, a wide range of different internal processes can be realized. In particular, intermediate W-bosons or gluons attached at interaction vertices can acquire such high energy that they can generate very heavy particles - Higgs bosons H and heavy t- quarks - in the associated production of particle-antiparticle. These then disintegrate under the action of intermediate bosons W to electrons, muons, tauons, neutrinos and their antiparticles. Higgs bosons can also decay into a pair of high-energy photons
g. Furthermore, repeated processes with intermediate particles can create multiple particles in a single collision - including quarks, which then hadronized. Fig.1.5.1.H shows an example of high-energy collision of two protons at the energy of a hundred GeV, where interactions with exchangeable gluons can also form heavy t- quarks, b- quarks, then W-bosons and finally leptons (electrons e, muons m, tauons t, neutrinos n) that fly out of the interaction area and can be detected. With an even higher energy of tens of TeV (not yet achieved ...) one of the more possibilities is the formation of the Higgs boson ("strong production" of H by the exchange interaction of energy quarks with gluons or W-bosons) and a series of subsequent decays into W-bosons and finally again leptons or quarks - fig.1.5.1.I. And, of course, this is accompanied by the hadronization of energy quarks. Fig. 1.5.1.I shows the formation of the Higgs boson by the so-called gluon fusion; other possibilities are W or Z fusion (analogous to Fig. D below, only instead of electrons there are quarks), or combined production with W or with t-t'-pair.
  In these high-energy collisions, other quarks of colliding protons also enter the interaction area - the interaction with gluons can then create a so-called quark-gluon plasma
(see below the passage "Quark-gluon plasma -"5th state of matter"," and in 1.3 passage "High-energy collisions of heavier nuclei. Quark-gluon plasma."), the hadronization of which creates other secondary hadrons (especially pions, nucleons), flying out of the interaction region. In Fig.1.5.1.H,I two interaction areas are marked. The first - "asymptotically free"- corresponds to high-energy interactions in which even quarks behave as free and their interaction can be described by Feynman diagrams; it is analogous to the interaction areas in other diagrams. The second interaction region corresponds to the hadronization of quarks, which cannot fly out alone, but in the gluon field generate further pairs quark-antiquark which combine in pairs and triples - fly out as hardon - mesons p and K, protons, neutrons, hyperons. These particles fly out often narrowly directed sprays, called jets, at a small angle around the direction of flight of the original energetic quarks.
  In quantum field theory (in the so-called perturbation access), Feynman diagrams are used as a guide for counting contributions from different kinds of possible processes with intermediate quantums into so-called matrix elements ( S-elements of scattering), indicating the probabilities of quantum transitions between states of a given system - here between the state before interaction and after particle interaction.
First, the corresponding Feynman diagrams are constructed, the outer lines of which correspond to the incoming particles of the initial state and the outgoing particles of the final state. The 1st approximation (diagram with 2 interaction vertices), 2nd approximation (4 vertices), ..., N-approximation (number of 2N vertices) are investigated. For each of these approximations, all different ones are drawn ( topologically non - equivalent) diagrams with the same outer lines and numbers of vertices. In each such diagram, specific terms (coefficients) containing (4-) momentum and the binding constant g of the respective interaction are determined for its individual parts - outer lines, inner lines, vertices. Then integration is performed across all momentums. The contributions of all the diagrams are finally added up.
.............. comes to add ?.................

Formation of new particles during interactions
A specific phenomenon in high-energy interactions of particles is the formation of new particles - the emission of additional particles that were not previously present. They can be either particles of the same species as entered into the interaction, or particles of a different species. We explain this phenomenon using Dirac's quantum concept of vacuum *), which is not "empty space", but is filled with virtual particles, resp. pairs of particles and antiparticles. If a sufficiently large gradient of a certain field is created during the interaction at a certain place - a sufficiently large energy is transferred - these virtual particles are transformed into real particles; we observe it as the emission of new particles. Occur at the same time a associated production of particle-antiparticle pairs. A necessary condition for the formation of new particles is the achievement of a sufficiently high energy of interaction - threshold energy, higher than
Smo.c2, where Smo is the total rest mass of the resulting particles.
*) Quantum field theory and unitary theory deal in detail with the mechanisms of particle formation. The above-mentioned Feynman diagrams are also used to represent them graphically.
Multiple interactions - cascades of interactions and sprays of particles
When the interaction of high-energy particles in a sufficiently voluminous medium environment, the effect of multiple interaction occurs. The secondary particles, released during the first interaction of the incident primary particle, cause further interactions, producing additional (tertiary) particles, which do the same. From one incident particle, a whole spray of secondary particles is formed in a cascade of interactions. As the evolving spray penetrates to the depth of the material, the number of secondary particles increases and their average energy decreases. Once this energy falls below a certain threshold, the multiplication process will stop and the energy of the particles will be dissipated by ionization and excitation; the number of particles in the spray will decrease until the spray finally disappears. In practice, we distinguish two types of cascade interactions :
Electromagnetic sprays
arising from the interaction of high-energy photons or electrons with atoms of matter. Secondary electrons and photons emitted during the primary interaction, due to paired e
- e+ production, Compton scattering, photoeffect and braking radiation, produce additional electrons (+ positrons) and photons; etc.
Hadron sprays
resulting from inelastic interactions of high-energy hadrons with atomic nuclei of the material. Nuclear fragments are formed and new secondary particles are produced - p, n,
p, K. The number of these secondary particles is approximately proportional to the logarithm of the energy n ~ ln E.
  In many cases in practice, this spray is not purely hadron or electromagnetic, but mixed. The hadron spray includes pions, which then decay:
p+, - m+, - + nm , po g + g; this leads to the formation of an electromagnetic electron-photon-muon spray that accompanies the hadron cascade. Thus, each hadron spray also has an electromagnetic component. And with the interaction of high-energy photons or electrons, photonuclear reactions emit protons and neutrons, which can enrich the electromagnetic spray with a hadron component. Cascades of interactions and sprays of secondary particles are observed in cosmic rays (see Figure 1.6.7 in 1.6, section "Cosmic rays") and in particle interactions on accelerators (in bubble chambers, trackers and calorimeters).

Effective cross section of particle interactions. Impact parameter .
Similar to chemical and nuclear reactions, interactions of elementary particles take place differently "willingly" - with different efficiencies or probabilities, depending on the type of interaction and energy of the particles. The probability of particle interactions can be illustratively expressed in a geometric way using the so-called effective cross section of the interaction. The effective cross section expresses the probability that the bombardment particle will interact with the target particle in a given specific way.
  The concept of the effective cross-section is based on the illustrative idea that the target particle (black disk in the picture) behaves as an "absorbing body" with a radius r with respect to the incident particle, which this particle either hits and the desired interaction occurs, or it does not hit (misses, flies around) and no interaction occurs. The larger the radius of this body, resp. its effective area
s = p .r2 - effective cross section, the greater the probability of interaction (probability that the particle "hits").

Expressing the probability of the interaction of a firing particle with a target particle using an effective cross section

The cross section may, but need not be directly related to the "geometric diameter" target particle rgeom or its "geometric cross section" sgeom = p.r2geom . For "attracting" particles, is s > sgeom , for repellent particles, is s < sgeom . In addition, the same firing particle can cause different interactions on the same target particle, the different probabilities of which are described by different partial effective cross sections. These effective cross sections no longer have anything to do with the geometric dimensions of the particles - they are the result of the internal mechanisms of specific types of interactions (the geometric dimensions of the particles were discussed above in the section "Size of elementary particles ...").
  The unit of effective cross section in the SI system would be m
2, which is, however, inadequately large and therefore the unit barn (bn) is used in nuclear physics: 1 bn = 10-28 m2, which has the order of magnitude of the proton geometric cross section due to strong interaction (resp. heavy nuclei - so this unit and its bizare name originated in the study of uranium nuclear reactions...).
  The effective cross section of the interaction is very closely related to the absorption coefficient, the so-called linear attenuation coefficient m, in the exponential law of absorption of ionizing radiation in substances. This connection will be clarified in the following 1.6 "Ionizing radiation", passage "Absorption of radiation in matter".
  For specific course of the interaction is important the impact parameter b: it is the geometric distance of centers effective "disks" interacting particles in which around fly throughs or intersect. In the case of small impact parameter b << r
geom with it is a central collision, at larger values of b it is a peripheral collision. If the impact parameter is greater than rgeom , resp. greater than the sum of the effective radii of the two particles (target and flying), there is no longer a direct interaction by the basic mechanism (strong short-range interaction), but particles can interact through their electric fields if they are charged (such a collision is sometimes called ultraperipheral).
Dependence of the effective cross section on energy
  For a given type of particles and interactions, the effective cross section is a relatively complex function of the energy of the incoming particle. The energy dependence of the effective cross-section often has a resonant character: if we change the energy of the interacting particle continuously, significant maxima appear on the curve of the effective cross-section around certain specific energy values. By their shape, these dependences resemble the dependence of current, voltage or impedance in RLC electrical circuits (containing ohmic resistance R, inductance L and capacitance C), on the frequency f of the AC electrical signal around the frequency f
res = 1 / [2p(LC)]. For effective cross section of this kind of interaction was already in 1936, derived important Breit-Wigner relationship *)
s = (l/2p)2.g.G2. 1 / [(E-Er)2 + (G/2)2] ,
where Er is the resonant energy,
G represents the width of the excited level of the intermediate state during the interaction, l is the wavelength of the particle, the factor g is a function of the spin ratio of the initial and final states.
*) Breit and Wigner derived this relationship for a special case of elastic scattering of an incident particle in the potential field of a target particle. However, with some modifications, this formula applies to all types of interactions exhibiting resonant maxima of the effective cross section.
  The presence of resonant maxima in the energy dependence of the effective cross section indicates the existence of certain dynamic processes in the interaction - the formation of bound systems, discrete excited states or intermediate particles.

Interactions of high-energy particles
In 1.3 and 1.6, interactions are discussed mainly at lower and medium energies, which lead to characteristic phenomena of excitation and ionization of atoms, or to nuclear reactions associated with the transmutation of atomic nuclei and the emission of nuclear particles. At low energies (less than about 1MeV), the total number of elementary particles before and after the interaction does not change, arise event. only photons that carry away energy during the deexcitation of excited states. If the energies of interacting particles (including gamma photons) exceed the threshold value 2.m
e.c2 = 1.022 MeV, new (secondary) particles can be formed during the reaction - a pair of electron e- and positron e+.
  Under the interaction of high energy particles means the reaction induced by particles with an energy which lies above the threshold for the production of mesons
p, which is above the energy 140 MeV in the center of gravity system. With increasing energy, such interactions can produce gradually more new secondary particles (mostly p- mesons) and also particles with higher rest mass - mesons K, nucleons and antinucleons, hyperons, bosons W and Z (at the highest energies of many TeV and more are also expected the production of Higgs bosons, supersymmetric particles, leptoquarks and other "exotic" as yet unproven particles).
  When atomic nuclei are bombarded by high-energy particles (eg protons), several nucleons and "splinters" are ejected - the "shatter" or fragmentation of nuclei is occur.
  At the highest energies (of the order of 100 GeV and higher), the interactions are already quite complex and diverse, a large number of secondary particles are produced. In a laboratory (target) system, a narrow beam of secondary particles is formed, especially pions
p, collimated forward in the direction of movement of the primary particle - a kind of nozzle or spray of particles. Furthermore, a wider cone of heavier particles and also gamma quanta is formed. In these reactions, the kinematic and dynamic effects of the special theory of relativity are fully manifested - sometimes referred to as ulrarelativistic. During high-energy collisions of heavy particles (protons and especially heavier atomic nuclei), a special mixture of locally free quarks and gluons may form for a short time - the so-called quark-gluon plasma (discussed in more detail below in the section "Quark structure of hadrons", passage "Quark-gluon plasma - 5th state of matter").
   The study of particle interactions at high energies is of great importance for understanding the structure of elementary particles and the nature of forces that operate between them. During a high-energy collision, particles penetrate each other "deep inside" and the result of the interaction can tell something about their structure. Due to quantum processes in the fields of strong, weak and electromagnetic interactions, high-energy collisions create new secondary particles, which are both interesting in themselves and carry important information about the nature of fundamental natural forces, including the possibility of their uniform understanding within unitary field theory. Particle collisions at high energies are a kind of "probe" into the deepest interior of matter *) - and at the same time into the processes of the formation of the universe
(see 5.5 "Microphysics and cosmology. Inflationary universe." book "Gravity, black holes and space-time physics"). Specific ways of particle interactions will be described below for individual types of elementary particles.
*) Let's also compare with the left part of Fig.1.0.1 in 1.0. "Physics - fundamental natural science".

Analysis of the dynamics of particle interactions
  High-energy interactions of elementary particles are studied using large accelerators (see section "
Charged particle accelerators" below). The accelerator itself is followed by very complicated and precise detection apparatus and systems *) that analyze secondary particles and radiation generated by the interaction of high-energy primary particles with the target material or in mutually oppossite collided beams. They contain a large number of individual detectors of various types (scintillation, semiconductor, ionization), located in strong and specially configured magnetic fields (for the analysis of the momentum of charged particles). By analyzing the type, charge and mass of these flying-out particles, their energies, momentum and emission angles from the site of interaction, a number of parameters of the interactions that occur can be reconstructed. From this it is possible to deduce the structure of elementary particles, the properties of acting fields and interactions, the existence of new hitherto unknown quanta and particles.
*) Large bubble chambers were previously used for this purpose (see 2.2, part "Detectors trace particle"). Now they are replaced by large and complex electronic detection systems (2.1, section" The arrangement and configuration of the radiation detectors") containing, inter alia, so-called trackers - electronic particle paths detectors. They mainly use multidetector semiconductor systems (2.5 "Semiconductor detectors"), or systems of special ionization chambers and scintillation detectors.
  Even when a particular intermediate particle decays immediately at the site of interaction (and therefore cannot be detected directly), the products of its decay carry some information about its properties. From the measured energies and momentum these secondry products, the mass of the original particle can be determined. If we plot on the horizontal axis the measured energy of the detected set of particles corresponding to the respective "channel" of decay - secondary particles on which the sought intermediate particle should decay - and plot on the vertical axis the registered number of cases (or normalized per unit energy of primary collided particles, e.g. protons), a small "bump" may appear on the otherwise smooth curve, indicating the existence of a short - lived particle of appropriate rest mass corresponding to the energy on the horizontal axis. Based on the quantum uncertainty relation between the lifetime
t of a particle and the uncertainty of determining its rest energy E = m.c2 (t.DE h), the lifetime t of the intermediate particle can be estimate from the stastistic "blur" of the rest mass values.
Dalitz diagram
At the output of detection systems surrounding the site of interaction, a large number of pulses of various sizes, shapes, temporal and angular correlations appear, carrying information about energies, momentums and other parameters of secondary particles. It is by no means easy to find your way around such a large amount of data. For clear display and kinematic analysis products of particle interactions the so-called Dalitz diagrams are sometimes used (diagrams of this type were first compiled by R.H.Dalitz in 1953 during the research of K-mesons and their decays). It follows from the laws of conservation of energy and momentum, that the kinematics of the interaction can be suitably parameterized by the square of the energy of the particles. On the axes of the diagram, the squares of the effective masses
energies of the pairs of daughter particles (products of interaction *), mostly p- mesons, are plotted (in GeV2 energy units).
*) If, for example, during the interaction of two primary particles P
1 and P2 : P1 + P2 A + B + C, three secondary particles A, B, C are formed, we plot m2AB on the X axis and on the Y axis the values of m2BC . These squares of masses are equal to the squares of the sums of the 4-momentums of the particles: m2AB = (pA + pB)2, analogously to mBC .
  If the studied type of interaction takes place directly, without being affected by dynamic processes of intermediate particles or resonant states (which is the same from a certain point of view...), the resulting particles are randomly distributed and the distribution of relevant measurement points on the Dalitz diagram is approximately homogeneous, filling the triangular area below the diagonal given the energy used. However, if a short-lived intermediate particle (or resonance process) is formed during the interaction, whose decay products are detected secondary particles, the distribution of measured points on the Dalitz diagram is inhomogeneous - local densities appear (peaks in the profile - slice of diagram) in the areas around the mass of the intermediate particle.
  Analyzes of this kind were previously performed manually with dots drawn on paper. They are now performed using powerful computer technology, diagrams are digitized and displayed using computer graphics, sometimes with color image modulation. Fourier transforms are also introduced to analyze the relationship between the time and energy spectra of the short-lived state of an intermediate particle or resonance. All these methodological approaches are useful not only in the analysis of particle interactions, but wherever we need to distinguish kinematic effects from dynamic ones, to prove the existence of some short-lived bound state that is not directly observable.
Energy dependence of the effective cross-section
This procedure is suitably combined with the analysis of the energy dependence of the effective cross-sections an interaction, whose possible resonant character is expressed by the above-mentioned Breit-Wigner relation. If there are resonant peaks in the energy dependence of the effective cross-section of the interaction and at the same time local densities and peaks are visible on the Dalitz diagram of the energy distribution of secondary particles, it is almost certain that dynamic processes of excited states or intermediate particles occur during the interaction.
Missing energy
If the studied interaction is accompanied by the formation of neutral weakly interacting particles, these cannot be detected in the normal way. Here is a certain possibility an analysis of the energy balance we determine the energies and momentums of other particles and, based on the law of conservation of energy and momentum, we determine the values of energy and momentum that an unknown particle carries away. From them we can then determine the rest mass of an unknown particle.
...? add-other types of diagrams + pictures ..? ...

Properties and interactions of the most important elementary particles
In this section we will briefly approach the individual most significant particles of the microworld, their origin and formation in the interactions of particles, their properties and the main ways in which they interact with each other and with other particles. In this brief description of the properties of elementary particles, we will not stick to the systematics outlined above, but will move from known, widespread and practically used particles to "exotic", less known and more hidden particles, whose significance for the structure and properties of matter is sometimes unknown.

are a quantum of electromagnetic radiation. They have zero rest mass, they move at the speed of light *), they carry energy E = h.
n, where h is the Planck's constant and n is the frequency of the electromagnetic wave of wavelength l = c/n. They are bosons with spin number 1. According to the laws of electrodynamics, photons are generally formed during all accelerated movements of electrically charged particles (eg braking radiation). They are emitted during deeexcitation in atomic shells (visible and UV radiation, characteristic X-rays - 1.1., passage "Radiation of atoms") and atomic nuclei (gamma radiation - 1.2, part "Gamma radiation") , where they carry away the corresponding energy difference of the excited states. Photons of gamma radiation also arise during annihilation of positrons with electrons e+ + e- 2g (1.6, part "Interaction of charged particles - directly ionizing radiation", Fig.1.6.1 below, passage "Interaction of positron (beta + ) radiation"), as well as in a number of other elementary particle interactions. Here we will consider mostly photons of higher energies - radiation g.
*) However, see the theoretical note on the possible influence of quantum fluctuations of spacetime on the speed of hard radiation g in 1.6: "Is high-energy g- radiation moving slower than light?".
  Interactions of medium energy photons with matter are described in 1.6, part "
Interaction of gamma and X - rays", it is mainly a photo effect, Compton scattering, formation of e-e+ - pairs. High-energy photons (> 10MeV) can, through their interactions, cause so-called photonuclear reactions, in which neutrons, protons, or multiple nucleons, deuterons, a-particle, are ejected from the nuclei. Above the threshold energy of gamma radiation of about 140 MeV, other particles are formed during the interaction, eg p -mesons: g + p n + p+ , g + p p + po, etc. At very high energies of gamma photons (> 300MeV) , a number of other particles can be generated, including heavy ones (cf. above "Interactions of high energy particles").
Photons, as a quantum of electromagnetic waves, were actually introduced by A.Einstein in 1905 during the study of the photo effect (1.1 "Atoms and atomic nuclei", Fig.1.1.1); the proper name "photon" was later proposed by the American chemist G.N.Lewis.

Electrons and positrons
Electrons e -
are basic, truly elementary, stable particles of matter that form the electron shell of atoms. The electron carries a negative elementary charge e = 1.60219.10
-19 C, its rest mass is me = 9.1095.10-31 kg (= 511keV/c2), it belongs to the leptons, it is a fermion with spin (1/2) h. The magnetic moment of an electron is e.h/4p me - the so-called Bohr magneton. According to the ideas of modern cosmology, electrons were formed in the earliest stages of the evolution of the universe after the Big Bang, during the separation of electromagnetic and weak interactions. In addition, electrons are formed in a number of processes and interactions of other elementary particles, such as in b- -radioactivity no p+ + e- + ne and in many other processes, as can be seen from the interactions of other particles described below. In addition to atomic and nuclear physics, electrons play a key role in electromagnetic phenomena, the vast majority of which are based on the motion of electrons that generate electric current.

1895: J.J.Thomson - discovery of electrons => first model of atom
The electron was discovered, as the first elementary particle of the structure of matter, in 1895 by J.J.Thomson during the study of electric discharges in gases in a cathode ray tube.

Positron e +
is an antiparticle to the electron, so it has the same mass and spin, the electric charge is the same size, but of the opposite (positive) sign. In a vacuum, a positron is a stable particle, just like an electron. However, as soon as it is in a material environment filled with atoms and therefore also electrons, it disappears in annihilation interaction with electrons: e
+ + e- 2 g (1.6, section "Interaction of charged particles - directly ionizing radiation", Fig.1.6.1 below passage "Positron (beta + ) radiation interactions"), producing two quantums of gamma radiation of 511 keV energies, flying out in opposite directions (at an angle of 180). This perfect angular correlation is advantageously used in gamma imaging by positron emission tomography imaging in nuclear medicine after the application of a positron beta+-radionuclide, e.g. 18F (4.3, section "Positron emission tomography PET").
Note : These patterns apply exactly only in the center of mass frame of reference of the positron and an electron. The energy of photons 2x511 keV is a consequence of the law of conservation of energy (resting energy of the electron and the positron is m0e .c2 = 511keV), the opposite direction of 180 is a consequence of the law of conservation of momentum. In the case of collisions of positrons and electrons of higher energies, the angle of inclination of annihilation photons would differ from 180. In the material environment, however, the positron and the electron have relatively low velocities at the moment of annihilation, so that the emitted quantums actually fly in almost opposite directions.

Just before the actual annihilation, the electron e- and the positron e+ can orbit around itself for a moment (they orbit the common center of gravity) - they form a special bound system (similar to a hydrogen atom) called positronium (Ps). The dimension of the "atom" of the positronium is twice the hydrogen atom, the binding energy of the positron is 6.8 eV. Depending on the mutual orientation of the electron and positron spins, the positronium can be either in the singlet state 1S0 with oppositely oriented spins - so-called parapozitronium p-Ps (1/4 cases), or in the triplet state 3S1 with consistently oriented spins - so-called orthopositonium o-Ps (3/4 cases).
  However, this system of positronium is unstable, the two particles approaching each other in a spiral under the emission of electromagnetic waves; in p-Ps in about 120ps they "fall" on each other and there is a self-annihilation on two photons g, each with an energy of 511 keV. In the case of o-Ps, annihilation to two photons is prohibited by quantum selection rules (related to the law of conservation of the spin momentum - each of the photons has spin 1), so o-Ps would decay in a vacuum with a relatively long lifetime of about 140ns emission of 3 photons with a continuous energy spectrum (the total energy of 1022 keV is divided by photons in a stochastic manner). In the substance, however, the positron bound in o-Ps much earlier is enough to annihilate with some "foreign" electron from the environment, which has the opposite spin orientation - again, two photons g with energies of 511 kV are formed.
  The annihilation of a positron with an electron produces 2 gamma photons in the vast majority of cases, as mentioned above. Sometimes, however, there may arise more, but with a very small probability (the probability that 2 + n photons will be formed during e-e+ annihilation is proportional to a-n, where a = 1/137 is the fine structure constant). If a positron interacts with an electron bound in an atomic shell, the extinction of such a pair may be accompanied by the emission of only a single photon, and some of the energy and momentum may be transferred to either the atomic nucleus or one of the other electrons; however, the probability of this process is very small and does not apply in practice.
  The lifetime of positrons in substances is in the order of hundreds of picoseconds. However, the exact value depends on local electron densities and configurations, which is used in the spectroscopic method PLS (Positron Lifetime Spectroscopy ....). Material tested locally irradiated b+- g emitter (usually 22Na), the lifetime of positrons is determined by measuring the delayed coincidence between the detection of photon radiation g of irradiating radionuclides (from 22Na, it is g 1274 keV) and the detection of the annihilation photons g 511 keV.
  In terrestrial nature, therefore, positrons do not normally occur permanently, they occur only for a short time during certain interactions of elementary particles and then (for about 10-10 -10-7 s) again annihilate with electrons. The most common process in which positrons are formed is b+-radioactivity caused by the conversion of the proton p+ in the nucleus into neutrons no, positron e+ and neutrino: p+ no + e+ + ne (1.2, part "Radioactivity b+"). Positrons are also relatively common products in the interaction of particles at high energies (will be shown several times below) and in the decay of muons and pions (see below "Muons m and tauons t"); thus they occur in secondary cosmic rays (see the passage "Cosmic rays" in 1.6). Positrons can also be formed with the aid of gamma radiation: if the higher energy gamma rays than 1022 keV, one way of its interaction with matter is the formation of an electron-positron pairs (1.6, section "Interaction of gamma rays and X" passage "Formation of electron- positron pairs").
  For completeness, we will mention one "exotic", not yet realized in practice, method of positron formation :
Breit-Wheeler process of e
+ e- pairs production
According to quantum electrodynamics the electron-positron pair could theoretically be formed even when two photons collide
g1 + g2 e+ + e- ; it is an inverse process to the above annihilation of a positron with an electron: e+ + e- 2g (G.Breit and J.A.Wheeler designed it in 1934). However, this two-photon process has a very low probability (slight effective cross-section), which would require extremely intense collimated beams of gamma photons with an energy higher than 511keV; upon detection, the desired effect would be covered many times by much stronger secondary radiation - so far it has not been possible... Another possibility of photoproduction could be the so-called multiphoton Breit-Wheeler process (...), in which high-energy photons, when passing through a very strong electromagnetic field, could decay into electron-positron pairs. Here is a possibility of realization in the near future using high-power laser systems ...
  History: In 1932, the positron first observed C.D.Anderson in cosmic rays detected by a Wilson nebula camera placed in a magnetic field, where a trace of particles with the same ionization properties as an electron appeared, but with in the opposite direction of rotation in a magnetic field, ie a "positive" electron.

Protons and neutrons
Protons and neutrons, collectively called nucleons, are the building blocks of atomic nuclei. These are heavy particles from the group of baryons, they show a strong interaction which ranks them among the hadrons - they are composed of 3 quarks. They are of natural origin - they originated in the "fiery furnace" of the Big Bang at the beginning of the so-called hadron era, in the first millionth of a second of the universe's existence. In addition, they arise in a number of processes and interactions of other elementary particles; during radioactive transformations of
b- , + there are mutual transformations of neutrons and protons (1.2, passage "Mechanism of decay b. Weak interactions.").
Protons, as nuclei of hydrogen, were discovered in the study of electric discharges in gases at about the same time as electrons (late 19th century). Neutrons were discovered only in 1932 by J.Chadwick during the bombardment of beryllium nuclei with alpha particles (1.1 "Atoms and atomic nuclei", part "Construction of the atomic nucleus").
Proton p +
carries a positive elementary electric charge of the same absolute magnitude e as the electron, its rest mass is m
p = 1.6726.10-27 kg = 1836.151 me = 938.256 MeV/c2. The magnetic moment of a proton is e.h/4p mp - the so-called nuclear magneton, which is 1836 times smaller than Bohr's magneton (simply put, we can imagine that at the same spin and charge, a heavy proton "rotates more slowly" than a light electron). A proton is a stable particle (omitting here some speculation about the possible decay of a proton *). The number of protons in the nucleus (proton number Z) also determines the number of electrons and their energy levels in the shell - and therefore the "size" of the atom and its chemical properties when combined with other atoms. The proton itself forms the core of the simplest element - hydrogen 1H1. Free protons are encountered in ionized hydrogen plasma and in nuclear reactions in which accelerated protons enter or are their products. Protons are the most common particles that are accelerated in accelerators for the purposes of nuclear physics (see the chapter "Charged particle accelerators" below). The number of protons in the atomic nucleus indicates the proton (atomic) number Z , which also determines the number of electrons in the atomic shell and thus the chemical properties of the atom - the position of the element in Mendeleev's periodic table.
*) Instability of proton ?
The so-called
grandunification theories admit the instability of a proton, which should decay into muons or positrons and into one neutral or two charged pions [p+ (m+ or e+) + (po or p+ + p-)] with a lifetime of the order of tp 1030 -1033 years. This decay would be caused by the conversion of a quark to a lepton via the X boson, and due to the enormous mass of the X boson, its probability is extremely small. Experiments so far give estimates of tp > 1030 years. These attempts to observe proton decay are made deep underground (due to cosmic ray shielding), where large water tanks are located, equipped with many photomultipliers that could detect faint flashes caused by the passage of fast particles formed as proton decay products. The most perfect device of this kind is the Superkamioka-NDE in Japan, which did not detect any proton decay, but was very successful in the detection and spectrometry of neutrinos (see the "Neutrinos" passage in 1.2 "Radioactivity").
Note: Another hypothetical and very curious mechanism could be the decay of a proton through a virtual black hole (4.8 "Astrophysical significance of black holes" in a monograph "Gravity, black holes and spacetime physics"). Black mini-holes emitting by quantum Hawking mechanism the particles that are generally different from those that the black hole swallowed, violates the law of conservation of baryon number (4.7 "Quantum radiation and the thermodynamics of black holes" in the same book). Therefore, if two quarks in a proton fall into a virtual black mikro-hole, it is possible to back emission of e.g. antiquark and leptons, thereby proton converted into muon or electron and pion.
Neutron n 0
is electrically neutral and its rest mass m
n = 1.6748 .10-27 kg = 1838.65 me = 939.55 MeV/c2 is slightly higher than the proton. In stable atomic nuclei, neutrons are stable, the free neutron (in vacuum) decays with a half-life of about 13 minutes by b--radioactivity of no p+ + e- + n'e into proton, electron and antineutrino. Free neutrons are not commonly encountered in terrestrial nature, in the upper layers of the atmosphere a smaller number of them are formed during interactions of cosmic radiation (1.6, section "Cosmic radiation"). However, they are common products of nuclear reactions and are also willing to enter into nuclear reactions (1.3, passage "Reactions induced by neutrons"). Intensive sources of neutrons are nuclear reactors, whether fission or so far experimental fusion thermonuclear (1.3, part "Fission of atomic nuclei" and "Fusion of atomic nuclei"). As laboratory neutron source are constructed as small specific accelerators of charged particles (mostly deuterons with tritium target) called neutron generators (see below "accelerators of charged particles," passage "neutron generators"), or radioisotope source consisting of a mixture a -radionuclide with light element (such as a mixture of americium and beryllium, the reaction a, n), or a heavy transuranic radionuclide (most often californium 252), during the spontaneous fission of which neutrons are released (1.3, "Transurans").
Origin of the masses of protons and neutrons
Protons and neutrons are much heavier than the sum of the masses of their quarks. E.g. the proton has a mass of 938MeV, while the mass of the "u" quark is 2MeV and the "d" quark is 5MeV. Therefore, most of the mass of a proton comes from the kinetic energy of the internal motion of its quark components. This is explained on the basis of quantum uncertainty relations, according to which the product of uncertainty in the position and momentum of a particle is greater than the Planck constant. Quarks are enclosed in a proton or neutron ("imprisoned") in a spatial area with a diameter of aprox. 10
-13 cm; this forced very small uncertainty in position quantum, implies considerable momentum and thus the kinetic energy of each of the quarks, at least about 200MeV. The kinetic energy balance of such three intensely oscillating quarks is approximately equivalent to the mass of the proton.
  If all quarks had the same mass, one would expect the proton to be slightly more massive than the neutron, because the electric charge of the proton (which the neutron does not have) contributes to its internal energy. However, the difference in the mass of the "u" and "d" quarks
(which is explained in unitary field and particle theories by interaction with the Higgs field - see below) causes the neutron (u, u, d) to be somewhat "heavier" than the proton (u, d, d). This difference in mass causes the instability of the free neutron, its b--decay into proton, electron and neutrino by weak interaction.
Antiparticles to protons and neutrons
Antiproton p'
- differs from a proton only in its negative charge and the opposite direction of the magnetic moment, in a vacuum it is also a stable particle. The antineutron n' 0 is a neutral particle like a neutron, from which it differs only in the opposite orientation of the magnetic moment, its half-life in vacuum is the same as that of a neutron, it decays according to the scheme n'o p'- + e+ + ne to an antiproton, positron and neutrino.
  Antiprotons and antineutrons are not commonly found in terrestrial nature, they are formed by the interaction of high-energy particles and then disappear by interactions with nucleons. Due to the law of conservation of the baryon number, antinucleons can only be produced in pairs together with nucleons. The most common way of producing antiprotons p' is in reactions p + p
2p + p + p' , resp. p + n 2p + n + p' ,
while the threshold kinetic energy of the firing proton (in the laboratory target system) is about 5.6 GeV, resp. 3.6GeV; however, if this interaction occurs during nuclear bombardment, the threshold energy of antiproton production may be lower (around 3GeV). Antineutrons are formed in similar reactions p + p
2p + n + n' , resp. p + n p + 2n + n', furthemore in reactions antiprotons p' + p n + n' , p' + n n + n' + p-.
  In antinucleon interactions, the most important are the interactions (p', p) of antiprotons with protons. At high energies, other heavy particles such as hyperons can be formed here, which will be mentioned below. At low energies of antiprotons or when they are stopped (see below), leads to nucleon pairs annihilation with the production of mesons, quantum gamma, or there is a reaction p' + p
n + n' occurs ("charge exchange"). The extinction of pairs (p', p) is a strong interaction, in which mesons p *) are most often formed (only in a small percentage of mesons K); the smallest number of formed mesons with respect to the law of conservation of momentum are 2 mesons p, but most of them enter more, most often 5 mesons - a typical interaction of this kind is: p' + p 2p+ + 2p- + po.
*) The formation of mesons p during the annihilation of an antiproton with a proton is due to the quark structure: antiquarks in the antiproton and quarks in the proton combine into quark-antiquark pairs, which are mesons.
  When an antiproton enters a substance, atoms are ionized by electromagnetic interaction, just like any other charged particle, thereby the antiproton braking and slowing down. During this deceleration may antiproton disappear when interacting with the nucleus, but can be slow (or almost stopped) so much, that it can be trapped by a proton (hydrogen nucleus) - a new "exotic atom" is formed, called protonium, consisting of a proton and antiproton orbiting a common center of gravity. Similarly, it can be captured by another heavier nucleus on some higher orbit (where eject the electron) and during its orbit it then passes to lower orbits, which is accompanied by the emission of either X-ray photons or Auger electrons. Finally, it is absorbed by the nucleus and disappears by interaction with a proton or neutron to produce pions.
Antiproton around which revolves positron constitute atom of "antihydrogen", which has similar properties as normal hydrogen. Antiprotons and antineutrons can form "anti-atomic nuclei" around which positrons can orbit in exactly the same configurations as the respective ordinary atoms - they are "antiatoms", that would have exactly the same chemical and spectroscopic properties like our atoms, within the "anti-world" - they would form antimatter -
(discussed above, the passage "Antiparticles, antimatter, antisworlds").
History: The antiproton was discovered in 1955 at an accelerator in Berkeley while bombarding a copper target with protons accelerated to 6.2 GeV. In 1956, an antineutron was discovered on the same accelerator: a beryllium target was bombarded with protons with the same energy and the resulting antiprotons were led to a system of scintillators and a Cherenkov detector connected in anticoincidence, where antineutrons were formed by the reaction of p'+ p n + n' with hydrogen nuclei produced antineutrons, which when interacting with nucleons in the Cherenkov detector were registered as intense flashes.

Neutrinos and antineutrinos (for more details, see the link "Neutrinos - "ghosts" among particles")
These are ubiquitous but almost elusive particles. Neutrinos
n and antineutrinos n' are the lightest and weakest interacting of all known types of elementary particles - they belong to the leptons. They are fermions with spin number 1/2, they do not carry an electric charge, they do not show a strong interaction, but only a weak interaction (and a universal gravitational interaction, which we are not interested in here from the point of view of elementary particle physics, can have certain Cosmological consequences). We recognize three types of neutrinos: electron neutrino ne , muon nm and tauon nt neutrinos, which, however, can spontaneously transform each other during the so-called neutrino oscillation. Neutrino as such is a mixing of the proper states of electron, muon and tauon neutrino and therefore there is a periodic transformation of one neutrino to another.
  Electron neutrinos are typically formed during the mutual transformations of neutrons and protons by
b-,+ -decay: no p+ + e- + n'e , p+ no + e+ + ne , muon and tauon neutrinos then during the decay of muons and tauons: m- e- + n'e+ nm , t- nt + e- + n'e , t- nt + m- + n'e , ......
In addition, neutrinos arise in a number of interactions of elementary particles in which weak interactions take place. Large amounts of neutrinos are formed during thermonuclear reactions inside the Sun and stars, from where, thanks to their very weak interaction, they easily penetrate outside and are radiated into the surrounding space. A extremely strong "flash" of neutrino radiation occurs during a supernova explosion
- see 4.2 "The Final Phases of Stellar Evolution. The Gravitational Collapse" of the book "Gravity, Black Holes and the Physics of Spacetime". There is also a huge amount of so-called relict neutrinos in the universe, originating from the lepton era of the universe just after the Big Bang. Neutrinos, along with photons, are among the most abundant particles in universe. Properties of neutrinos, their origin, detection methods and possibly the cosmological significance of neutrinos are described in more detail in 1.2 "Radioactivity", part "Neutrinos - "ghosts" between particles".
Neutrinos were introduced as hypothetical particles by W.Pauli in 1930 in the study of the energy balance of b- decay (see 1.2, part "Radioactivity beta", Fig.1.2.3), their name and specification of properties come from E.Fermi. Neutrino was experimentally demonstrated only in 1956 by experiments outlined in the mentioned reference "Neutrinos...".

Muons m and tauons t
Muons m - and m +
(they are antiparticles each other), also referred to as "heavy electrons", are medium-heavy particles with mass m
m = 206 m e, carry a negative or positive electric charge of the same size as the elementary electron charge; there are no neutral muons without electric charge. Muons are unstable particles that decay with a half-life of 2.10-6 s. to an electron , resp. positron, and two neutrinos: m- e- + n'e + nm , m+ e+ + ne + n'm . This decay has the character of a weak interaction and is similar to the radioactive decay of beta; also the energy spectrum of electrons or positrons here is continuous, the maximum energy is 53 MeV.
  Muons occur in terrestrial nature in secondary cosmic rays (see the passage "Cosmic rays" in 1.6). They are formed in the upper layers of the atmosphere (above 10 km) during the collisions of protons and other particles of primary cosmic radiation with protons and neutrons in nitrogen and oxygen nuclei in the atmosphere. In these primary collisions, p-mezons are formed first, which decay into muons during about 2.510-8 s, which move with a kinetic energy of about 4 MeV at a relativistic speed. Due to its lifetime of 2.10-6 seconds, according to classical mechanics, the muon would fly only about 500 meters and then disintegrate - so virtually no muons should hit the Earth's surface. However, due to the relativistic dilation of time , the muon "lives longer" from the point of view of the observer on Earth and has enough time to hit the Earth's surface. This experimental fact that the muon flies a path 20 times longer than would correspond to its lifetime in classical mechanics, is convincing evidence of the effect of slowing the flow of time according to a special theory of relativity.
  The most common way of forming muons is during decay
p -mesons: p- m- + n'm , p+ m+ + nm (see the following passage "Mesons p and K"). The interactions of muons with nucleons proceed according to the scheme: m- + p n + nm , m+ + n p + nm , .....   
  If a negative muon
m- enters into matter, it can (after its slowing down by ionization) be captured by the Coulomb field of the nucleus and form a peculiar bound system similar to an atom - the so-called muon atom or mesoatom. A positive m+ mion passing through the medium can in turn capture the electron and form an unstable bound system of the m+ mion and the orbiting electron e-, called the mionium; it is a system analogous to positronium and has a structure similar to a hydrogen atom.
The muon m was discovered in 1936 by C.D.Anderson and S.H.Neddermeyer while studying cosmic rays in the Wilson nebula chamber (similar to a positron).
Tauons t- and t+
(they are antiparticles each other), also referred to as "superheavy electrons", are very heavy particles with mass m
t 3484 me 1177 MeV/c2, carrying a negative or positive electric charge of the same magnitude as the elementary charge of an electron. Tauons are highly unstable particles that decay to an electron or muon and two neutrinos with a half-life of 3.10-13 s: t- e- + n'e + nt , t- m- + n'm + nm . However, due to their high rest mass, tauons are able to decay even into hadrons, especially pions p-, p+, po and tauon neutrinos, eg. t-  p- + nt , t-  p- + po nt , t-  p- + p+ + p- +nt , etc.
Tauon t was discovered in 1974-77 by a team led by M.Perl during experiments with high-energy collisions of positrons and electrons in the beams of the accelerator at Stanford. During the collisions of electrons with positrons, t+ and t- pairs were formed, which flew only a short distance (about 1 mm) and then decayed into electrons, muons and neutrinos. The formation of tauons was proved on the basis of the detection of charged particles, analysis of their energies and angular distribution (by the methodology mentioned above "Analysis of the dynamics of particle interactions").

Mesons p and K
p -mesons (also called pions)
are the most common type of new secondary particles, formed by particle interactions at high energies exceeding about 300MeV; at even higher energies (above
1 GeV) K-mesons and hyperons are also formed.
  The mesons
p and K have the following common properties: they are medium-heavy particles with spin 0 (thus belonging to the bosons), show strong interactions (they are hadrons) and are very unstable. According to the standard model of particles, they consist of a bound quark and an antiquark.
  Charged mesons p - and p +, which are antiparticles to each other, carry a negative or positive elementary charge of the same size as an electron, have a rest mass 2.4898.10-25 g 273 me 140 MeV/c2 and with a half-life 2.55.10-8 s disintegrate (by weak interaction) to muons and neutrinos: p- m- + n'm , p+ m+ + nm (muons then decompose further into electrons and neutrinos). During this decay, kinetic energy is released (mp -mm).c2 34 MeV, of which the muon m carries out a smaller part of about 4.2 MeV and the rest of the kinetic energy of less than 30 MeV is obtained by the muon neutrino nm .
  In addition to particle interactions in accelerators, pions are formed for a brief moment in the upper atmosphere during the interactions of high-energy protons from primary cosmic radiation with nucleons in the nuclei of nitrogen, oxygen and carbon; they immediately decay into muons (see the "Cosmic Radiation" passage in 1.6).
  The neutral meson p o has a rest mass of 264 me 135 MeV/c2 and with a very short half-life 0.9.10-16 s decays (by electromagnetic interaction) into two quantum gamma: po g + g.
Note : In terms of internal structure, mesons are a bound quark-antiquark system. However, this system is unstable and its disintegration can be simply understood as a process of "annihilation" of a quark-antiquark pair; either by a weak interaction via the intermediate boson W , or electromagnetically directly on the quantum g (cf. the corresponding Feynman diagram in Fig.1.5.1). It is a bit analogous to the positronium mentioned above, which is also an unstable bound state of a particle-antiparticle pair (e- - e+), which annihilate to quantum g .
  p- mesons have played a varied and interesting role in the history of nuclear physics. For a long time (40s-70s), they were considered to be exchangeable particles, mediating strong short-range nuclear interactions of protons and neutrons in the nuclei of atoms (comes from H.Yukawa). The fact that pions are often formed during high-energy collisions of protons and neutrons also seemed to indicate this. Idea p -mezons as carriers of strong interactions, however, did not work in the end. It turned out that the essence of a strong interaction lies deeper - it lies in the internal quark structure of protons and neutrons. During the interactions of protons and neutrons, pions are formed not as exchangeable particles, but because p -mesons are lighter and simpler particles also composed of quarks (and their antiparticles), just like nucleons. Nevertheless, p- mesons are the most important of all unstable "exotic" particles; they may have perhaps a practical use, see eg 3.6, section "Hadron radiotherapy".
K mesons ,
also called kaons, are more than 3 times heavier than
p- mesons.
  Charged mesons K + and K - , which are mutually antiparticles, carry a positive or negative electric charge of the same size as an electron, have a rest mass 966.6 me 494 MeV/c2 and with a half-life 1.24.10-8 s decay into p -mesons, muons and neutrinos: K+p++po, K+m++n, K+p++p++p-, K+p++po+po, K+po+m++n, K+po+e++n; by analogy (associated) also K-.
  The neutral meson K 0 has a mass of 974.2 me 498 MeV/c2 and decays very rapidly into p -mesons and also into muons, electrons and neutrinos by two types of decays :
two- particle decays : K
o p+ + p- , Ko po + po, - (half-time 0.9.10-10 s) ;
three-particle decays: K
o po+po+po, Ko p++p-+po, Ko p+,-+m-,++n, Ko p-,++e+,-+n, - (half-time 5.7.10-8 s).
  The fact that the meson Ko decays with two different half-lives and different processes, can be explained by the assumption that the meson Ko is a quantum "mixture" of two neutral particles Ko L ("Long") and Ko S ("Short"), which have different lifetimes and different decay patterns. These facts are interpreted as the observed meson Ko being internally a "mixture" or superposition of Ko and its antiparticle K'o. Between these two states, the neutral kaon spontaneously "oscillates".
Interactions of mesons p and K 
p- and p+ interact with nucleons at low energies mainly by reactions: p- + p n + g , p+ + n p + g , at high energies pions there is also a combined production of kaons, hyperons and antihyperons, eg p- + p K+ + K- + n , p- + p L + Ko, etc. - for further reactions, see the section on hyperons below.
  When interacting with the substance,
p- mesons may be (after appropriate braking by ionization energy losses) captured in orbit around the nucleus (similar to electrons in an atom), so for a very short time a mesoatom is formed with a pion p-, which is then absorbed by the nucleus and there it combines with a proton (p- + p n + g).
Formation of mesons
p and K 
p -mesons are formed mainly as new secondary particles during interactions of protons with nucleons, if the kinetic energy in the laboratory (target) system is higher than 2.mp.c2 300 MeV. There can be several reactions of this type :
p+n+p+, p+p p+p+po, p+n n+n+p+, p+n p+p+p-,
p+n+po, n+n n+p+p-, n+n n+n+po , ....,
while these reactions can take place both on free nucleons and on nucleons bound in the nucleus. Pions can also be produced by photonuclear reactions of hard gamma radiation:
g + p n + p+ , g + p p + po, whose gamma radiation threshold energy is about mp.c2 140 MeV.
  Mesons K are formed by the so-called associated production in pairs either together or in pairs with hyperons, either by mutual interactions of nucleons or
p- mesons with nucleons. Examples of such interactions are: p + p L + K+ + p , p- + p K+ + K- + n , p- + p L + Ko, etc.; other combinations with hyperons are given in the following section.
The strangeness of particles

These K-mesons, as well as the hyperons mentioned below, have some special - "strange" - properties that we do not encounter in other particles. These are asymmetries in the production and decay of these particles. These particles are formed in high-energy hadron collisions with a high probability - pair production by strong interaction. However, their decay is usually relatively slower (on the order of 10-10 s) through weak interaction. To explain this situation, a new quantity or (additive) quantum number called strangeness S was introduced (for ordinary particles is S = 0, strange particles have S = 1, 2, hyperon W even S = -3), which is preserved in strong interactions, but not in weak interactions. This explains that with strong interactions of ordinary particles, strange particles are formed in pairs, the sum of the strangeness of which is zero, but by a weak interaction, the strange particles can decay into particles without strangeness.
  To explain the new quark model of hadrons, a new quark "s" (strange) has been introduced, which carries strangeness; quark s has strangeness S = -1, antiquark s' has S = 1, other quarks S = 0. The presence of the quark "s" in a two-quark combination is characteristic of strange mesons K, if "s" occurs in a three-quark combination, there are hyperons - Fig.1.5.3.

The heaviest particles known to date
(except tauons), resulting from high-energy particle interactions, are hyperons. All hyperons are fermions, mostly with spin 1/2, except W- which has spin 3/2. Furthermore, all hyperons are hadrons showing a strong interaction and are highly unstable particles with a very short lifetime. We know 7 types of hyperons (+ their antiparticles), which we briefly list here :
L o is electrically uncharged, has a mass of 2183 me 1116 MeV/c2, lifetime 2.5.10-5 s. and disintegrates according to the schemes: L p + p- (66%), L n + po (34%).
S + with a positive elementary charge has a mass of 2327 me 1189 MeV and with half 0.8.10-10 s. decays per nucleon and pions: S+ p + p0 , S+ n + p+.
S - with negative elementary charge has weight 2340 me 1197 MeV and with half-life 1.65.10-10 s. decays into neutron and pion: S- n + p-.
S 0 without electric charge has a mass of 2332 me 1193 MeV and with a very short half-life close to 10-20 s it decays into a hyperon lambda and a photon gamma: So L + g.
X - with negative charge, weighs 2585 me 1321 MeV and with half-life 1.7.10-10 s decays into hyperon lambda and pion: X- L + p-.
X 0 - uncharged has weighs 2566 me 1315 MeV and half 3.10-10 s decaying into lambda hyperon and pion: X0 L + p0.
W - with negative charge has a weight of 3405 me 1675 MeV/c2 and with a half - life 1.5.10-10 s decays into hyperons and mesons: W- Xo, - + p-, o , W- L + K- .
Note: In a very small percentage of cases, other possibilities of hyperon decay were observed, eg L p + e- + n , S+ p + g , Xo p + p-, and many others.

  Hyperons show strong interactions, so they can enter the nucleus and be bound there by nuclear forces - a so-called hypernucleus or hyperfragment is created. In a typical hypernucleus, one of the neutrons is replaced by the hyperon Lo; such hypernuclei then represents NAL. E.g. in nuclear emulsions irradiated with mesons K- from the accelerator, hypernuclei 9BeL were observed. Hypernuclei are unstable formations that decay in two ways: by meson decay or by nucleon decay. In the meson method, the hyperon L inside the nucleus decays according to the scheme L p + p- , or L n + po, so for example the hypernucleus 9BeL decays into the meson p-, the proton p+ and the nucleus 8Be4 (which in this case then decays into two alpha-particles 4He2). During nucleon decay, L + p p + n, or L + n n + n reactions occur, so that, for example, the mentioned 9BeL hypernucleus would decay in the following way: 9BeL 4He + 3He + n.

Similar to nucleons, there are antinucleons, so for each of these hyperons there is a corresponding antihyperons (all these hyperons are separate, they are not antiparticles, as is the case with mesons
p- and p+ or m- and m+). According to the principle of charge symmetry, antihyperons have the same mass, spin and lifetime as hyperons, but the opposite signs of el. charge, baryon number and magnetic moment. The decay patterns of antihyperons are also charge-associated with the decay patterns of hyperons, as well as the reactions of particles in which antihyperons are formed are analogous to hyperons (there is often "associated" production of hyperons and antihyperons or mesons - see below). It should be borne in mind that antihyperons to charged hyperons have opposite signs of el. charges, eg antihyperon S'- has a positive unit charge, so we could more accurately label it as ( S'-)+.
  Hyperons formed by the interaction of protons, antiprotons,
p and K mesons with nucleons at high energies (> 5 GeV), wherein the strong interactions of the type (nucleon-nucleon) or (p + nucleon) two particles from the group of mesons and hyperons (meson + meson, hyperon + meson, hyperon +antihyperon) are formed simultaneously - there is a combined or associated production of hyperons, antihyperons and mesons, eg.:
p + p
2p + L + L' , p + p p + L + K+ ,
. ...........
- + p W- + K-+ Ko .
  Hyperon paths, resp. of their decay products are observed in Wilson nebulae chamber, nuclear photoemulsions and bubble chambers. Already in 1947 C.C.Butler and G.D.Rochester observed in the study of cosmic rays in a cloud chamber tracks of two particles rising from one point - further research showed that it was a Ko meson decaying into mesons p- and p+ and the hyperon L crumbling on proton p+ and meson p-. When accelerators with sufficiently high energy made it possible to form beams of protons and mesons p, all other hyperons and regularities of their associated production with mesons K were discovered during the study of their interaction in bubble chambers and photoemulsions.

Form during some interactions of high-energy particles (such as
p+, - + p+ p+, - + p+, or interactions of a proton with an antiproton to form several p- mesons) and immediately decay, their lifetime is about 10-23 to 10-20 seconds. They are manifested only by a significant resonant maximum in the energy dependence of the effective cross section of the given interaction, or by densities and peaks on the Dalitz diagram of energies of secondary particles, which indicate the formation of some temporarily bound state. We recognize baryon resonances and meson resonances (such as meson r or some types of mesons *K). Resonances are often not even considered special particles, they are called quasiparticles. Rather, they are only temporarily excited states created by the interaction of two or more baryons or mesons, which decay as soon as they fly beyond the region of the strong nuclear interaction in which they originated. Due to the extremely short lifespan, they probably have no significance for the structure and properties of matter. However, their study is important for better penetration into the subnuclear structure of hadrons, their quark structure and understanding the properties of strong interactions within quantum chromodynamics (QCD). Some meson and baryon resonances are marked below on the quark diagram in Fig.1.5.3.

Bosons W - , W +, Z 0
These bosons are intermediate particles mediating weak interaction (Weak int.) within the Weinberg-Salam model of unification of electromagnetic and weak interaction.
- and W+ carry a negative and a positive elementary charge of the same size as an electron, they have a mass of 82 GeV/c2, they are their antiparticles to each other. W-bosons mediate mutual b -conversion of neutrons and protons (according to the scheme in Fig.1.2.5 in 1.2 "Radioactivity", passage "Mechanism of decay b. Weak interaction."). In this radioactivity b the W-bosons causes conversion of "u" and "d" quark inside nucleons, which themselves W remain virtual - it immediately decays into the resulting quark, electron or positron and neutrino.
  The neutral Z
0 boson has a mass of 93 GeV and is its own antiparticle. Z0 is less important than W, it does not show much in Earth nature or in the present universe. However, it was apparently more significantly used in high-energy processes in the extreme conditions of the very early universe (possibly also during a supernova explosion..?...) - it can mediate mutual interactions between neutrinos (1.2, passage "Interaction of neutrinos with particles and matter").
  When W or Z is formed by the high-energy interaction of particles, they are highly unstable (with a lifetime of approx. 3
x10-25 sec.*) and then break down into leptons and neutrinos; typically: W- e- + n', W+ e+ + n, Zo m+ + m- (or e+ + e-). Or for quarks and antiquarks. At very high energies, there are many other possibilities for their interactions, including the production of heavy particles such as Higgs bosons. Feynman diagrams of some important interactions bosons W, Z0 are illustrated in Figures 1.5.1.D, F, G, H, I . Particle interactions caused by the exchange of charged intermediate bosons W are sometimes referred to as "weak charged currents", reactions caused by an uncharged Z0 boson as "weak neutral currents".
*) Particles with such a short lifetime cannot be directly detected experimentally (they disintegrate before they have time to fly out of the place of interaction, they will not reach any detector...). Only their decay products can be detected. Our detectors at accelerators are unable to detect neutrinos at all (they have no electric charge and hardly interact with anything), they can only be proven indirectly by measuring a certain value of the missing energy or momentum in the overall balance of energy and momentum.
  Intermediate bosons W
-, W+, Z0 were indirectly experimentally demonstrated in 1983 in interactions in opposite proton-antiproton beams of the 270GeV 270GeV Super Proton Synchrotron at CERN.

Hypothetical and model particles
For the sake of completeness, we will briefly mention some "exotic" particles, which should exist according to certain more or less verified theories and models, but most have not yet been directly experimentally proven - they remain hypothetical or model particles.
are model "building" particles of hadrons
(as outlined below - "Quark structure of hadrons"). Quarks are fermions with spin 1/2 and carry a one-third electric charge -(1/3) e, +(2/3) e. A total of 6 types of quarks have been introduced, each with its own antiparticle - an antiquark. The individual quarks and quark model of hadrons are briefly described below. Quarks are the primary carriers of strong interaction, mediated by gluons. At the same time, however, they may be subject to mutual internal transmutations under the influence of a weak interaction mediated by intermediate bosons W-, W+, Z0 (the main manifestation of this quark transmutation is radioactivity b , see Fig.1.2.5). Free quarks have never been observed - see the following section "Gluons" and below the section "Quark-gluon plasma".
Gluons (glue - holding quarks "glued together" in hadrons)
are particles that mediate strong interactions between quarks (and with their "residual manifestations" also nuclear interactions between nucleons). They are bosons with spin 1, have zero rest mass, have no electric charge, but carry the so-called "color charge" *), which characterizes different types of quarks. Like a photon, a gluon does not have an antiparticle (it is its own antiparticle). The gluon interaction of quarks has special properties. If the quarks have high energy and are close to each other, the gluon interaction is negligible and the quarks behave as free particles - so-called asymptotic freedom. However, when the quarks move away from each other by about 10-13 cm, the gluon interactions begin to act intensively and strongly bind the quarks to each other - the quarks are "trapped" in hadrons. Further discussion is below in the section "Quark-gluon plasma".
*) A photon that mediates an electromagnetic interaction does not itself carry the charge of that interaction (electric charge); photons do not interact with each other. However, gluons carry a "color" - the charge of a strong interaction, so they can interact with each other. They could theoretically create bound systems - so-called gluonium.
- are hypothetical sub-quark particles that could make up quarks (see the "Preon Hypothesis" passage below).

are the quantum of gravitational waves. Gravitational waves are predicted by the general theory of relativity as a physics of gravity and spacetime; they are solutions of Einstein's equations of the gravitational field, similarly to Maxwell's equations of electrodynamics implies the existence of electromagnetic waves. Gravitational waves differ from electromagnetic waves in their very slight effect on matter, and in their so-called quadrupole character. The hypothetical graviton has zero rest mass, moves at the speed of light, its spin number is 2.
  Gravitational waves have alredy been directly detected, although this is at the limits of current experimental techniques. However there is no hope for experimental demonstration of gravitons in the foreseeable future. Gravitational waves are discussed in detail in 2.7 "Gravitational waves" in the book "Gravity, black holes and space-time physics". A skeptical note on the reality of the existence of gravitons is there in the passage "Gravitons - a quantum of gravitational waves? ".
Higgs bosons
- they are quantum of the so-called Higgs-Kible *) scalar field, that in the unitary calibration field theories is introduced into the Lagrangian for purpose of so-called spontaneous disruption of symmetry of the electroweak interaction
(see, e.g. B.6 "Unification of fundamental interactions" in the book "Gravity, Black Holes and the Physics of Spacetime"). This field also leads to some intermediate bosons gaining mass (rest mass) and the corresponding interactions becoming short-range forces - they are mainly W and Z bosons of (electro)weak interactions. In this Higgs mechanism the rest mass of the particles is created by interaction with the ubiquitous Higgs field, which permeates the entire universe; the stronger the interaction of a given particle with this field, the greater its mass. Some quantum, such as photons, do not affect this field and therefore have no rest mass, other particles attract the Higgs field and add mass to them. This could explain why some intermediate bosons are so heavy, while other particles, such as electrons, are very light. Simply put, the Higgs bosons should be part of an invisible quantum field that fills a vacuum in space and causes material particles in the universe to form material structures; without them, there would be no world as we know it. If some basic building blocks did not gain mass, the universe would look completely different: Particles without a rest mass would fly freely through space at the speed of light and would never form atoms, from which stars, planets and life would then form ...
*) This hypothesis was first introduced in 1964 by the authors P.Higgs, F.Englert and R.Brout, G.Guralnik, C.Hagen and T.Kibble. The Higgs field in 1967 was used by S.Weiberg, A.Salam and S.Glasshow to build the theory of electroweak interaction with heavy intermediate bosons W
, Z.
  The Higgs boson H itself has a high rest mass, in the order of hundreds of GeV *). Higgs bosons could be formed by a strong interaction in high-energy proton collisions by the exchange interaction of energy quarks with gluons or W-bosons (so-called gluon fusion, Fig.1.5.1.I, W or Z fusion, or associated production with W or with t-t ' pair), or an electro-weak interaction at electron collisions eg by interactions e+ + e- Z* Z + H (H-emission), or again by W or Z fusions - see Fig.1.5.1.D. Higgs bosons are highly unstable particles with a lifetime of only about 10-22 seconds. Therefore, they cannot be detected directly, but only on the basis of the analysis of secondary particles formed during their decay - their decay products. If the Higgs boson is formed during a high-energy interaction of particles, it is assumed that it will decay very quickly into other energetic particles. The simplest decay H g + g per two gamma photons could occur even at lower masses around 100GeV. If the Higgs boson has a mass greater than 160 GeV, it can decay into two W-bosons: H W + W, which then decay into two leptons and two neutrinos (as mentioned above in the passage "Bosons W-, W+, Zo"). At a mass H higher than about 180 GeV, the decay can lead to two Z-bosons: H Z + Z, which decay into 4 leptons - by pairs of muons m+ + m- or electrons e+ + e-. In case the Higgs boson is heavier than about 500 GeV, other ways of its decay may occur, eg H b + b', or H t+ + t-, others may or may not go through intermediate Z-bosons; finally, they can result in the production of quarks, whose hadronization would create sprays (jets) of particles. Feynman diagrams of some possibilities of formation of Higgs bosons and their decay are given above in the section "Feynman diagrams" (in Figure 1.5.1.D, I).
*) Collision experiments (on Tevatron and LEP accelerators - see "Large accelerators" below) previously provided only the lower limit for the mass of the Higgs boson about 170 GeV/c2. After all, according to supersymmetric models, there could be several species of Higgs bosons: light scalar ho , heavy scalar Ho, positively and negatively charged H.
Discovery of the Higgs boson 
At the ICHEP2012 conference in Melbourne, Australia, on July 4, 2012, the discovery of a new boson whose properties are consistent with the Higgs boson was announced, based on data from ATLAS and CMS experiments at CERN. Careful analysis of about 60,000 cases of photon pair detection (derived from high-energy proton collisions) found a small
(but significant, about 160 photon pairs) peak on the photon number -to-energy curve, in the energy range around 126 GeV. This peak should probably come from the 2-photon decay of the Higgs bosons. The level of reliability of detecting a new particle by detecting its decay products is 5s. Further experiments are needed to make sure it is a Higgs boson and not another unknown particle. For this discovery, the Nobel Prize was awarded to P.Higgs and F.Englert in 2013.

Source: CERN-LHC
Discovery of the Higgs boson at the LHC great accelerator by detecting its decay products - here two opposite photons of gamma specific energies on the ATLAS detection system.

Higgs boson - a "divine" particle ?
In the popularization literature, it is often stated in the journalistic bonmot that the Higgs boson is a kind of "divine particle" that gives the universe mass. That's not quite true. More than 99% of the ordinary ("radiation") matter that makes up the universe, ordinary matter, and our bodies is made up of protons and neutrons. These consists of quarks whose mass, associated with the Higgs mechanism, represents only about 5% of the mass of protons and neutrons. With the Higgs field substantialy related only the mass of the W and Z bosons and the mass of leptons, but these represent only a small part of the mass of the Universe.
The importance of the Higgs boson lies in the fact, that it was the last undiscovered particle of the standard model, the discovery of which confirms the (otherwise undetectable) Higgs field, without which the standard model could not explain experimentally measured masses of leptons, quarks and intermediate bosons - force carriers. Without the Higgs mechanism, quarks would be massless and would not create protons and neutrons, atomic matter would not exist...
Supersymmetric particles  
In supersymmetric unitary theories of elementary particles, each basic particle is assigned its so-called superpartner - each boson has its fermion superpartner and fermion, on the other hand, has its boson counterpart. These "partner" particles have not yet been observed. This is explained by the fact that boson-fermion supersymmetry is disturbed; this means that the mass of the superpartners is not the same, but the supersymmetric partners to the known particles have a much higher mass, so we cannot observe them at the energies available to us. The names of these particles are formed by the suffix "ino" (for interaction bosons) or by the prefix "s-" (for fermions) to the name of the starting particle. The most frequently discussed supersymmetric particles are gravitins, photins, or neutralins :
are quantum of the calibration field in supergravity unitary field theory (graviton superpartner), they have a 3/2 or 5/2 spin.


are weakly interacting particles with spin 1/2, introduced as a supersymmetric partner of photon.
s - particles
Supersymmetric particles to other fermions are sometimes discussed:
s-leptons as superpatters to leptons, eg s-electron, s-muon, s-neutrino (also called neutralino - should have a high mass of tens or hundreds of GeV); or to the quarks - s-quarks.
Higgsino - a supersymmetric fermion to the Higgs boson.
Other hypothetical particles:
are very light
(rest mass approx. 10-5 -1 eV/c2) hypothetical particles with spin 0, which should interact with the surroundings by weak and gravitational interaction. They are considered possible particle candidates for dark matter in the universe.
Within quantum chromodynamics, disturbances of the combination of charge symmetry and parity in quark theory are introduced in solving the CP-problem. CP symmetry, which is disturbed by weak interactions, should theoretically be disturbed even by strong interaction. Since this is not observed experimentally, additional symmetry has been introduced into quantum chromodynamics (which is spontaneously disturbed), the quantum of the respective field being a new type of particles called axions (their supersymmetric partners are called axina). Relic axions could perhaps have formed in the very early universe in the lepton era. It is assumed that even in a small percentage they could be formed during the scattering of photons on electrons, so their intensive source could also be the interior of the Sun.
  Recently, some possibilities have been discussed as to how it would be possible to detect such particles. The interaction of an axion with electrons or a very strong magnetic field could lead to the production of a quantum of electromagnetic radiation - a microwave photon - which could be detected. Experiments are even being attempted with laboratory production of axions by means of interactions of intense photon beams from powerful lasers with electrons in a strong magnetic field, with subsequent detection during the reverse conversion of axions to photons, again in a strong magnetic field. All unsuccessful so far...

The above (so far hypothetical) particles - gravitin, photin, axions - are sometimes collectively referred to as "weakly interacting material particles" - the abbreviation WIMP (Weak Interacting Massive Particles). They interact weakly and gravitationally with the environment. They are predicted by the supersymmetric extension of the standard model. They could form an essential component of the so-called dark matter in space (see eg 5.6 "
The future of the universe. Time arrow. Hidden matter." in the book "Gravity, black holes, and physics of space-time"). They haven't been detected yet...
Magnetic monopoles
- a hypothetical particle dual respect to electrical charge. The magnetic monopole arises when exchanging the electric and magnetic quantities in Maxwell's equations and subsequent application of quantum field theory.
Classical electromagnetic theory does nor allow magnetic monopoles: one of Maxwell's equations div B = 0 says that the magnetic field is non-source with closed lines of force, ie magnetic monopoles do not exist (see eg 1.5 "Electromagnetic field. Maxwell's equations" in the book "Gravity, black holes and the physics of space-time"). Magnetic monopoles were introduced as an attempt (at least hypothetical) formal equalization, or establish symmetry, with electricity and magnetism. They have never been detected, they do not exist in our nature, their hypothetical presence just after the big bang was nullified by the inflationary expansion of the early universe (5.5 "Microphysics and cosmology. The inflationary universe.").
Leptoquarks X , Y
- hypothetical vector bosons X and Y (called leptoquarks, they cause transitions between quarks and leptons) introducing in the so-called grandunification GUT theories (already mentioned B.6 "Unification of fundamental inetractions" in "Gravity, black holes and spacetime physics"). They should have a very high weight on the order of mX ,Y ~ 1015 GeV/c2, so far beyond the possibilities of experimental proof in large accelerators...
are hypothetical (model) one-dimensional elementary structures of the order of 10
-33 cm (Planck's length), whose variously excited vibrational states and interconnections should be the basis of all particles and fields according to the so-called superstring theory - the basis of unitary field theory unifying all 4 interactions in nature. The strings can be open or closed. Depending on the way the strings vibrate, different weights, charges, spins, etc. are created. Such strings could then form the basic particles (fermions - quarks, electrons, ... and bosons - photons, gluons, ...) of a standard model.
  The generalizations of superstrings are the so-called
p-branes, which can have more (p) spatial dimensions and evolve in multidimensional (mostly 11-dimensional) spacetime.  The theory of superstrings is briefly discussed in the final part of B.6 "Unification of Fundamental Infections" of the book "Gravity, Black Holes and the Physics of Spacetime".
Tachyons (Greek: tachyos = fast)
are purely speculative particles that can move only at superluminal speeds and have (in connection with the known relationship of mass versus velocity m = m
o/(1-v2/c2) in a special theory relativity) imaginary mass. The motivation for the introduction of tachyons is only speculation about a kind of symmetry with respect to the speed of light, there is no physical arguments for them; rather, they would raise serious problems with the principle of causality. From the point of view of the theory of relativity, tachyons are briefly discussed in the passage "Tachyons" 1.6 "Four- dimensional space-time and special theory of relativity" of the mentioned book "Gravity, black holes and space-time physics".
"Shadow" or mirror matter - Catoptrons ?
At the end of our brief overview of the "zoology" of hypothetical particles, we mention a somewhat vague idea of the so-called mirror matter, which could perhaps hiden coexisting with "our ordinary" matter. The hypothesis is based on experimentaly measured non-preservation of parity in weak particle interactions (discussed below - "
CPT symmetry of interactions"). The idea arose that mirror symmetry could be restored if for every "our" observed fundamental particle there was a hidden, "shadow" partner ("twin") - a mirror particle whose interaction involves the opposite violation of parity. Our common particles are "counterclockwise", mirror particles are "clockwise", overall parity symmetry is maintained. Parity can then be spontaneously disrupted by the Higs mechanism; in the case of undisturbed parity symmetry, the masses of the particles and their mirror partners are the same; in the case of parity disturbance, the masses of the mirror partners are different. Miror particles are somentimes collectivery refered to as catoprons (Greek katoptro = mirror ).
  Mirror matter, if it exists, interacts only very weakly with ordinary matter. This is because the forces between the mirror particles are mediated by mirror bosons, which are generally different from the intermediate bosons of "our" matter. The mirror mass is therefore practically unobservable *), at least not by direct methods, optically. The exception is gravitation, so mirror matter should have gravitational effects - it could therefore be a candidate for the still mysterious dark matter in the Universe (discussed in more detail in 5.6 "
The Future of the Universe. Arrow of Time. Hidden Matter.)" monograph "Gravity, black holes and space - time physics").
*) In superstring theories, mirror particles are sometimes even placed not in "our" 3- dimensional space, but in three other "extradimensions".

Unitary symmetries and multiplets of particles
The large number of elementary particles discovered in high-energy interactions naturally led nuclear physicists to try to systematize them and introduce unitarization schemes - to create a kind of periodic table of particles, analogous to Mendeleev's periodic table of elements
(1.1, part "Bohr's model of the atom" and "Interaction of atoms", passage "Periodic chemical properties of atoms"). In particular, each baryon and lepton is assigned a baryon number B and a lepton number L (particle +1, antiparticle -1), which are preserved in all interactions. Significant similarities and symmetries between some elementary particles, especially hadrons, were found.
  If we look away from the electric charge, protons and neutrons, for example, can be considered as two states (doublets) of one particle - a nucleon. Similarly, the pions p+, po, p- form a triplet of similar particles. When studying the strong interactions themselves, which are charge-independent, we can disregard the charge. To describe these similarities and symmetries, a new quantity isotopic spin or isospin T was introduced *). Nucleons have an isospin T = 1/2, with the projection of the isospin T = +1/2 corresponding to a proton and a T = -1/2 neutron. The pions were assigned isospin T = 1, with projections -1, 0, +1 for p-, po, p+. In the system of interacting nucleons and pions, the law of conservation of isospin applies.
*) It was based on a formal analogy with ordinary spin, where a particle with spin 1/2 occurs in two states with spin projection -1/2, +1/2 and a particle with spin 1 in three states with spin projections -1, 0 , +1. Isospin T is a vector in the imaginary (auxiliary) "isotopic space". In general, a particle with isospin T can occur in (2.T + 1) states with isospin projections on the reference axis: -T, (-T + 1), (-T + 2), ..., -1, 0, 1, ..., (T-2), (T-1), T.
  Another important step was the discovery of some "strange" (unexpected) properties of the interactions of mesons K and hyperons in their combined pair production, which led to the introduction of the concept of strangeness described by the quantum number S ("Strange"). Later we were introduced general quantum number called hypercharge Y = B + S, the sum of baryon number B and strangeness S. It turned out that both isospin T and hypercharging Y are preserved during strong interactions. This extended symmetry led to the construction of a baryon-decuplet multiplet (3/2
+), which, however, lacked one place at the time; was thus the prediction of the hyperon W, which was soon actually discovered.
  The individual hadrons were drawn in special diagrams, where the horizontal axis showed the projection of isospin T
z , the vertical axis the hypercharge Y and the oblique axis the electric charge Q. The connectors of the thus marked multiplets of particles formed regular geometric shapes - triangles, hexagons and their combinations, see below Fig.1.5.3. Such an analysis of unitary symmetry (found in 1964 by M.Gell-Mann and Y.Ne'eman) showed that the system of hadrons can be very well explained by the hypothesis that hadrons are composed of subparticles called quarks - baryons from a triplet of quarks, mesons from a pair of quarks, as will be outlined in the following passage.

Are elementary particles really elementary ?
Let us now try to look at the "elementality" and the internal structure of the basic building blocks of matter. An important guide for assessing the "elementality" ("fundamentality") of particles can be whether the particle spontaneously disintegrates (transforms) or does not disintegrate into other types of particles. According to current knowledge, a photon and an electron can be considered as truly internally "uniform", compact elementary particles without an internal structure, which always arise or disappear as a whole and are not transformed into other types of particles. The neutron and proton can transform with each other with the participation of electrons, positrons and neutrinos; they cannot, therefore, be "elementary" in the true sense of the word. The same applies to
p- mesons and hyperons. So generally hadrons ...
Note: Since many particles are compound, the designation "elementary" is misleading here. However, it is a common name, similar to the name "atom", which no longer means "indivisible". In recent years, however, the word "elementary" has often been omits and speaks only of "particles".
Bootstrap model of hadron interactions

The "predecessor" of the quark model was the so-called bootstrap hypothesis of hadron interactions developed by G.F.Chew in the 1960s. No more fundamental particles were found to be behind the properties of the interactions, but it was assumed that they were essentially the "same" hadrons (including hadron resonances) acting in a kind of feedback (bootstrap, self-booting). In particle physics, this concept is now only marginal and is not generally accepted ...
Quark structure of hadrons
The above described systematics of hadrons shows that significant so-called unitary symmetries can be found in their properties. Based on these symmetries, the so-called quark model of hadrons was compiled in 1964
(authors M.Gell-Mann and Y.Ne'eman), according to which all hadrons are composed of even more "elementary particles" - quarks.
  The word "quark", which has no linguistic meaning, was taken over by the authors of the quark model with a significant dose of recession from the play by the writer James Joyse.
  Quarks are fermions with spin 1/2 and with a third electric charge: -(1/3) e, +(2/3) e, each quark has its antiparticle - antiquark. To explain the system of hadrons using an additive quark model, a total of 6 types of quarks were gradually introduced, the most important of which are two: "u" (up), "d" (down) - nucleons are composed of them. The third quark "s" (strange) is the bearer of "strangeness". The quark "b" (bottom) participates in the violation of the CP symmetry. The characteristics of all quarks are given below in a clear table in the section "
Standard model - unified understanding of elementary particles".
  Mesons are composed of two quarks - a quark-antiquark combination (q q). In the case of opposite orientation of the spins of both quarks, we get the so-called scalar mesons with spin s = 0, eg
p+ = (u d), p- = (d u), po = (u u) + (d d). If one of the quarks is "s", these are strange mesons K+, -, 0.... In the parallel orientation of the spins in the quark-antiquark pair, so-called vector mesons with spin s = 1 creates, which we observe only as meson resonances with a very short lifetime (approx. 10-23 s) - meson r+, - , 0 or *K+, - , 0.
  Baryons are composed of three quarks, wherein the spins of these quarks can be oriented so that the resulting spin baryon is s = 1/2, or s = 3/2. E.g. proton p = (u u d) and neutron n = (d d u) with spin 1/2, or hyperon
L0 with spin 3/2.
  Baryons containing the "s" quark are called hyperons (the properties of hyperons have been described above).
  The system of mesons and baryons in terms of quark structure is schematically grawn by the diagrams in the following Fig.1.5.3

Fig.1.5.3. Schematic representation of unitary symmetry and quark structure of hadrons.
Note 1: For consistency with text where wavy fonts are not available, antiparticles are marked with dashed lines (').
Note 2:
The same quark combinations differing in higher spin correspond either to a single particle (eg
r, D), or are denoted by the same symbol as a known particle with antiparallel spins of the same quarks and the index "*" (eg *K, *S).

In addition to these basic multiplets, a number of other combinations can be created from "exotic" quarks c, b, t *), whether (pseudo) scalar or vector; some of them have already been experimentally proven. Eg :
D-mesons - contain c-quarks: D
+ (c, d '), Do (c, u'), strange Ds (c, s'), charmonium (c, c') ,
B- mesons - contain b-quarks: B
+ (u, b'), Bo (d, b'), strange Bs (s, b'), Bc (c, b'), ypsilonium (b, b') .
B-mesons (especially neutral B
o) are produced in particle-antiparticle pairs at the LHC (LHCb experiment mentioned below) to investigate their asymmetric production and decay with CP symmetry breaking.
  All these combinations behave only as resonant states with a very short lifetime (shorter than about 10
-13 sec). They are formed for a short time during high-energy interactions of electrons, protons and other particles. They decay in a number of different ways (lepton and hadron) into electrons e , photons g, muons m , neutrinos ne, m, t , kaons K,0, partly also pions p 0.
*) The top quark t, which is the heaviest (approx. 170 MeV/c2), decays so quickly after its formation (typically into a b-quark and W-boson) that it is not enough to form hadron bound states, at him does not occur hadronization and formation of jets .
Origin of the mass of hadrons
Hadrons are much heavier than the sum of the masses of their quarks. E.g. the proton has a mass of 938 MeV, while the mass of the "u" quark is 2 MeV and the "d" quark is 5 MeV. Therefore, most of the mass of a proton comes from the kinetic energy of the internal motion of its quark components. This is explained on the basis of quantum uncertainty relations, according to which the product of uncertainty in the position and momentum of a particle is greater than the Planck constant. Quarks are enclosed in a proton or neutron ("trapped") in area 10
-13 cm; this forced very small uncertainty in position quantum implies considerable momentum and thus the kinetic energy of each of the quarks, at least about 200 MeV. The kinetic energy balance of such three intensely oscillating quarks is approximately equivalent to the mass of the proton.
  The difference in the mass of quarks "u", "d", "s"
(which is explained in unitary field and particle theories by interaction with the Higgs field) then causes differences in the masses of mesons p and K, as well as baryons - protons, neutrons and different species of hyperons.
 A virtual "sea of quarks" ?
The basic idea explains hadrons as composed of two or three "valence" quarks, bound together by the strong interaction of the gluon field. However, according to the concept of quantum field theory, it is expected that in addition to "real, valence" quarks, virtual quark-antiquark pairs should also be present in hadrons, spontaneously arising and then annihilating. They could form a kind of virtual "sea of quarks" inside hadrons, which could "materialize" during high-energy interactions and participate in the mechanisms of the formation of emitted particles, quark-gluon plasma and its hadronization ..?..

Imprisoned quarks. Jets. Hadronization of quarks.
The success of the quark model naturally led to intensive efforts to find individual quarks experimentally. However, no particles with a third electric charge could be found in either the high-energy laboratories on the accelerators or in the cosmic rays. If quarks exist at all, they must be very strongly bound in the nucleons *), they cannot be released. Quarks therefore remain hypothetical particles, resp. model, which very elegantly explain the properties of hadrons, but whose existence has not been directly proven.
*) Impossibility to obtain free quarks
Very strong bond makes it impossible to obtain free quarks for the following reason: In an attempt to tear the quarks apart in a hadron by supplying more and more energy (such as by inelastic interactions of firing particles, Fig.1.5.4), this energy will eventually be so high that it exceeds the threshold energy for the formation of a new quark-antiquark pair. These newly formed quarks then immediately combine in pairs or triplets with the original quarks in the gluon field. Although we "broke" the original hadron, we do not get free quarks, but again only bound systems of two or three quarks, ie hadrons.
  An analogous situation is known from classical magnetism when dividing a permanent bar magnet having a north and a south magnetic pole. If we break the magnet into two parts, in an effort to separate the south and north poles, the magnetic domains will be reconfigured to form two magnets, each with a north and south pole again. It is therefore not possible to separate and produce a magnetic "monopole" south or north, analogous to how it is not possible to separate and release individual quarks from the hadron ...
  The asymptotic freedom of quarks and their hadronization is mentioned even below.

  Indirectly, however, the quark model was supported by the results of experiments with electron scattering on protons, in which the angles and energies of scattered electrons and protons were measured. At lower energies (up to about 1GeV) the proton behaves like a compact "ball" with a radius of
1 fm (= 10-15 m). However, at high energies, the behavior of protons is completely different; for the first time, such an experiment with scattering of high-energy electrons (with energies higher than 1010 eV) on nucleons was performed on the SLAC accelerator in Stanford (1960-70 - J.I.Friedman, R.E.Taylor, H.W.Kendall et al.). In such a "hard bombardment", the nucleon did not behave as a compact particle with a uniform charge distribution, but as a system of three very small scattering centers (about 10-16 cm) in which the electric charge is concentrated. R.Feynman called these particles inside the protons partons. However, the direct identification of quarks and partons was hindered by a contradiction - on the one hand, partons in nucleons behaved as free in experiments, on the other hand, quarks are so strongly bound that they cannot be released from nucleons.
  To understand the specific properties of the quark structure of hadrons, the so-called quantum chromodynamics (QCD,
Greek chromos = color) was created in the 1970s, which is a field theory of strong interaction. Within the QCD, the concept of the so-called asymptotic freedom of quarks was outlined (the binding potential of quarks is close to zero at very small distances 1 fm) and the hypothesis of a perfect trapped quarks in hadrons whereby quark can not exist as free particles, but only bonded hadrons - binding potential is growing rapidly with the distance, to completely release quark would be required infinitely large energy (compelling reason discussed above in footnote "Inability to obtain free quarks"). The strong interaction between quarks in QCD is mediated by a vector calibration field, whose zero rest mass quantum, called gluons, play a similar role here as photons in quantum electrodynamics, where they mediate electromagnetic action between charged particles.
  According to some hypotheses, quarks could be composed of even "smaller" particles, called preons- see below the section "Standard model - uniform understanding of elementary particles", passage "Preon hypothesis".

Fig.1.5.4. Schematic representation of the mechanism of interaction of a high-energy electron with a proton.

At very high energies, during hard and deeply inelastic collisions of electrons with protons, a number of secondary particles are formed, which fly out unisotropically in some kind of directed "jets". A detailed analysis of the angular distribution and energy of particles in jets showed the following mechanism of interaction, which can be divided into two stages (Fig.1.5.4): During the 1st stage, a high-energy electron, in interaction with the proton, transfers part of its kinetic energy to one of the quarks, which after this scattering moves for a short time practically freely (asymptotic freedom) inside the proton; similarly, the remainder of the proton formed by the two remaining quarks. However, the quarks will not be released from the proton. Once the distance between the accelerated quark and the rest of the proton exceeds about 1 fm (10-15 m), the 2nd stage occurs: the forces between them begin to increase sharply and in the quark-gluon field the quarks and antiquarks are produced, which are formed into mesons and baryons - the so-called "hadronization" of the quark-gluon plasma *). The result is the emission of two angularly collimated sprays of particles - jets, which fly out approximately in the directions of flight of the incident quark and the rest of the proton in the first stage. These jets are actually traces of quarks. The quark structure of hadrons manifests itself in a number of high-energy interactions.
*) We can simply imagine that the quarks in hadrons are connected by a kind of "strings" (gluon tubes) that hold them together as "rubber fibers". When "trying to escape" quarks, ie when the distance between quarks increases, this string "tears" into shorter strings of about 1 fm in length, corresponding to mesons and baryons (the free ends of the string lead to the formation of a new pair of quark and antiquark). This older idea was often used in the early 1970s. A more convincing reason was discussed above in the note "Impossibility to obtain free quarks".
Quark-gluon plasma - "5th state of matter"
Under normal circumstances, quarks cannot be free, they are always bound by a strong interaction into hadrons. When the hadron mass is heated to an extremely high temperature higher than 1012 K, then the kinetic energy density is many times higher than the energy density in the nucleus, the mean free path of the quarks is smaller than the radius of the nucleus. At these very high temperatures and densities, the hadrons are pressed so close together that they "intertwine" with each other's quark structure and lose their "identity". There is such an amount of gluons in the space between the quarks, that their force interaction "shields" the attraction between the quarks. Mater in this state is for a short time formed by an equilibrium mixture of (asymptotically) free quarks and gluons. This highly "exotic" state of matter is called quark-gluon plasma.
  Quark-gluon plasma is sometimes considered to be a kind of "fifth state" of matter: the three commonly known states are solid, liquid, and gaseous; at high temperatures, or by the action of strong electric fields, discharges or radiation, an ionized gas is formed - a plasma consisting of free electrons and positive ions or atomic nuclei - referred to as the 4th group; and nuclear quark-gluon plasma is Group 5. In connection with this analogy and with the idea of the asymptotic freedom of quarks in the gluon field, it could be expected that the quark-gluon plasma will have the character of an ideal gas of only weakly interacting quarks. However, complex experiments on accelerators, combined with a thorough analysis of the data from the particle detectors, have shown that it behaves rather like a strongly interacting almost ideal quark-gluon liquid, showing superfluidity properties. Residual interactions , the relative strength of which is comparable to the van der Waals forces observed in classical fluids , appear to occur in this plasma .
  Quark-gluon plasma is formed only for a small moment during collisions of high-energy particles - hadrons and especially heavier atomic nuclei - on accelerators
(where complex sprays of secondary particles - baryons, pions, kaons, are monitored using complex detector systems, see "Large Accelerators" below) , or in cosmic rays. In the context of nuclear reactions, the quark-gluon plasma is discussed in 1.3, passage "High-energy collisions of heavier atomic nuclei".
  If no other forces act, in a short moment approx. 10
-22 sec. quarks and gluons are re-trapped from the quark-gluon plasma into hadrons - the quarks begin to hadronize in pairs (p and K mesons are formed) and triplets (baryons are formed - mostly protons and neutrons, in smaller amounts hyperons can also be formed, see below a small passage "Strange quark matter?"). The quark-gluon plasma disappears, a number of particles fly out of the place of extinction...
  It is assumed that just such a quark-gluon plasma formed the mass of the universe in its initial stages - the so-called hadron era - a few microseconds after the Big Bang
(discussed in more detail in 5.4 "Standard cosmological model. The Big Bang. Shaping the structure of the universe." monograph "Gravity, black holes and the physics of spacetime"). Formation quark-gluon plasma at high energy collisions in accelerators are therefore sometimes referred to as a kind of laboratory "small bang" or "Little Big Bang". The only place in the universe where a stabilized quark-gluon plasma in large numbers could perhaps occur are the central regions of neutron stars (4.2, passage "Internal structure of neutron stars" of the same book); however, we cannot look at it there - we will be permanently dependent on the study of its highly unstable state during collisions in accelerators..!..
Strange quark matter ?

However, it has been hypothesized (E.Witten, 1984) that if a quark-gluon plasma contained a sufficient number of "strange" s -quarks (in addition to the usual quarks u and d forming nucleons), it could prevent hadronization and such "strange quark mass"can be stable. In situation, when the quarks are very "pushed" close to each other and all lower fermion states are occupied, the quarks s practically cannot be transformed into u quarks , because there is no longer a free quantum space for such newly formed quarks. Opposite transformations can occur, so that an equilibrium configuration of quarks u, d, s is established in fermion gas, which is more energy advantageous than hadronization. The resulting formation could then be stable, held together by a strong interaction. The strange quark mass is able to absorb neutrons, decompose them into quarks and form another strange quark mass. It is thought that smaller fragments of strange quark matter could survive from the hadron era at the beginning of the evolution of the universe, or could form during a supernova explosion. There is no experimental evidence for such an exotic state of matter yet. Some astrophysical aspects are mentioned in 4.2 "Final stages of stellar evolution. Gravitational collapse" of the already mentioned book "Gravity, black holes and space-time physics").

Stability and instability of quarks, hadrons, nucleons
The temporal stability or instability of particles is generally due to the complex interplay of strong, electromagnetic and weak interactions, determining the quantum processes of transformation mechanisms and the energy ratios between particles that are "at play". In hadrons, these basic particles are quarks. In the nucleons that make up atomic nuclei in our nature, they are the "u" and "d" quarks. Their stability, or mutual transformations, implies the stability or instability of protons, neutrons and other hadrons. In neutrons and protons, these transformations are caused weak interaction :

Schematic representation of the mechanism of b- neutron decay (top) and b+ -proton transformation (bottom) by quark transmutation within the standard model of elementary particles.

From an energetic point of view, the differences in the mass of the quark "u" and "d" determine the possibilities of these transformations. If the mass differences between the "u" and "d" quarks are too large, the spontaneous transformation of protons or neutrons inside the nuclei can occur.
  But the decay of neutrons in the nucleus A, leading to the radioactivity beta
-, NAZ --> NBZ+1 + p + e- + n, cannot occur when the mass-energy inequality
                md <  mu + me + E
Dem + EB   ,
where m
d and mu are the masses of the quarks "u" and "d", EDem = 1.7 MeV is the electromagnetic contribution to the mass difference between the proton and the neutron and E B is the binding energy of the neutron inside the nucleus. Similarly, beta+ transformations of protons, NAZ --> NBZ-1 + n + e+ + n, cannot occur in nuclei when the mass-energy inequality
                mu <  md + me
- EDem + EB    .
At a given mass of m
d and mu quarks and protons and neutrons with beta- or beta+ radioactivity, the binding energy EB of a neutron or proton in the nucleus according to the shell model is basically decisive. The binding energy of protons and neutrons in nuclei differs in detail for different nuclei, for medium and heavy nuclei the average is EB = 8 MeV - see the graph in Fig.1.3.3 in 1.3., section "Fission and fusion of atomic nuclei. Nuclear energy". The properties of beta radioactive transformations are analyzed in more detail in 1.2, section "Beta radioactivity".
  So that there could be a free separate stable proton - the nucleus of hydrogen, to prevent its spontaneous conversion p --> n + e+ +
n to neutron and positron, the inequality
                md >  mu
- me + EDem  must be met .
And in order for there to be a stable hydrogen atom that could not spontaneously convert to a neutron by the electron capture reaction p + e
- --> n + n, the condition
                md >  mu + me + E
Dem  must be met .

What keeps the world together? - and/or: 4 types of interactions in nature
All the results of previous physical and scientific research show that all structures and phenomena in nature are conditioned by the action of only four basic types of interactions :

An interesting rule of the hierarchy of interactions turns out : a particle that is subject to some of the 4 basic interactions is automatically subject also to all weaker interactions.

Symmetry of interactions ( C P T )
An important role in understanding the interaction of particles is played by the properties of symmetry - whether and how the behavior of the physical system changes during a certain (imaginary or actual) transformation of coordinates or other parameters of particles. By symmetry we mean such transformations of quantities describing a given physical system that leave the form of the laws of motion of this system unchanged (for a general physical-mathematical analysis of symmetries and conservation laws in field theory, see B.6 "
Unification of fundamental interactions. Supergravity. Superstrings.", passage "Symmetry in physics" book "The gravity, black holes and the physics of space-time"). Here we briefly mention three basic types of symmetry in the interactions of particles, their combinations and their disruption :
C-symmetry , charge association ( Charge)
- is in the replacing all particles in the system with their antiparticle with opposite charge. If such a system will behave as the original particles, mark it as a C-invariant. The basic laws of the world and antiword are actually the same. The existence of only left-handed neutrinos and dextrotatory antineutrinos, however suggests, that C-symmetry may be violated in weak interactions.

P-symmetry , mirror inversion - parity symmetry
- consists in the mirror inversion of all positions and orientations of particles in the system, including the exchange of left - handed and right - handed angular momentum. In the macroworld and for most processes in the microworld (strong and electromagnetic interactions), P-symmetry is preserved. However, in the decay of K-mesons due to weak interaction, as well as in the
b- decay of nuclei (eg 60Co), certain asymmetries were observed, disrupting right-left symmetry - violation of the law of conservation of parity *).
*) Until the mid-1950s, it was assumed that parity was maintained in all particle interactions (similar to the macro world) - that the law of conservation of parity applied. In 1956, T.D.Lee and Ch.N.Yang began to investigate the validity of parity conservation in weak interactions, admitting its disruption, and designing appropriate experiments. The decisive experiment was carried out in 1957 by the Chinese-American physicist Ch.-S.Wu (with a team of collaborators - E.Ambler, R.W.Hayward, D.D.Hoppes, R.P.Hudson) on the b- decay of cobalt cores 60Co. Sample 60Co, cooled to a very low temperature (0.01 K by adiabatic demagnetization - so that thermal movements do not disturb the orientation of the nuclei) was placed in a strong magnetic field that oriented the magnetic moments and spins of the nuclei in a precisely defined direction. Using scintillation detectors, the angular distribution of the flying beta electrons with respect to the direction of orientation of the momentum (spin) of the nucleus was measured. An anthracene scintillator was used for the actual measurement of electrons b , the other two scintillation detectors NaI (T1), placed perpendicular to each other, registered the anisotropy of the accompanying radiation g to monitor the achieved degree of orientation of the cobalt nuclei. Two series of measurements were performed for two opposite directions of the magnetic field vector B depending on the temperature. Asymmetry in the angular distribution of radiation b was monitored by the relative number of pulses in the anthracene scintillator as a function of temperature: for low temperatures (high core orientation) about 20% asymmetry was observed, at higher temperatures (with decreasing degree of cobalt core orientation) the degree of angular asymmetry in electron emission decreased; with the disappearance of the nucleus orientation, the asymmetry in the angular distribution of the emitted electrons also disappeared. If P-symmetry is valid, the number of electrons flying at a certain angle f should be the same as the number of electrons flying in the opposite direction 180 - f . However, asymmetry in the angular distribution of electrons b was reliably determined, indicating violation of P-symmetry - failure to maintain parity .
  In addition to radioactivity
b , non-preservation of parity in weak interactions is also reflected in the decays of mesons K (kaons) into mesons p (pions), which were described above in the section "Properties and interactions of the most important particles", passage "Mesons p and K". Mesons K and p have negative parity. When a charged K decays into three charged pions (eg K+ p+ + p+ + p-), the parity before and after decay is negative. However, there is also a decay of a charged K (with negative parity) into one charged and one neutral meson p , eg K+ p+ + po; this resulting system of two mesons p has a positive positive parity - the parity is not maintained. When these two possibilities of 2- and 3-pion decays of a newly discovered meson into states with different parities were discovered in 1953, it was considered to be decays of two different particles, referred to as J and t particles. However, further measurements have shown that these putative two particles have the same mass, charge and lifetime - that particles J and t are the only particle that have been named K and that can decay in two (or several) ways, some of which do not retain parity.
T-symmetry - inversion of time
- consists in reversing the direction of time flow, in examining whether all processes in the system can take place in the reverse order. From a mechanical point of view, we swap the initial and final states of the particles and reverse the vectors of their motion velocities. The basic laws of electrodynamics and gravity do not change when the direction of time is reversed. For large statistical sets of particles, time-reversed processes at the microscopic level are possible in principle, but their probability is very small - in accordance with the 2nd Act of Thermodynamics, the resulting macroscopic processes are virtually irreversible (see for example "
Determinism - chance - chaos?" 3.3 in the book "Gravity, black holes and spacetime physics"). It turned out, moreover, that the T-even symmetry entirely true on the level of colision of two particles, is disturbed by the action of weak interactions.
Combined symmetry
Therefore, since the actual C, P and T symmetry may be impaired, at least in processes involving weak interactions, it was examined whether the symmetry not restored when combination of respective transformations :

CP - symmetry
is created by replacing the left and right simultaneously exchange particle antiparticle. Even here it is shown that some decay of K
0- mesons to pions *) in about 0.2% of cases they disrupt CP-symmetry.
*) This is a quantum mixed state of meson K
0 and anti-K0, in which two different states called KL (with a longer lifetime of approx. 10-8 s) occur with a negative value of combined CP and KS (with a shorter lifetime of approx. 5.10-10 s) with a positive value of CP. Both of these states break down by weak interaction in two different ways. The short-lived meson KS decays in two particles into two p- mesons, the longer-lived KL then usually into three pions, or a pion and a muon or an electron and a neutrino. In experiments at the accelerator Brookhaven in 1964, however, it was the KL observed insensitive "dopant" disintegration into two mesons p, representing a state with a positive CP value. The value of CP thus changed from negative to positive - a violation of CP symmetry was proved. Violation of CP symmetry also occurs during decays of K0 into pions and leptons: KL p+ + e- + n ', KL p- + e+ + n , in which the decay to form positrons is about 0.2% more common than electrons.
CPT - symmetry
is created by: replacing particles with antiparticles + replacing left with right + reversing the passage of time. Within the relativistic quantum field theory in 1957, W.Pauli formulated the CPT-theorem on maintaining combined CPT symmetry. Here it is shown that no experiment yet contradicts this symmetry - the validity of CPT-symmetry is assumed .
Disruption of symmetry
If there were always and everywhere absolute and perfect symmetry, the world would be very dull and would not be characterized by the observed diversity; there would not even be matter in the usual sense, there would be no atoms, the universe would consist of scattered particles and radiation. The disruption of C or CP symmetry in the microworld probably had very important consequences in the earliest stages after the creation of the universe: it led to a slight predominance of matter over antimatter - to the baryon asymmetry of the universe. In the period before the great unification of interactions, X and Y particles, so-called leptoquarks, caused  transitions between quarks and leptons. Due to the violation of CP symmetry, these processes took place slightly asymmetrically - for about 108 mutual transformations, one transformation took place more towards matter than towards antimatter. The subsequent annihilation of matter and antimatter at the end of the hadron era thus left a certain small predominance of the particles forming the matter, of which the universe now consists. For more details see 5.4 "Standard cosmological model. Big Bang. Formation of the structure of the universe." and B.6 "Unification of fundamental interactions. Supergravity. Superstrings." in book "Gravity, black holes and spacetime physics".

The role of interactions in the functioning of the world
The meaning and role of individual types of interactions in nature can be illustrated
(although perhaps too popular and simplified, for which I apologize to colleagues...) in the following thought experiment. Imagine that there is a God who is absolutely omnipotent and who decides to practically "test" the importance of individual interactions for the construction and functioning of the universe ("isn't some of them useless?"). To this purpose, he will experimentall "switch off" or "cancel" individual types of interactions and observe what he will "do with the world?" :
God will say : "Well, from now on I am canceling gravity !".
What would happen? There will be a weightless state immediately, we will float, which we might like for a while. Apart from the catastrophic events here on Earth (drop of atmospheric pressure to zero, spillage of water from the oceans, escape of the atmosphere into space, rupture of the earth's crust and volcanic catastrophe), it immediately occurs to us that the Earth will leave its orbit and fly away from the Sun into space. In reality, however, he will not make it! In the meantime, the Sun would explode like a gigantic thermonuclear bomb, and in about 20 minutes a huge wave of hot plasma would reach the Earth, in which the whole Earth would evaporate. In this way, they would end all stars, so that the universe would be filled with hot plasma and then cooling gas, all structures would dissolve and eventually disappear in the "thermal death" of the universe. So not exactly a happy ending...
If God said, "I cancel the electromagnetic interaction ! ",
all atoms would immediately decay into nuclei and separate electrons - all structures would disappear again and turn into plasma.
If God canceled the strong interaction ,
all atomic nuclei would immediately decay (electrically explode) and thus all complex atoms; there would remain only hydrogen
1H1 .
Cancellation weak interaction
should be somewhat more complicated and less straightforward consequences, because the weak interaction produces no bound system (type of atoms and their nuclei). In addition to stopping
b-decayment would probably be extinguished by thermonuclear reactions inside the Sun *). Without a weak interaction, massive stars would not collapse into a neutron star, but the star would probably remain in the degenerate electron gas stage. However, if the abolition of the weak interaction occurred already in the early stages of the evolution of the universe, baryon asymmetry and the predominance of matter over antimatter would not arise. There would be no cosmic nucleosynthesis (neither primordial nor stellar) and the whole universe would consist only of particles and radiation. If the hypothetical abolition of the weak interaction occurred in the Lepton era, the number of protons and stable neutrons would be the same; in primordial and stellar nucleosynthesis, not only would stable nuclei known today be formed, but all isotopes would be stable - nuclear "monsters" with a large number of neutrons or composed only of neutrons would also be formed, light nuclei composed only of protons and the like. The chemical composition of the universe would be completely different from what we observe (and in any case unsuitable for the origin of life).
*) Thermonuclear synthesis in stars begins with the fusion of two p+ protons, which produces the 2H deuteron and emits a positron and a neutrino: p+ + p+ 2H1 + e+ + ne . The actual bonding of a proton and a neutron in a deuteron is the result of a strong interaction, but the necessary conversion of one of the protons to a neutron (the bound state of two protons does not exist) in the process p+ no + e+ + ne is the result of a weak interaction. Without weak interactions, the fusion would not take place, the Sun and the stars would not shine !
  So we see that none of the fundamental interactions are useless, they are all "vitally important"! In order for the world to look and function in its current way, it is even necessary that the force ratios of individual interactions (coupling constants) have exactly the values we observe - for a more detailed discussion see 5.7 "Anthropic Principle and Existence of Multiple Universes" of the book "Gravity, Black Holes and the physics of spacetime", or the work "Anthropic Principle or Cosmic God".

Standard model - unified understanding of elementary particles
A huge amount of experimental knowledge about the properties and interactions of elementary particles, obtained in the 50s-80s, processed and unified in the spirit of a number of quantum-theoretical concepts, resulted in the so-called standard model of elementary particles and their interactions, which here can be briefly and simply summarized as follows :
  The basic "building blocks" of matter are fundamental fermions - quarks and leptons :

Quarks : u , d , c , s , t , b .
Leptons : electron e, mion m, tauon t; neutrinos - electron n e , the muon n m , tauon n t .
  These fundamental leptons and quarks are divided into three generations (see 3 columns in the table). Each generation is composed of two leptons and two quarks, with the corresponding particles of different generations differing significantly only in their masses; other characteristics are the same.

The reason why such a repetition of structures occurs particles in large mass scales, we do not know yet - this is one of the important questions of contemporary particle physics and probably also unitary field theory. A more detailed discussion is provided below in the section "
Preon Hypothesis".

A system of fundamental particles of matter and quantum fields, forming the basis of the current standard model of particles.
The magnitude of the charge q is given in multiples of the charge of the electron (e), the rest mass m of the particles in MeV, unless otherwise stated.

Between these basics quarks and leptons acts fundamental interactions - gravitational, electromagnetic, strong and weak forces. Within the quantum field theory, these forces can be described by the exchange of intermediate particles - intermediate bosons. Leaving aside gravity, which plays virtually no role in the microworld *), these intermediate bosons have spin 1 (referred to as vectors, in connection with the mathematical formalism of their theoretical description) :
Photon - a quantum of electromagnetic field, mediates electromagnetic interaction (usually mark it g).
W+ , W- , Z - heavy bosons mediating weak interaction, eg quark transformations inside hadrons (Fig.1.2.5).
Gluons g - carriers of strong interaction between quarks.
*) The role of gravity in the microworld is a permanent topic of discussion for physicists, especially in connection with the unitary field theory, see B.6 "Unification of fundamental interactions" of the book "Gravity, Black Holes ...". Gravitons have spin 2.
  Due to the electromagnetic interaction, during the collisions of charged particles in a variable electromagnetic field, photons of radiation
g are generated, electrons and positrons are born and annihilated.
  Due to weak interaction there is also the formation of electrons and positrons together with neutrinos
(from intermediate bosons W), the mutual transformation of individual types of quarks inside hadrons - and thus the transformation of neutrons and protons (radioactivity b), mesons and hyperons. The weak interaction, due to its property of violating the invariance to the combined spatial and charge inversion of CP, probably also caused the baryon asymmetry of the universe - the predominance of matter over antimatter.
  The strong interaction that perfectly binds the quarks inside the hadrons, binds the nucleons in the atomic nuclei by its "residual manifestation"; in addition, it causes a number of interactions between elementary particles, in which new mesons and baryons are formed in the quark-gluon field during the "hadronization" process.
  All these processes among the few species of leptons and quarks cause all the variety and diversity of our world. The standard model, which summarizes practically all our knowledge about elementary particles, is on the one hand a great triumph of the physics of the microworld, because it explains with great accuracy the behavior of various phenomena between particles. On the other hand, it is clear that the standard model cannot be a complete and definitive theory of the microworld, because it is incomplete. First, it does not include gravitational action and the unification of gravity (general theory of relativity) with quantum theory. Furthermore, in some aspects it is too phenomenological in nature - it contains many free parameters such as some particle masses and binding constants of interactions that the standard model cannot predict and must be determined experimentally. A really complete theory should be able to determine these parameters numerically - for example, what should be the value of electric charge of an electron and its mass, similarly proton and other particles, what is the force (or ratios of forces - binding constant) of individual interactions, etc.
Preon hypothesis
According to the standard model of elementary particles, the basic "building blocks" of matter are fundamental fermions - quarks and leptons. The question arises as to whether the hierarchy of the structure of matter is thus finite? Or is each "elementary" particle made up of other, even more "elementary" particles? The above table of the division of quarks and leptons into 3 generations shows, among other things, that the properties of particles are repeated in large mass scales. This suggests (by analogy with the periodic table of elements *) the possibility that differences between generations stem from the arrangement of even smaller building blocks of matter in leptons and quarks. These hypothetical building "stones" of quarks and leptons have been called of preons (Greek
pre = before ).
*) D.I.Mendelev compiled a periodic table of elements when he noticed that certain chemical properties of the elements were repeated. Atomic physics later explained this as a consequence of the structure of atoms. It could be similar in particle physics. Even 12 known fundamental particles have some recurring properties. This may indicate that they are not in fact basic and elementary, but that they are composed inside of even smaller particles, the arrangement of which determines their special properties..?..
  Based on some (highly uncertain) results of scattering experiments, it was hypothesized that quarks (and perhaps leptons) could be composed of even "smaller" particles, called preons. Each quark could be made up of three preons. According to the Salam and Pati model, these are somons determining generation (3 species, zero charge), flavones determining "smell" (2 species, charge 1/2) and chromones determining "color" (4 species, charge 1/6). An alternative model proposed by Harrari, Shupe and Seidberg considers quarks and leptons to be a combination of three preons (so-called rishons) of two types, one with an electric charge of +1/3 and the other with zero charge, each of which has its antiparticles with opposite electric charge -1/3 and 0. The electron would be a combination of the preons "---", the positron "+++", the quark "u" would consist of "++ 0", the electron neutrino of "000", etc.
"Force-carrier" mass bosons would consist of combinations of 6 preons, eg W+ = "+++ 000", the photon would be a pair of preon and antipreon "+ -". The excited states of the preon system could correspond to individual generations of particles. At the next level of the hypothesis could be pre-preons, pre-pre-preons, etc., depending on how many undiscovered levels still exist in matter..?..
  Several preon models have emerged, trying to explain different quarks and leptons by combining different numbers of specific types of preons. So far, it's all just speculation and numerology (after all, this was in the beginning also quark model of protons, neutrons and other hadrons). Any experimental confirmation of the preon hypothesis is still lacking. It could be supported by experiments with particle collisions at the highest energies, if they showed that quarks and leptons have a non-zero size (previous experiments show rather the point character of quarks and leptons). There are also some theoretical problems related to very small dimensions (less than about 10
-15 cm) of preons and their localization, which according to the quantum principle of uncertainty should imply unacceptably large effective momentum and thus mass, many orders of magnitude higher than corresponds to real weights - a mass paradox.
What we are composed of 
We humans, the surrounding nature and all the objects we come in contact with are composed of quarks "u" and "d" and electrons. There are fields acting between them - electromagnetic, strong and weak interactions. Other types of quarks and leptons are used only in high-energy processes of particle interactions in accelerators and cosmic rays, as well as in some turbulent astrophysical processes.

Problems and possibilities of extending the standard particle model ?
After the discovery of the Higgs boson, the standard model of matter was practically closed, it had no missing elements, basically explain all the observed experimental facts. Nevertheless, there are many uncertainties. For the theoretical ones, hopes are placed in future unitary field theories. However, there is no explanation of the dark matter in the universe, which is five times more massive than the mass known to us, described by the standard model
(5.6 "The future of the universe. Arrow of time. Dark matter. Dark energy." in the book "Gravity, black holes .... )...... .......
 Are there new yet undiscovered particles ?
In common experiments, particle interactions manifest themselves mostly directly, explicitly during collisions either by scattering or reactions, with the disappearance and creation of new particles. This is explored in detail. However, hidden - virtual, vacuum - interactions also take place in quantum physics. According to quantum field theory, the vacuum is filled with virtual pairs of particles and antiparticles that are constantly created and then disappear. If this happens in the immediate vicinity of a "real" particle, even for that brief moment of their virtual existence, they can interact slightly with the real particle, which will somewhat change its physical parameters. One such parameter that can be affected by interactions with virtual particles in the vacuum is the particle's magnetic moment
(1.1, passage "Quantum angular momentum. Spin. Magnetic moment.").
Anomalous magnetic moment of the muon. Experiment g-2.
The magnetic moment of an electron is e.h/4
pme - the so-called Bohr magneton (1.1, passage "Quantum angular momentum. Spin. Magnetic moment."). The so-called gyromagnetic ratio g is introduced for the excitation of the magnetic field by the rotational movement of particles, which is the ratio of the excited magnetic moment and the mechanical moment of momentum of the rotating particle, here spin. For an electron and muon with spin 1/2, this coefficient should be g=2. But in the 1950s it was measured that the g value of the electron is slightly greater than 2 (.........). It was attributed to the influence of interactions with virtual particles of the vacuum - the slightly increased value of g arises from contributions from interactions of virtual pairs of all elementary particles that exist.
  The actual measured value of the gyromagnetic ratio
g of fermions - electrons, muons - or its difference from 2, contains information about what all elementary particles exist in nature and participate in vacuum virtual interactions. Muons are 207 times more massive than electrons, so the vacuum virtual particles act much more strongly on them, and the difference between the actual g and the default value of 2 is larger here. Measuring the g-2 difference for a muon can thus provide an independent idea of whether only existing Standard Model particles contributed to it, or whether the increased value is an indication of the existence of other yet undiscovered particles..?.. Challenging measurements of this kind are therefore called "muon experiments g-2" (g minus two).
  In vacuum virtual interactions, all particles and quantum fields existing in nature should be used - known and possibly even the others not yet discovered (the vacuum "knows about them", virtually contains them...). Experiments of the
g-2 type can reveal them to us in advance, without the need for their "physical production". However, they do not give us any information about their properties, or whether they are one new particle or several. To do this, we need to physically create them for a moment in collision experiments and deduce their properties from the detection of their decay products. That will be the task of the new, larger accelerators...
  The experiment begins with a beam of a large number of protons (approx. 10
12 /s.) from the accelerator, which upon impact on the target produce, among other particles, a large number of pions, which quickly decay into muons. The muon+ beam is then guided into the magnetic ring. The g-2 measurement itself is carried out in a magnetic ring with a very homogeneous magnetic field, in which a large number of muons circulate in the ring under the influence of a strong magnetic field at a speed close to the speed of light. During this circular flight, the spin and magnetic moment of the muons precess around the magnetic field vector. At the same time, muons constantly decay into positrons and neutrinos. Neutrinos fly away without interaction. The positrons, which travel in the same direction as the muons before decaying, are detected by a series of detectors located on the inside of the magnetic ring. They are, on the one hand, PbF2 scintillation detectors and a series of trackers based on ionization chambers, which register the trajectory of positrons from the decay of muons. The energy, time and location of arrival of the decay positrons are measured. The frequency of precession depends on the value of the magnetic moment, i.e. on the gyromagnetic ratio g.
  The first experiment of this arrangement took place in the years 1997-2001 in Brookhaven, further measurements under more modern and more precise conditions continue from 2018 in Fermilab. The result of the experiment so far is the value
g = 2.00233184110(82). The calculated theoretical value according to the standard model is g = 2.00233183620(86). Thus, the experimental and theoretical values differ only slightly - from the eighth decimal place. If the g-2 experiments confirmed an anomaly indicating the existence of unknown elementary particles - the existence of particle physics beyond the standard model, it would be a great stimulus for the construction of new, larger accelerators.
  But there is another possibility: What if the anomalous value of the muon's magnetic moment was inaccurately calculated in the current version of the standard model? The final objective results of these demanding studies will hopefully be obtained in a number of years...

Unification of interactions - unitary field theory and elementary particles
Although the reduction of the huge diversity of phenomena and structures in nature to a mere 4 basic types of interactions involved between a few types of elementary particles (actually quarks and leptons), is the imposing contribution of physics to a unified understanding of the world, for physicists it still is not enough. They have even higher ambitions: to create a definitive final theory or a unified theory of everything
(TOE - Theory Of Everything) - to unify the existing four types of interactions into a single interaction, described by a unitary field, whose quantum properties would then describe all kinds of elementary particles.
  Unitary field theory forms a very special part of theoretical physics with links to nuclear and particle physics, as well as to the theory of relativity, astrophysics and cosmology. It thus lies outside the scope of our treatise on nuclear and radiation physics. For further details, we can refer to special literature, on these pages, for example, to Chapter B "
Unitary Field Theory and Quantum Gravity" in the book "Gravity, Black Holes and the Physics of Spacetime".

Particle accelerators
For the study of the properties, structure and interactions of elementary particles, the production of artificial radionuclides, as well as for applications in various fields of science and technology (including medicine), it is necessary to use particles accelerated to high kinetic energies. Since the natural radioactive substances provide limited intensity and especially energy of emitted particles, it is necessary to turn to artificial acceleration of particles. We can artificially accelerate only stable *) electrically charged particles - electrons e-, positrons e+, protons p+, deuterons d+, helium nuclei He++ = a-particles and the nuclei (ions) of heavier elements. High-energy particles without charge (such as photons g, neutrons no, neutral pions, ...) and short-lived particles (p- mesons, hyperons, ...) can then be obtained secondarily - by interactions of accelerated charged particles with other particles in a suitable target.
*) The only unstable particles that can basically be accelerated are
m muons, whose lifetime of 2.2 microseconds, in co-production with relativistic time dilation, enables multiple movements along a circular path in the accelerator for a period of approx. 0.1 s. sufficient for effective acceleration . Muon accelerators - colliders - can be promising for obtaining high energies due to minimal synchrotron radiation and for realizing "clean" collisions, in which all the energy is available for the creation of new secondary particles (it is discussed at the end of this chapter in the passage "Muon accelerators?") .
  Devices that accelerate charged particles by strong electric and magnetic fields are called accelerators. The actual acceleration of charged particles is caused by an electric field (electric component of the electromagnetic field of intensity E) by its force acting on the charge F
e = q. E, the magnetic field is used to change the path of charged particles *). Or, the variable magnetic field induces an electric field, which causes an accelerating effect.
*) A magnetic field alone cannot accelerate, because the Lorentz force F
m = q. [v x B] acts in a magnetic field of intensity B perpendicular to the direction of motion of the charged particle at velocity v, so that it does not perform any work. It only appropriately changes direction, curves the path of the charged particle, without changing the velocity or energy.
An X-ray tube can already be considered the simplest particle accelerator (3.2 "X-ray diagnostics") - it is a linear electrostatic accelerator of electrons, the source of which is a hot cathode, the (inner) target is an anode, braking (+ characteristic) X-rays come out. The first real accelerator was built in 1931 by R.J. van de Graff using electro -mechanical high voltage generator (called by its name), in 1932 J.D.Cockcroft and E.T.S.Walton using a cascade voltage multiplier (a system of rectifier diodes with suitably connected capacitors). An accelerated proton energy of about 0.5 MeV was achieved, with which the first nuclear transmutation caused by artificially accelerated particles. The first circular accelerator (cyclotron) was designed by E.O.Lawrenc also in 1932. Thus began the era of the use of accelerators in nuclear physics.
Cosmic accelerators
The processes of accelerating the building blocks of matter also take place in nature, often on a much larger scale and intensity than we can artificially. In stormy processes in stars and galaxies, there are processes that act as "cosmic accelerators" of particles. In particular, three mechanisms of particle acceleration in space are discussed :

Fermi mechanism of continuous diffusion acceleration during repeated interaction of particles with moving large clouds of ionized gas, with the interaction of magnetic and electric fields in space.
Supernova explosion, in which the outer parts of the star expand at a speed close to the speed of light, while in the resulting shock wave, protons can be accelerated to energies of up to hundreds of TeV in the rapidly expanding ionized mass.
Absorption of matter through a black hole, when a large amount of matter attracted by a black hole creates a so-called accretion disk around it, in the lowest central area of which there is an extremely strong heating of the absorbed substance descending in a spiral into the black hole. Along the axis of symmetry of this thick rotating disk, a "funnel" then escapes from the inner part a stream of particles and radiation - the so-called jet , which contains particles accelerated to very high relativistic energies.
  These mechanisms (and possibly other hitherto unknown ones) produce high-energy cosmic radiation - for details from the point of view of radiation physics, see 1.6 "Ionizing radiation", section "
Cosmic radiation", from the point of view of astrophysics and cosmology, see chapter 4 "Black holes" in the book "Gravity, Black Holes and the Physics of Spacetime".

Basic division of accelerators
In terms of purpose and use, accelerators can be divided into two groups :
Small accelerators for industrial and medical use ,
where extremely high energy is not required (usually units up to tens of MeV), but it is often desirable to achieve relatively high flow (fluence) particles so that the desired technological, analytical or therapeutic effect is sufficiently effective. These are relatively small devices with the dimensions of the acceleration chamber in the order of tens of centimeters to several meters. Such accelerators are the most common, they are often also produced industrially and in series.

Large accelerators for research in nuclear and particle physics ,
where it is usually crucial to achieve the highest possible energies of accelerated particles; high effective energies of order TeV and higher for interactions can be achieved only by using method collider, as discussed below. To study interactions with a low effective cross section, it is also necessary to achieve a high flow of high-energy particles (often only one interaction out of several billion is "the right one"!). These are unique devices with large dimensions (tens and hundreds of meters, the largest up to several kilometers!); they are part of complex laboratory systems with complex detection apparatus. The construction of such facilities takes many years and is very costly - up to billions of dollars. The issue of large accelerators will be briefly discussed below
- passage "Large accelerators".
The smaller structure we investigate, the larger instrument we need 
When examining the microworld is manifested interesting at first glance paradoxical regularity: the smaller the object investigate or influence, the bigger - larger and more powerful - equipment we need. This trend is not new, and there hass actually manifested itself in the optical field. For the observation of millimeter objects we can do with an ordinary magnifying glass, for the study of cells we need a more complex and larger microscope, for the study of processes in the cell nucleus we can no longer do without a relatively large and complex electron microscope. In general, to observe a given object, we need radiation with a shorter wavelength than the effective dimensions of the object.
  Even more complicated is the situation in the study of the smallest "elementary" particles of matter, where specific properties of their interactions come into play. Repulsive forces between particles can prevent the desired interaction, different types of processes can take place under the same conditions, new particles are often formed with a short lifetime. To understand the structure of elementary particles and the nature of forces, which acts between them, it is necessary to realize particle collisions at the greatest possible energies. In such collisions, the particles penetrate each other "deep into their interiors" and the result of the interaction can tell something about their structure. Due to quantum processes in the fields of strong, weak and electromagnetic interactions, high-energy collisions create new secondary particles, which are both interesting in themselves and carry important information about the nature of fundamental natural forces, including the possibility of their uniform understanding within unitary field theory. Particle collisions at high energies are a kind of "probe" into the deepest interior of matter - and at the same time into the processes of the formation of the universe
(see 5.5 "Microphysics and cosmology. Inflationary universe." books "Gravity, black holes and space-time physics").
  It can be said, that large accelerators are the most powerful "microscopes" *) into the interior of matter and with a bit of exaggeration also the largest "telescopes", which allow "oversight" to very early stages of development of universe. This is not, of course, a direct physical observation of the phenomena at the beginning of the universe, but their experimental simulation, if possible.
*) In the spectrum of "research tools" in Fig.1.0.1 it lies on the left margin (1.0., part "Methods and tools of nature study").
  Regarding the type of accelerated particles, some types of accelerators are "universal" and can in principle work for different types of particles if provided by an ion source; linear accelerators or synchrotrons have this property. Other types are able to accelerate only certain types of particles, eg betatron only electrons. In practice, however, accelerators are mostly "specialized" in their design and are divided into electron, proton and heavier ion accelerators.
Accelerator luminosity
The intensity (abundance) with which the accelerated particles interact depends on their flux density. It is characterized by a quantity called the luminosity of the accelerator L [cm
-2 s-1], which is the number of particles per cm2 per second (a kind of "luminosity", "aperture"). On large colliders, the luminosity reaches L 1031-1033 cm-2 s-1, for accelerators working with a fixed target, it is up to L 1035 cm-2 s-1.
    According to the method of technical implementation and the shape of the path on which the particle acceleration takes place, we divide the accelerators into two basic types:
linear (LINAC) and circular (cyclic) - both types will be described in more detail below. We will mention one more interesting and possibly promising type of accelerators (belongs to the category of linear, but its principle differs fundamentally), which is still in the stage of research and development :
Laser plasma accelerators LWFA
A new interesting and promising method of accelerating charged particles (especially electrons) is the use of very intense electromagnetic beams from high-power lasers. When an intense light beam from a laser passes through a gaseous medium, the gas is ionized and plasma is formed. If we irradiate a gaseous medium with a very intense short pulse of laser light, a plasma trace is created in the medium, which entrains the released electrons. While passing through the plasma laser pulse ponderomotive force expels electrons out from areas of its HF. impulse, so that a wave or a furrow of deflected electrons is formed behind it in the plasma. The electrons move in a positive ion environment and, under the action of Coulomb's electric force, return to their equilibrium positions
(which "over-vibrates"), with a periodic deflection of the electron set relative to the ion set (which in the high frequency field due to its substantially greater mass almost not enough to move) - to the oscillations of electrons in the Coulomb field, accompanied by a periodically variable electric field. This creates a kind of rippling trace concentration of electrons and the electric field intensity - plasma wave or "furrow field " (Wakefield), similar to a rippling trail or furrow left behind by a ship floating fast on the water surface. The frequency of electron oscillations in a plasma wave (plasma frequency) is wp = [rp.e2/(eome)], where me is the mass of the electron, e is the charge of the electron, rp is the density of the plasma (number of particles per m3) eo permittivity of vacuum. During the oscillations of electrons in a plasma wave, an alternating electric field with an amplitude of intensity Emax = me. wp.c/e is created. Thus, the accelerating electric gradient in a linear plasma wave can reach a maximum value of E = c.(me.rp/eo), proportional to the square root of the plasma density. For density plasma rp 1018 particles/cm3 achieved by accelerating gradient values E 1GeV/cm, which is about 2-3 orders of magnitude higher than in linear accelerators.
  The longitudinal component of the oscillating electric field in this plasma wave can accelerate electrons under certain circumstances (synchronized energies and momentum), which are carried on an electric field wave (similar to the high frequency linear accelerators described below). When using a laser with focused picosecond pulses of high intensity (approx. 1018 W/cm2) a very intense longitudinal acceleration field is created, which can accelerate electrons to energy of about 50 MeV (in top laboratory experiments energy of the order of GeV was achieved, but the electron yield is so far very small).
  Experimental accelerators on this principle given the name LWFA (
Laser Wakefield Accelerator - laser accelerators trought the furrow field, here Wake = track behind the boat, furrow), in image on the left part. Their advantage is very small dimensions *). The rapid progress of laser technology promises the possibility of effective acceleration, controlled by several sequential laser pulses (one pulse excites a furrow field, the other a subsequent pulse releases into it, "injects" electrons). If this technology can be brought to the stage of practical applicability, then such a tiny "table" LINAC, accelerating electrons into energies of tens and hundreds of MeV in a laser-excited plasma wave in a centimeter path, would find wide application in research, industry and medicine.
*) In the case of plasma accelerators, the acceleration field can have a much larger gradient than with conventional electrostatic or radiofrequency accelerators (linear and circular, described below). In conventional electronic accelerators, the intensity of the accelerating field is limited by the electrical strength of the insulators and the corona discharges in the accelerator tube. This limited value of the accelerating gradient requires a long accelerating tube to obtain high energies. The field gradients in the plasma are 2-3 orders of magnitude stronger than in conventional radiofrequency accelerators, leading to much shorter acceleration path lengths.
Laser acceleration of protons

Experiments are also performed with laser acceleration of protons. Direct laser acceleration of protons does not work, heavy protons are not enough to respond to a rapidly changing field in a plasma furrow. It is necessary to use a two-stage method, schematically shown in the right part of the figure :
1. Short high-power laser pulses first accelerate electrons to high energies of the order of GeV using the LWFA method.
2. These high-energy electrons then pass through a proton-electron accelerating tube, into which protons are injected simultaneously (synchronously), pre- accelerated in a small accelerator to an energy of about MeV (this is for better synchronization and more efficient energy transfer between electrons and protons). Attractive Coulomb forces act between groups of electrons and protons, which slows down the electrons and accelerates the protons (picture on the right). High-energy electrons thus transfer energy to protons with their electromagnetic field, "drag" them behind them and accelerate protons to energies of the order of 100 MeV. At the outlet of the tube, the electron and proton beams are then separated by means of an electromagnet.
  If this technology can be brought into practical use, large cyclotrons and the complex distribution of protons to irradiation facilities in proton therapy (3.6 "Radiotherapy", part "Hadron radiotherapy") would be replaced by small compact laser accelerators, which could be easily mounted in the gantry of individual irradiation devices in existing radiotherapy rooms ...

Combining multiple accelerators
For some special experimental and technical applications, two or more linear or circular accelerators are combined into one larger system. This is mainly to obtain very high energies of particles, which are first pre-accelerated in smaller accelerators and then injected into a large accelerator for final acceleration (see "
Large accelerators" below). Some newly developed systems for proton radiotherapy (3.6 "Radiotherapy", part "Hadron radiotherapy") they combine pre-acceleration of protons in a smaller cyclotron with definitive acceleration in a linear accelerator for better electronic regulation of proton energies to target the Bragg maximum depth dose to the tumor area.

The primary and secondary radiation from accelerators
Accelerated charged particles form so called primary beam , which can be used in two ways :
Direct use of the primary beam ,
which after incidence at the appropriate target (or in interaction of opposite bundles - collider) evokes the required interaction for the study elementary particles, production radionuclides, radiotherapy or for another radiation analytical or technological process. The target here can be irradiated technological material, or even the patient's body - tumor tissue ("
The use of secondary radiation ,
which arises from impact and interaction primary accelerated particles with a target. The type and properties of this secondary radiation depend mainly on the type and energy of the primary particles and also on the material and design of the target. For accelerated electrons, it is mainly braking radiation
(bremsstrahlung) g (continuous spectrum similar to X-rays, but significantly higher energy). Accelerated protons, when interacting with target nuclei, can provide secondary neutrons, p- and K-mesons, antiprotons, hyperons, etc., depending on energy. Secondary radiation can be emitted in so-called secondary beams for own use. In the medical field, the most common use of braking g-radiation from an electron accelerator in radiotherapy (see 3.6 "Radiotherapy", in the stage of experiments is the therapy of p--mesons or antiprotons).
  The beam of high-energy particles, whether primary or secondary, can be used for the respective interactions either inside the accelerator where it is formed (an internal target is installed), or it can be directed and led out of the accelerator by means of suitable electromagnetic fields. Using vacuum transport tubes, it is then led to the laboratory space, to interact with the atoms and nuclei of the outer target
(see also the "Target" passage below). We will mention here three specific ways of using secondary radiation produced by accelerators, which have practical use also outside of nuclear physics :
Accelerators as generators of braking g- radiation  
If the accelerated particles are electrons, then when they hit a target made of heavy material, most often tungsten, braking electromagnetic radiation with a continuous spectrum is generated. Its maximum energy is almost equal to the kinetic energy of accelerated incident electrons. This is a very common way of producing hard photon radiation for use in nuclear physics, analytical methods (3.4 "
Radiation analytical methods of materials") and especially in radiotherapy (3.6" Radiotherapy "). As electron accelerators previously used to be a betatron, now mostly a linear accelerator (both methods are described below, see also 3.6, section "Isocentric radiotherapy", Fig.3.6.1).
Accelerators as neutron generators
Accelerators in a special arrangement can serve as electronic sources of neutron radiation - so-called neutron generators. Neutrons are formed or released in a number of particle and nuclear reactions. From the point of view of easy and efficient production of neutrons, the reactions of tritium and deuterium nuclei are the most advantageous. It is enough to accelerate the deuterons to an energy of about 100-200 keV and let them fall on a target containing tritium to cause a nuclear reaction
2D1 + 3T1 1n0 + 4He2 (+17.6 MeV), at which they release neutrons. A fairly small "table" linear accelerator is enough for this. The analogous reaction D + D 1n0 + 3He (+3.3 MeV) is less advantageous because it has a lower effective cross section and deuterons must be accelerated to a higher energy, about 1MeV. The basic arrangement of such a neutron generator consists of three main parts: an ion source, an acceleration and focusing system, and a target. Diluted deuterium is filled into the ion source, which is ionized by an electric discharge. Ionized deuterium atoms - deuterons - are fed from this plasma by an electric field between the electrodes of the acceleration and focusing system. A tritium target is bombarded with an accelerated beam of deuterons; tritium is bound in the form of a hydride in a thin surface layer of the absorber, most often titanium, zirconium or scandium, the base material of the target is cooled, for high performances a disc-shaped rotating target is used (the beam then hits each of its places only for a very short time, during which the exposed place does not overheat and the heat is enough to dissipate - similarly to X-ray with a rotating anode). The nuclear reaction of deuterium with tritium is exothermic and almost monoenergetic neutrons with an energy of about 14 MeV *) fly out of it (they fly out of the target practically isotropically to the whole spatial angle). With a deuteron energy of 200 keV and a beam intensity of 1 mA, a yield of about 2.106 neutrons/second is achieved. In an effort to achieve high neutron yields higher than about 2.1011 n/s., the tritium target is rapidly depleted. Therefore, special closed acceleration systems were developed - so-called neutron tubes, filled with a diluted mixture of deuterium D and tritium T (regulated replenishment, with helium removal). Both of these types of ions, D+T generated by the discharge in the ion source, are simultaneously accelerated and bombarded with a target in the surface layer of which the same concentration of D and T atoms stabilizes; the required reaction then occurs in the impact of accelerated D on T in the target, even in the impact of accelerated T on target D. Recently, miniature neutron generators have also been designed (laboratory, "desktop"), using high frequency D and T ion acceleration. The schematic drawing of the principle of neutron generators will be supplemented ... (for now see the indicative illustration at the end of 4.3, section "Neutron- stimulated emission computed tomography NSECT").
*) The direct use of these high-energy neutrons is suitable for neutron-stimulated nuclear gamma-spectrometric analysis. For neutron activation analysis, it is necessary to slow down these neutrons in a moderator.

   Neutron radiation finds application in neutron activation analysis (3.4, part "
Neutron activation analysis"), in some radiation technologies, is also tested in radiotherapy (3.6, part "Hadron radiotherapy").
Accelerators as synchrotron radiation generators
A very special way of using secondary radiation from the accelerator is to use synchrotron radiation *). It is electromagnetic radiation that is emitted by a charged particle as it moves along a curved path. In terms of the function of circular accelerators, it is a "parasitic" and unfavorable phenomenon that "consumes" the kinetic energy of the accelerated particles and prevents high energies, especially electrons. However, the UV and X-ray components of synchrotron radiation can be used in some applications in materials analysis as well as in biology and medical diagnostics. Therefore, special accelerators for synchrotron radiation production are constructed, as briefly described below.
) This name originated from the fact that this radiation (in the visible part of the spectrum) was first observed in 1947 at the GE synchrotron in New York while accelerating electrons in a circular orbit. Intense synchrotron radiation arises in universe during the rapid movement of electrons in a strong magnetic field around compact objects, especially neutron stars, which are observed as pulsars - in more detail 4.2. "Final phases of stellar evolution. Gravitational collapse", part "Pulsars", Fig.4.3, books "Gravity, black holes and space - time physics". Here, however, we will deal with the artificial production of synchrotron radiation on accelerators.
   Particle with rest mass m
o and charge e, moving with kinetic energy E along a path with radius of curvature R, according to the laws of electrodynamics (see 1.5 "Electromagnetic field. Maxwell's equations." monograph "Gravity, black holes and space-time physics"; follows from Larmor's formula (1.61 ') ) emits the electromagnetic waves of power P = (2/3).(e2.c/R2).[E/moc2]4. It can be seen from this relationship, that radiation is relevant only for light charged particles, electrons or positrons moving with high energy, ie with a relativistic velocity, along a strongly curved orbit. At slow motion (non-relativistic velocity), the orbiting particle appears as an oscillating electric dipole, emitting weak monochromatic radiation with a frequency given by the period of circulation (similar to a transmitting antenna), in practically all directions (with the radiation diagram according to Fig.1.4 of said reference). However, as a particle moves at a relativistic velocity, electromagnetic radiation is emitted in a narrow cone whose axis is tangent to the orbit of the particle at a given point. The opening angle of this cone is approximately equal to mo.c2/E. The external observer will see the radiation only during the time when this cone intersects its position ("beacon effect"). As the particle moves in a circular orbit, the fixed observer or detector will register radiation pulses whose frequency is given by the particle's orbital period T = L/c, where L is the length of the orbit. The spectrum of the synchrotron radiation S itself consists of a number of harmonic components, which are so "blurred" due to the continuous motion in orbit that the resulting spectrum appears continuous, with a maximum energy around ESmax [keV] 2400.Ee3 [GeV] /R [m] 0,6.B[T] .Ee2 [GeV] (motion of an electron with kinetic energy Ee along a path with a radius of curvature R , under the influence of a magnetic field of intensity-induction B). In the region of energies higher than ESmax , the spectral intensity of radiation decreases rapidly.
Experiments with synchrotron radiation have previously been performed on synchrotrons designed to accelerate electrons
("parasitic" use). Later, however, special single-purpose accelerators were constructed, optimized for the production of synchrotron radiation (2nd generation). They do not contain any target, nor are any particles emitted from them. The electrons are accelerated in the accumulation ring  - an evacuated polygon-shaped tube, in the rounded tops of which bending magnets are placed. Electrons are injected into one of the straight sections, while in the other there are accelerating electrodes (high frequency resonator). The particles are supplied with only as much energy as is electromagnetically radiated, so that electrons can circulate in the tube for a long time (electrons that fall out of circulation due to collision with residual gas atoms in the tube are replenished from the injector). Synchrotron radiation is taken from curved paths in diffraction peaks. For some types (3rd generation), special magnetic devices are inserted into the beam path in straight sections of the tube, consisting of a series of magnets with periodic alternation of the direction. Their task is to wave the path of electrons horizontally or vertically. They are called undulator ("crimping") with a weaker field, and wiglers (Wiggle - flutter, tremble) a strong magnetic field (approximately 10T). In the undulator, the electron path is wavy only weakly, which leads to the emission of a harmonically modulated signal, an almost monochromatic wave, the wavelength of which is given by the so-called undulator equation : l = [lU/2(1-v2/c2) ]. (l + K2/2) with undulator parameter K = e.Bo.lU/2pme.c. In these equations, lU is undulator period (spatial distance opposite polarity electromagnets undulator), e is the electron charge and me its rest mass, Bo the maximum value of the magnetic field, c speed of light. By changing the energy (velocity) of the electrons or the intensity of the magnetic field, it is therefore possible to change the wavelength of the output radiation in a wide range. In the strong magnets of a wigler, the electron paths curve sharply periodically, which leads to intense radiation of synchrotron radiation of shorter wavelengths.
  To produce synchrotron radiation are starting to use also a linear electron accelerator (4th generation sources), whose densified cloud (bunch) when traversing the long undulator interacts with the electromagnetic wave excited, by himself created. Electrons are therein slightly accelerated or slowed down (depending on whether they are in phase or antiphase) by so-called ponderomotive force, which is formed inside the electron clouds of redistribution of electron density with fine longitudinal structure of the spatial period corresponding approximately to the wavelength of the radiation - the so arises mikrobunching. In this regular "micro-cloud" structure, synchronization and coherent composition of electromagnetic radiation from individual micro-clusters of electrons can be achieved. If the electrons emit synchronously with the same phase, the output radiation reaches many times higher intensity and a considerable degree of coherence. This spontaneous "self-amplification" of radiation from the periodically "self" -modulated electron cloud in the undulator is analogous to the formation of radiation in lasers - it is a kind of "laser" with free electrons (FEL - Free Electron Laser). The electrons leaving the undulator are deflected by means of a magnetic field and led away (to the absorber or for possible further use) so as not to contaminate the photon radiation output beam. FEE systems are currently being experimentally tested on large linear electron accelerators
(the highest electron energy used so far was 14 GeV at the SLAC accelerator in Stanford, where the undulator length was 112 m with 33 segments with a magnetic field of 1.25 T; output coherent X-rays reached 8.25 keV and a fluence of 1012 photons in a 0.07 ps pulse).
  With the energies of accelerated electrons E
e 2-10 GeV, it is thus possible to obtain a wide range of wavelengths even in the X-ray region. The main advantage of these specialized sources of synchrotron radiation, also sometimes referred to as "photon factories", is the high intensity of radiation, its narrow angular collimation, pulsed character, good definability, stability and adjustable parameters.

Basic parts of accelerators
Before we deal with individual types of accelerators, we will mention four basic components that all accelerators have :
The source of accelerated particles (ion source)
emits the required type of particles, such as electrons, protons or heavier ions, to the "starting" point of the acceleration system. In the simplest case, it is an ionization tube containing the appropriate dilute gas (eg hydrogen H), where ions are formed (for hydrogen they are protons p
+) in a smoldering discharge between the cathode and the anode (at a voltage of about hundreds volts to tens of kV) and they are guided by a thin capillary through a "suction" electrode into the acceleration system. To obtain heavier nuclei (ions), a discharge in dilute gas (containing the relevant element) is used at a sufficiently high voltage to cause ionization even on the K shell. This produces ions with different degrees of ionization, from which the required nuclei (ions with the highest degree of ionization) need to be separated by means of an electric and magnetic field and introduced into the acceleration system.
  For electron accelerators, the source is a simple heated cathode (electron thermoemission) equipped with suitable accelerating and focusing anodes - an "electron gun" - similar to a screen. Event. the cathode can be provided with a grid for electronic regulation of the electron flow.
  Recently, laser sources have also been developed, in which the emission of particles is generated by a high concentration of energy from short and very intense laser pulses impinging on a suitable target. This creates primary clouds (bunch) of particles, electrons or ions, which are then accelerated in a pulsed high-frequency mode in accelerators or in a laser "furrow wave"
(the above-mentioned "Laser Plasma Accelerators LWFA").
  It is more difficult to obtain antiparticles for acceleration. Positrons are obtained by bombarding a target made of a material with a high proton number Z (eg tungsten) with accelerated electrons, while the electromagnetic interaction in the field of nuclei produces, among other things, positrons e
+. Similarly, antiprotons p' must be obtained by bombarding a suitable target with protons accelerated to energies higher than 3 GeV, where the reactions p + p 2p + p + p' occur, among other things.
  In large high-energy accelerators, injectors are sometimes used as a source of particles for acceleration - "pre-accelerated" particles are injected into the main chamber by an auxiliary linear or circular accelerator (with energy unit up to tens of MeV or GeV) and then accelerated to the required high energy (GeV or TeV).

Acceleration chamber, tube
The space in which particles move and accelerate has different shapes and sizes, depending on the type of accelerator. It can be a narrower or wider, shorter or longer tube linear or circular shape, flat cylindrical chamber. There must be a high vacuum to prevent disturbing collisions of particles with the gas atoms.
Acceleration electrodes, electromagnetic field
An acceleration system of electrodes or wave resonators is located in the evacuated acceleration chamber or tube, where an accelerating force is created by the synchronized action of the electromagnetic field on the passing charged particles. The accelerator system is powered by a power supply -
see the section "Electrical supply of accelerators" below.
The target ,
on which the beam of accelerated particles falls, is either internal - is located inside the accelerator system, or external - the particle beam is led out of the accelerator tube. Further, the target may be material (usually solid), or may be replaced by an interaction region, where the particles collide in the colliding beams
(see "Colliding beams" below). Also, secondary particles produced on the inner target (such as p or K mesons) are by to magnetic and electric fields sometimes they exported in the form of a beam into the laboratory space, where measuring apparatus (detection devices, bubble chambers, trackers, etc.) are located. When accelerated particles hit an (solid) target, most of the kinetic energy of the particles changes to heat - the bombarded target heats up. In order to prevent its thermal damage or evaporation of the target substance, it is necessary to dissipate this heat loss (it can be hundreds of watts) - the target is fixed on a solid metal base with a cavity cooled by flowing water (similar to anodes of power X-ray tubes). Neither the target nor the interaction region have the special accelerators for synchrotron radiation production mentioned above.
   A target, or generally a place where accelerated particle interactions occur, is usually equipped with a secondary particle detectors. In simpler cases, it is used to monitor emerging nuclear reactions. In large accelerators for the study of particle interactions, it often consists of a whole complex detection system, enabling a detailed analysis of paths, charge, energies, momentums and other characteristics of secondary particles arising from high - energy interactions - see 2.1, section "Arrangement and configuration of radiation detectors".

Colliding beams - colliders
When an accelerated particle hits a (fixed, immobile) target and collides there with another particle or nucleus, only a small part of the kinetic energy of the incident particle is actually consumed for its own interaction, because according to the law of action and reaction, part of the energy of the incident particle is converted into kinetic energy of the reflected particle and newly formed particles. The kinetic energy in the center of gravity system (CMS) of both particles is important for the result of the interaction - only this is actually "consumed" for its own interaction *). A significant increase in the effective energy of the interaction can be achieved, by the incoming and target particles moving against each other with comparably high kinetic energies (or momentums). Both such particles then practically stop during the collision and almost all of their kinetic energy can be used for their own interaction and the formation of new particles. This is the method of colliding beams without the use of a classical target: the two particles whose interactions we want to investigate, are accelerated to high energies and in opposite beams they are directed against each other, so that they collide head-on and interact of each other. Both beams are accelerated either in one tube (eg electron-positron beams) or in two different tubes. At a given location of the acceleration ring, the two beams of accelerated particles, flying in opposite directions to each other, are focused by the action of a magnetic field and guided so as to collide head-on. Devices of this kind are called colliders and make it possible to study the interactions of particles at significantly higher effective energies than in the case of classical accelerators with fixed targets - currently up to TeV is achieved. The site where the opposing beam interactions occur, the interaction region, is surrounded by a complex detection system
(as mentioned above, see also the "Large Accelerators, LHC" section) for a detailed study of secondary particles. Colliders are used only for exploratory research of particle interactions at very high energies, with the formation of new "exotic" particles.
*) The relationship between the energy of the interaction in the laboratory and the center of gravity reference system is given by the dynamic analysis of the collision using the law of conservation of energy and momentum. When a particle of rest mass mo, moving with the kinetic energy E, hits the same particle at rest, the effective energy of the interaction Eef = E1/2 (mo.c2)1/2. If, for example, a proton with a kinetic energy of 400 GeV collides with a target proton at rest, only the energy of 28 GeV remains for the interaction production of new particles. With increasing energy, the energy efficiency of the interaction decreases sharply. E.g. to achieve an effective energy Eef = 6TeV, we would have to irradiate protons with a kinetic energy of about 2.104 TeV with a fixed target (which, even with the use of powerful electromagnets with B = 7T, would require a circular proton accelerator with a circumference of about 105 km - larger than the Earth's circumference!). However, in the case of a collision of the same particles, which move against each other with the same kinetic energy E, the whole energy Eef = 2.E is available for the interaction - it is therefore the only practically usable way to achieve very high effective energies of interactions.
  In order for the collisions to be sufficiently frequent, it is necessary to ensure a very high intensity of both beams (luminosity). Therefore, special accumulator rings are used on some accelerators, in which accelerated particles (eg protons and antiprotons) accumulate from several doses in a strong magnetic field, and only after reaching sufficient intensity does a collision take place in the opposing beams.

Linear accelerators
Linear accelerators accelerate charged particles by applying an electric field during they linear movement along a straight path. A linear accelerator is often abbreviated Linac (Linear accelerator ). We can divide them into electrostatic (high voltage) and high frequency.

Fig.1.5.5. Simplified scheme of linear accelerator electrostatic (left) and high frequency (right).

  The basic scheme of the electrostatic linear accelerator is on the left in Fig.1.5.5. From the ion source, the required particles (electrons, protons, deuterons, etc.) enter to the acceleration system, formed by several coaxial metal cylindrical electrodes V1, V2, ..., Vn, between which a gradually increasing high voltage is distributed U1, U2, U3, ...., Un . Through an electrostatic field, charged particles with charge q in a linear path are accelerated to energy E = q. (U1 + U2 + U3 + ... + Un) given by the sum of the voltages at the individual electrodes. The gap between two successive cylindrical electrodes acts on the flying particles like an "electric lens" (similar to a screen), focusing a stream of particles into a narrow beam that ultimatelly hits the target. The accelerating electrodes are supplied with high voltage either from an electronic cascade multiplier (a system of suitably connected diodes and capacitors) or from an electrostatic-mechanical Van de Graff generator. Voltages from a few hundred kilovolts up to about 5 MV are used; higher voltages are difficult to achieve for the formation of corona and spark discharges *).
*) These problems with electric shocks they are formed in material environments - in air, dielectrics, insulators. For interest, we can have a small discussion, how is it in a vacuum? :
What is the strongest electric field can be ?  
In classical (non-quantum) physics, the electric field in a vacuum can be arbitrarily strong, almost to infinity
(in the material environment, however, this is limited by the electrical strength of the dielectric). From the point of view of quantum electrodynamics, however, even in a vacuum there is a fundamental limitation caused by the existence of mutual antiparticles of electron and positron: it is not possible to create an electric field with intensity stronger than Ee-e+ = me2 c3/e.h = 1.32 . 1016 V/cm, where me is the rest mass of the electron or positron. When this intensity is exceeded, the potential gradient is higher than the threshold energy 2me.c2 and a pair of electrons and positrons is formed, which automatically reduces the intensity of the electric field. Such a strong electric field has not yet been created, with conventional electronics this is not possible; one possibility in the future could be strong pulses from extremely powerful lasers...
  A more efficient way to accelerate charged particles to a very high energy in a linear path without the use of extremely high voltage is realized in high-frequency linear accelerator, the simplest diagram of which is shown in Fig.1.5.5 on the right. Charged particles from the ion source Z enter the acceleration system of cylindrical electrodes V1, V2, V3, ... ,Vn , which are connected to an alternating voltage U(t) = Uo.cos(w.t) = Uo.cos(2pf.t) with amplitude Uo and frequency f. Odd cylinders are connected to one pole, even cylinders to the other pole of a high-frequency high-voltage source. If a positive particle arrives with charge q and mass m from the source Z in the phase when the first cylindrical electrode V1 has a negative potential -Uo, then it obtains the energy E1 = q.Uo and the velocity v1 = (2q.Uo /m), so that the length l1 inside the cylinder V1 flies through time t1 = l1/v1. If the frequency f of the AC voltage is chosen so that the accelerated particle enters the gap between cylinders V1 and V2 at the time when the polarity reverses and cylinder V1 has a positive and V2 negative potential, the particle is again accelerated by energy q.Uo, ie it already has energy 2.q.Uo. If the synchronization between the frequency f, the voltage Uo and the electrode lengths lk *) is chosen so that the polarity of the alternating voltage is always reversed during the passage between the individual cylindrical electrodes Vk, these "synchronous" particles will reappear as they pass through each electrode and again and again accelerate.
*) As can be seen from Fig.1.5.5 on the right, to achieve synchronization, the length of the cylindrical electrodes V
k must gradually increase as the particle velocity increases. This is no longer the case when a speed close to the speed of light is reached, when the speed of the particle practically does not increase during acceleration; with kinetic energy only the relativistic mass of the particle increases.
  It is also worth noting that the actual electrical acceleration of the particle occurs in the gaps between the electrodes, while inside the metal cylinder, where the electric field gradient is close to zero (electric field is shielded), particles fly through inertia (this also applies to the electrostatic accelerator on the left side of the figure).
   The development of these accelerators proceeded by increasing the frequency f, using cavity resonators instead of cylindrical electrodes. Newer linear accelerators use a waveguide to create an accelerating field, divided by suitable disk protrusions into a series of resonant cavities and fed at a frequency of several GHz (most often around 3 GHz) from a klystron or magnetron generator (briefly described below). A high-frequency alternating electromagnetic field is generated in the waveguide in the form of a gradual or standing electromagnetic wave. If the accelerated charged particle moves in synchronism in the field of this carrier wave, a constant accelerating force given by the electrical component E of the electromagnetic wave acts on the particle. Particles for acceleration are injected into the acceleration system of cavity resonators or waveguides from an ion source, or electron nozzles in the case of electrons, in the form of "clusters" (bunch) in pulse mode, in precise electronic synchronization *) with an accelerating high frequency field.
*) In order for a constant accelerating electric force to act on a particle in a high-frequency field, it must enter the waveguide acceleration system in a suitable phase and at a speed close to the phase velocity of the wave - the synchronization condition must be met. The pulse mode of the ion source (or electron nozzle) and the high-frequency generator is controlled by an electronic circuit equipped with special power switching components - it is either a special thyratron tube or a semiconductor thyristor. The accelerating waveguide system consists of several specially shaped metal (copper) resonant cavities, lined up in a row. Electrons are injected in pulse doses into the acceleration system from an electron nozzle ("cannon") with an energy of about 30-50 keV, protons from an ion source with significantly higher energy. The resonant cavities at the beginning of the acceleration system have a shorter length and distances from each other, the others lengthen so that the phase velocity of the electric field coincides with the increasing velocity of the particle. The whole system is a bit similar to Fig.1.5.5 on the right, but instead of cylindrical electrodes there are a number of resonant cavities and instead of conductors supplying alternating voltage, a waveguide from a magnetron or klystron leads to the initial part of the tube.
   Small linear electron accelerators (Linac) are now very often used in radiotherapy - see 3.6 "Radiotherapy" (where they gradually pushed out previously used betatrons), mainly as a source of hard braking radiation (bremsstrahlung) gamma with energies of about 6-18 MeV. Large high-frequency linear accelerators with a carrier wave are used for energies up to tens of GeV, they are also designed for several TeV. They are either used as separate basic devices, or they can be used to pre-accelerate particles - as injectors for large synchrotrons (see below, Fig.1.5.6 top right). Unlike circular accelerators, where particles are repeatedly accelerated many times by one acceleration system, in a linear accelerator there is a gradual acceleration in many acceleration systems arranged in a straight line. Even when using high gradients (up to 100 MV/m) and high frequencies (up to 30 GHz) to achieve high energies (up to TeV), the length of the largest linear accelerators is several kilometers!

Circular accelerators (cyclic)
A very effective way to accelerate charged particles to high energies is to accelerate them many times in an electric field, into which the particles are repeatedly returned in a circular path by the action of a magnetic field *). On a particle with charge q is applied not only electrical accelerating force F
e = q.E, but also the Lorentz force Fm = q.[v x B], acting in a magnetic field of intensity B perpendicular to the direction of motion of the charged particle at velocity v. This magnetic force causes the charged particle to move in a circular path with radius R = m.v.c/(q.B). If an electric accelerating field (in the tangential direction) is applied synchronously at suitable places in this circular path, the particles will be periodically accelerated during each its orbit.
*) This magnetic field is generated by electromagnets - coils whose winding pass a strong electric current. Recently, superconducting electromagnets have often been used, which significantly reduces the consumption of electrical energy (the physical principles of superconductivity are briefly discussed above in the section "Fermions as bosons; Superconductivity").

The basic type of circular accelerator is a cyclotron
(the first small cyclotron was constructed by E.O.Lawrenc as early as 1932), the principle of which is schematically shown in the left part of Fig.1.5.6 :

Fig.1.5.6. Left: Schematic representation of a cyclotron. Right: Schematic representation of a synchrotron.

Between the poles of a strong electromagnet, in a flat circular vacuum chamber, two hollow metal half-cylinders in the shape of the letter D, so-called duants of radius R, are mounted, between which there is an acceleration gap. The duants are made of a conductive non-ferromagnetic material such as copper or brass. Duants D1 and D2 are connected to an AC voltage source U = Uo.cos (2p f.t) with frequency f (depends on the strength of the magnetic field and the mass of accelerated particles - protons, deuterons or heavier nuclei; usually around 20MHz), so there is an alternating electric field in the gap between the duants. The charged particles enter the center of the acceleration gap from the ion source "]". As a result of the force exerted by the electric field in the gap on a particle with charge q and mass m , the particle is drawn into one of the duants (which has just the opposite polarity) with a certain velocity v1. Inside the duant, where the electric field is shielded, by the action of a strong magnetic field B the particles describe a semicircle with radius r1 = m.v1 / (q.B) (this radius is given by the balance between centrifugal force and Lorentz magnetic force: m.v12 / r1 = q.B.v1) . The time taken for a particle to pass through this semicircle is T = p.r1/v1 = p.m/(q.B) - we see that this time (half-period) of a particle's orbit does not depend on its velocity v1 or its radius of travel r1 ; the frequency of the circular circulation of the particle is thus f = q.B / (2p m) and is constant *), because m , q and B are constants in a given arrangement. If the duants are supplied with alternating voltage at this frequency f (the condition of resonance or synchronization is met), then at the moment when the particle describes the semicircle in the first duant and finds itself again in the acceleration gap, the polarity of the duants is already opposite and the particle will be accelerated again by the electric field, so that it flies into the second duant at a higher velocity v2 > v1 . In the second duant, it will move again in a circle, but now with a radius r2 = m.v2 /(q.B), which is larger than r1 , but with the same period and frequency of circular motion. In the same way, the particle is then accelerated again and again each time it passes through the gap between the duants , moving in circles with an increasing radius r , i.e. in a spiral (Fig.1.5.6 left). From the last path of its maximum radius (close to the radius of the duants R), the accelerated particle is deflected electrostatically or magnetically and led into the space of the target, which it encounters and causes the appropriate nuclear processes there.
*) It is a so-called isochronous cyclotron (Greek isos = same, chronos = time ) - uniform in time, regular, with a constant frequency. The technical solution for maintaining the isochronous function of the cyclotron even for the high - relativistic - energies of accelerated particles will be outlined below in the section "Isochronous cyclotron - relivistic".
Movement and acceleration of particles in a cyclotron
To clarify the laws of cyclotron acceleration, we will analyze the motion of a particle with charge q and mass m in the magnetic field of intensity (induction) B in a cyclotron of radius R, to whose duants an alternating voltage of amplitude Uo and frequency f is applied. When a particle moves at velocity v in the direction perpendicular to the magnetic field, it will be acted upon by the Lorentz force F = q.B.v in the direction perpendicular to the magnetic induction vector B and the velocity v. Its path is thus curved into a circle, creating a centrifugal force. The motion of the particle will then be given by the equilibrium between magnetic and centrifugal force: q.B.v = m.v2/r. The radius r of the circle along which a particle moves, that is r = m.v/q.B. The period T circulating particles along the circle is equal to the circumference 2pr, divided by the velocity of the particles: T = 2pr/v = 2p.m/q.B. Particle circulation period T therefore does not depend on its velocity (nor energy). The time between the individual passages of the particle through the acceleration gap between the duants is thus still the same during the acceleration. In order for a cyclotron to accelerate a particle each time it passes through the acceleration gap between duants, the frequency 1/T with which the particle orbits in the magnetic field must be equal to the frequency f of AC voltage sources: f = q.B/2p.m .
   The particle enters from the ion source to the center r=0 of the cyclotron with almost zero kinetic energy. Each time it passes through the gap between the duants, it gains the kinetic energy
DE k = q.Uo when accelerated by the voltage Uo . When flipping between duants n-times, it gains the kinetic energy Ek and velocity v: Ek = n.q.Uo = 1/2 m.v2, => v = (2 Ek/m). It will move along a circle of radius r = m.v/q.B = [(2m Ek)]/q.B. Therefore, if we have a cyclotron of radius R with magnetic field B , the maximum energy of accelerated particles Emax = R2.q.B /2m, while the number of cycles between duants will be n = Emax / Uo .q.
Practical example: A cyclotron with a radius of 38 cm with a magnetic field of 1.5 T will accelerate protons at a frequency of 22 MHz to a maximum energy of 15 MeV. At a supply voltage (amplitude) between duants 50 kV , the protons orbit approximately 300 times before reaching maximum energy.
Note: The maximum energy of accelerated particles
(of a given species with charge q and mass m ) in a cyclotron depends only on the radius R and the magnitude of the magnetic field B, not on the supply voltage of the duants. This could give the impression that to accelerate even to high energies, it might be enough to supply the duants with a low voltage of about 10 V and the particles would gain the required energy of tens of MeV after several million cycles.. This would perhaps be possible for individual particles in principle. However, when accelerating a beam of many particles, mutual repulsive forces are manifested, scattering the beam, fluctuations and turbulence - if the path is too long, most particles would not reach the maximum radius at all, they would end up on the walls of the duants. For efficient acceleration, it is therefore desirable to use as high a voltage (amplitude) of tens of kV as possible to power the cyclotron duants, so that the number of cycles is max. several hundred.
Synchrocyclotron - relativistic
The principle of cyclotron operation outlined above will work at a constant frequency only until the mass of the accelerated particle can be considered constant, ie only in the non-relativistic region. If we want to use a cyclotron to accelerate particles to higher energies, when the speed of the particles is already comparable to the speed of light, the inertial mass of the particle m ceases to be constant, but increases with increasing speed: m = m
o/(1-v2/c2). At the same rate, the radius R = mo.v/[q.B.(1-v2/c2)] increases and the frequency decreases - at circulation of particles in a constant magnetic field: f = [q.B/(pmo)].(1-v2/c2). In order for the particle to continue to be accelerated even in this relativistic region, it is necessary to modulate the frequency of the accelerating voltage so that it is still in resonance with the frequency of the particle's circulation; or amplify the magnetic field. A cyclotron modified in this way with "synchronization" is called a synchrocyclotron or a relativistic cyclotron (the name "phasotron" also appears in the older literature). These devices work in pulse mode, where the frequency of the accelerating voltage on the duants is modulated and changes about 50 times per second, from about 25 MHz at the beginning of the cycle to about 12 MHz at the end of the cycle (depending on the strength of the magnetic field and the mass of the accelerated particles). Synchrocyclotrons are used to accelerate protons to energies up to about 1 GeV.
Isochronous cyclotron - relativistic
An alternative to the synchrocyclotron is the so-called isochronous cyclotron, which operates at a constant frequency and time-constant magnetic field, but the intensity of the magnetic field increases with radius; this is achieved by special shaping solenoid pole pieces *). This leads to greater curvature of the more distant path of the accelerated particle, compensation of the higher inertial mass of the particle and maintenance of the cyclotron resonance at a constant frequency
(and without the need for time modulation of the magnetic field strength). Isochronous cyclotrons are used for proton energies up to about 500 MeV, while in the continuous mode they are able to produce a significantly higher flux of accelerated particles than synchrocyclotrons in the pulse mode.
*) However, this radial gradient of the magnetic field has a diverging effect on the orbiting particle beam in the transverse direction. This must be compensated by so-called magnetic focusing: the pole pieces of the electromagnet are divided into several segments (mostly 8, is schematically shown in Fig.1.5.6 above) in which the magnetic gradients of stronger and weaker fields alternate in the azimuthal direction (modeled protrusions - segments - on the surface of the attachments), which have a focusing effect on the beam of moving particles. For better focusing, the segments of the pole pieces are often used they shape in spiral (Fig.1.5.6 above). The isochronous cyclotron is therefore also sometimes called the AVF (Azimutal Varying Field) cyclotron.
Acceleration of negative ions
In a cyclotron, heavy positively charged particles are accelerate as standard - protons, deuterons, alpha particles, or heavier nuclei such as carbon
12C. In special applications, however, an interesting modification is used to increase the "effective power" of the cyclotron: the acceleration of negative ions. Hydrogen or deuterium atoms are supplied with two electrons in an ion source in an electric discharge, creating negative H- or D- hydrogen
ions with two electrons. These are then accelerated in the cyclotron. The technology of accelerating negative ions in the cyclotron brings two advantages :
-> Possibility to produce more external radiation beams with different energies
A thin film is inserted into the path of accelerated negative ions in the appropriate path, which "strippes", removes their two electrons - the desired p
+ or d+ are created . This reverses the direction of their curvature in the magnetic field, which causes them to be rapidly brought out of the cyclotron field into the external beam of the corresponding energy. This technique thus allows the simultaneous production of several external beams of different energies, which can be used independently.
-> Possibility to increase the fluency power of the external beam from the cyclotron
For small cyclotrons used for the production of radioisotopes
(1.4, passage "Production of artificial radioisotopes") is an important requirement of high intensity - fluent power - proton or deuteron beams. At energies around 40MeV thrive achieve a relatively high current in the inner beam of about 2-5 mA. This maximum output can be used fully only during the irradiation of the internal target which is installed inside the vacuum beam tube. For routine production of radionuclides is however most advantegous bring out the particle beam to irradiate the outer targets. In conventional cyclotrons accelerating positive particles resulting beam extracted electrostatic deflector. At the baffle of the deflector is generated a considerable dissipative heat, which is a limiting factor for achieving a high fluency performance of the extracted beam.
   These disadvantages are largely eliminated by negative ion acceleration technology. After the necessary acceleration of the negative ions, efficient proton extraction takes place by stripping H
- in a thin carbon foil, which retains both electrons and releases a heavy positive hydrogen nucleus p+ or D+, with minimal thermal dissipation. This achieves significantly higher performance of radionuclide production in the outer target. This is especially important for the production of larger activities of short-term radioisotopes for scintigraphic diagnostics (4.8 "Radionuclides and radiopharmaceuticals for scintigraphy")  and biologically targeted radionuclide therapy (3.6 "Radioisotope therapy") in nuclear medicine.

S y n c h r o t r o n
To accelerate particles to very high energies, the radius of their orbits comes out too large in the circular accelerator, so that the cyclotron method with spiral motion of particles in a flat vacuum chamber is no longer practically applicable. In order for the perfect vacuum space not to be enormously large, as well as for electromagnets, it is necessary to use circular accelerators with a fixed circular path. In order for the charged particle to accelerate and stay on a solid circular path with radius R, it is necessary that with incresing velocity v(t) of the accelerated particles, both the frequency f(t) of the accelerating voltage and the intensity of the magnetic field B(t) increase synchronously with time. Magnetic field can no longer be constant, but is also a function of time B(t). Such a synchronously operating accelerator with a fixed circular path is called a synchrotron
(in the older literature there was also the name "synchrophasotron", "bevatron", "cosmotron").
   A schematic picture of its principle is in the right part of Fig.1.5.6. The particles are accelerated in a vacuum tube with a diameter of about 3-8 cm (mostly of elliptical cross-section), twisted into a circle with a diameter of hundreds of meters to several kilometers (!). The tube is surrounded by a large number of segments of dipole electromagnets (for large instruments even more than 1000 segments), which excites the magnetic field keeping the particles in a circular orbit. The synchrotron accelerates the already pre-accelerated particles, which are injected into the acceleration chamber from a suitable injector, which is usually a linear or circular accelerator with an energy of about 20-100 MeV *). Accelerated electrodes supplied with alternating high voltage are placed together with the magnets in suitable places of the circular path, the frequency f of which is synchronously modulated so that the particle comes between the electrodes at a time when the polarity ensures further and further acceleration of the particle. Simultaneously with the frequency, the intensity B
(for historical reasons called magnetic induction ) of the magnetic field also increases.
) Multi-stage pre-acceleration is also needed for large devices- first a linear accelerator, then a smaller synchrotron, which injects particles into the main accelerator (synchrotron); for the highest energies even a cascade of several synchrotrons in a row - see below "Large Accelerators", LHC.
   The synchrotron operates in a pulsed mode, where protons entering in the accelerator tube at regular doses from the injector at energies of the order of 100 MeV perform several million circulation during an acceleration cycle lasting about 3-5 seconds, accelerating to the order of 100 GeV to several TeV; the magnetic field increases from a tenth of Tesla to a few Tesla during the acceleration cycle. The acceleration cycle is periodically repeated about 5-10 times per minute.
   At the end of the acceleration cycle, the particles fall on either the inner target, or are led out by an electromagnetic field to the outer target, or are fed to an accumulation ring to realize particle interactions in the opposing beams. When a beam of protons, for example, hits a target, a number of particles of various kinds are formed, from which we can "separate" particles of the desired species with a system of electric and magnetic fields, focus them into a beam and aim them at another target. We obtain secondary bundles of eg antiprotons, pions, muons, kaons, hyperons. Variable electric and magnetic fields are used to separate particles, and magnetic lenses are used to focus the beams, mostly in a quadrupole arrangement, where two magnetic fields intersect, the gradients of which gradually focus the beam in the vertical and horizontal directions.
   At large values of radius R, which must reach several kilometers to achieve high energies of the order of hundreds of GeV, it is necessary that the cross-section of the accelerating tube is as small as possible - in order to achieve the required high vacuum (< 10-6 mm Hg) and that the costs of manufacturing electromagnets, as well as the demands on their electrical input, are not enormously high. After being injected into the accelerating tube, the particles make radial and vertical oscillations around their basic circular path. In addition, the particles in the beam tend to diverge in all directions because they are consistently charged and therefore repel each other. If the particles are not to impinge on the walls of the tube, the accelerated particles must be kept in orbit with high accuracy, so that the amplitude of the radial and vertical oscillations must be kept as low as possible, as well as the scattering of the particles. In other words, there is a need for strong focusing, in which the cluster of injected particles concentrates during acceleration and forms into an intense narrow beam rapidly flying particles. This strong magnetic focusing is realized so that the synchrotron electromagnet is composed of a large number of suitably shaped segments which have alternating positive and negative magnetic field strength gradients. These magnetic field gradients act alternately in the radial and vertical directions as continuous and scattering magnetic lenses, which ultimately lead to a double focusing of the beam in both directions. With newer large accelerators, the solenoid coils are often superconducting .
   Large synchrotrons are very expensive unique devices, built in major world research centers in the field of nuclear physics and elementary particles, mostly in broad international cooperation (construction costs amount to several billion dollars). The accelerator itself is followed by very complicated and precise detection apparatures and systems *), which analyze secondary particles and radiation generated during ultrarelativistic interactions of high-energy primary particles with the target material or with each other in opposing beams. By analyzing the type, charge and mass of these particles, their energies, momentum and emission angles from the site of interaction, a number of parameters of the interactions that occur can be reconstructed. From this it is possible to deduce the structure of elementary particles, the properties of acting fields and interactions, the existence of new hitherto unknown quanta and particles- see above "Analysis of the dynamics of particle interactions". The issue of large accelerators will be briefly discussed below - the section "Large accelerators".
*) For the methodology of radiation detection, see Chapter 2 "Detection and spectrometry of radiation", detection systems of high-energy particle interactions are generally outlined in 2.1, section "Arrangement and configuration of radiation detectors".

A circular induction electron accelerator is called a betatron (it produces "artificial
b- radiation", which are fast electrons, otherwise known from beta radioactivity). The principle of the betatron is schematically shown in Fig.1.5.7 on the left.

Fig.1.5.7. Left: Schematic representation of the betatron. Right: Schematic representation of a microtron.

The accelerating tube of the betatron has the shape of a ring (toroid) made of electrically non-conductive material (glass, porcelain) with a high vacuum inside. The tube is located ("strung" as one thread) between the pole pieces of the solenoid fed by alternating current. Electrons are injected into the accelerating tube at an appropriate time (the appropriate phase of the AC period) by an electron nozzle consisting of a hot cathode, a grid, and an accelerating and focusing anode - a similar "electron gun" as a screen. The time-varying magnetic field induces a swirling electric field in the tube, the electromotive force of which, directed along a circular path, accelerates these electrons.
   From an electronic point of view, a betatron is actually a "transformer" whose primary winding is supplied with alternating current and whose "secondary winding" (of one "thread") is an accelerating tube in which electrons, accelerated by induced electromotive force, move in a vacuum (instead of winding wires). In a circular orbit, electrons are maintained by a magnetic field. The acceleration of electrons occurs only in the first quarter sinusoidal course of alternating voltage in the electromagnet. At the appropriate moment of the ascending part of the sinusoid, electrons are injected, which are accelerated, the magnetic field increases, the electrons spiral inwards and orbit for some time along a stationary path in which they are constantly accelerated. After reaching the peak of the quarter-period, the vortex electric field weakens, reverses its direction, and the electrons would eventually be inhibited. At the same time, however, the magnetic field weakens and the electrons begin to spiral along the outer edge of the tube, where they hit the target or are brought out for external use.

Some types of betatrons have a radial magnetic field gradient and an acceleration phase set so that the electrons move in a spiral inward at the end of the acceleration cycle and the target is located at the inner edge of the accelerator tube.
   Electro-mechanical analysis of the trajectory of an electron during acceleration induced by an electric field E along a circular path of radius R (combining Faraday's law of electromagnetic induction u = -d
F/dt = 2p.R.c.E with an accelerating electric force along a circular path q.E, perpendicular Lorentz magnetic force q.[v x B] = q.v.B and centrifugal force m.v2/R) leads to the condition of equilibrium acceleration of the electron in the path of radius R: 2pR2.B = F, or magnetic flux F through the surface p.R2 the paths of the electron must be twice the flux that would flow through the path if there was a homogeneous magnetic field of intensity B over the whole surface. This "betatron condition" is ensured by a suitable shaping of the pole pieces of the electromagnet.
   The electromagnet of smaller betatrons is often powered by alternating current from a normal 220V electrical network with a frequency of 50Hz, the power input is units up to tens of kW. The radius of the circular path is tens of centimeters. During the acceleration cycle, which lasts about 5 milliseconds, the electrons perform about 2 million cycles, while the induced electromotive force accelerates to about tens of MeV. Then they hit either the inner target (while exciting the gamma braking radiation), or they are brought out in a beam - they are then used for electron irradiation, eg for technical or medical purposes. Hard gamma braking radiation has the same use.
   Betatrons are used for electron energies up to about 300 MeV. However, at high energies it is necessary (similarly to the cyclotron) to perform synchronization due to the increase in the mass of electrons with their energy. By combining the betatron and synchrotron principles, a betasynchrotron is formed which accelerates the electrons in a circular orbit inside the vacuum ring first on the betatron principle by means of alternating current electromagnets, after which this pre-accelerated electrons are further accelerated between the electrodes to which the synchronized frequency high-frequency accelerating voltage is applied.
   Smaller betatrons were widely used in radiotherapy in the 1970s-1990s
(see 3.6 "Radiotherapy"), mainly as a source of hard braking gamma radiation with energies up to about 40MeV. In recent years, however, betatrons have been virtually displaced by linear electron accelerators, which have the advantage of smaller dimensions, higher electron flux intensities, and easier beam modulation options.

A special, rarely used, type of circular electron accelerator is the microtron, sometimes referred to as the "electron cyclotron". Its activity is schematically shown in the right part of Fig.1.5.7. A flat cylindrical chamber with a high vacuum is placed in the magnetic field between the pole pieces of a strong electromagnet, similarly to a cyclotron, but instead of duants an electric acceleration system is mounted at the edge of the chamber - a cavity resonator, powered by high frequency voltage from a magnetron or klystron generator (frequency f is a few GHz). Electrons fly through this resonator many times, where they are returned in a circular orbit by a magnetic field, accelerating to higher and higher energy during each pass. Due to the increased kinetic energy, the radius of the electron path after each pass through the resonator is always larger and larger. In order for the electron to come between the resonator electrodes in the correct phase of the high-frequency voltage period and be able to be accelerated again, the resonance frequency condition 2
p.f = k.e.B/(mo.c) must be met, according to which the circular frequency of the accelerating voltage must be an integer k-multiple of said fraction, where e is the charge of the electron, B is the magnetic induction, m o is the rest mass of the electron.
   The electrons for acceleration are injected with an electron gun, or are obtained by emissions from the walls of the resonator. Microtrons are sometimes used to accelerate electrons to energies of several MeV, their advantage is the achievement of high flux intensities of accelerated electrons in the beam. Monoenergetic electron beams can be extracted from individual paths, lower energy electrons from smaller paths, of maximum energies from the largest path at the edge of the acceleration chamber.

Electrical supply of accelerators
The particles in accelerators obtain their high kinetic energy by the action of electromagnetic fields, ie by converting part of the electrical energy with which the accelerators must be supplied. Devices as complex, as accelerators in general must be equipped with complex electronic apparatus, containing several types and sources of electrical supply :
n The supply of accelerating electrodes
is the basic electrical supply, that supplies its own electrical energy to accelerate charged particles. X-rays tubes and electrostatic linear accelerators have a high DC voltage - tens of kilovolts, up to several megavolts. In high-frequency linear accelerators and circular accelerators, the accelerating electrodes are powered high-frequency alternating voltage with a frequency of the order of MHz to several GHz
(electronic circuits producing this RF voltage are briefly described below in the section "High-frequency voltage generators").
n Power supply of the ion source
The accelerating particles themselves are also obtained electrically in the ion source. It is simplest for electrons obtained by thermoemission from a glow cathode, which is powered by a glow current from a glow transformer
(220V is transformed to 6-24V, glow current about 2A-20A). Protons and heavier ions are obtained in an electric discharge supplied with a direct voltage of hundreds to several thousand volts.
n Power supply of magnetic solenoid coils
Strong solenoids are used to shape the path of accelerated charged particles, consisting of coils supplied with an electric current of many tens to several thousand amperes. With conventional electromagnets, it is energy-consuning, heat is generated, the electromagnets must be cooled. The largest part of the electrical energy for powering accelerators is mostly consumed by electromagnets. In newer large accelerators, superconducting coils are often used in electromagnets.
The issue of electromagnets in accelerators is discussed in more detail below in the section "Electromagnets in accelerators".
n Vacuum and cooling system power supply
To provide high vacuum in the accelerator tubes are used powerful vacuum pumps. Cooling the tube (along with superconducting electromagnets) to low temperatures can also help maintain a high vacuum, at which point any remaining air will freeze on the tube walls. In many electrically powered components, much of the electrical energy is converted into heat, which needs to be dissipated by ventilation system or other cooling systems. Although superconducting electromagnets do not generate heat directly, cooling helium must be recycled in liquefiers. All this technical "background" of the accelerator contains a number of electric motors, which are powered either directly from the AC network (220V), or are controlled electronically.
n Power supply for control and regulation electronics
The operation of accelerators is entirely conditioned by the exact time and intensity interaction between electric and magnetic fields in different parts of the accelerator system. This must be ensured by complex electronic circuits, currently controlled by digital computer technology.
Note: For the simplest "accelerator", which is an X-ray tube, the power supply diagram is drawn in Fig.3.2.2B in 3.2.2 "X-rays - X-ray diagnostics", part "Sources of X-rays".

High-frequency voltage generators
The acceleration electrodes of most types of accelerators are powered by alternating high-frequency voltage or RF electromagnetic waves. Frequencies of the unit up to hundreds of MHz can be prepared in conventional oscillators with inductive-capacitive LC circuits, equipped with tubes or, more recently, semiconductor transistors. Very high frequencies (needed, for example, for linear high-frequency accelerators, microtrons, etc.) arise in high-frequency generators, which are equipped with special tubes - magnetrons and klystrons, which can work as high-frequency oscillators with very high frequencies (HF) of the order of GHz. Gyrotrons are used for the highest frequencies.
The magnetron
is a cylindrical vacuum diode, the center of which is a heated cathode, around which is a coaxial anode. An electrical voltage is applied between the cathode and the anode. In addition, the diode is inserted into a longitudinal magnetic field (between the pole pieces of the electromagnet, for simpler applications a permanent magnet is sufficient), the direction of which is parallel to the cathode - Fig.1.5.8 at the bottom left. The electrons emitted from the cathode are thus affected by a combined cross-field - the radial electric field between the cathode and the anode and the longitudinal magnetic field of the outer magnet. The electrons emitted by the cathode are attracted to the cylindrical anode, but the paths of the electrons are curved by the Lorentz magnetic force, so that at a certain value of the anode voltage and the intensity of the magnetic field, the electrons no longer fall directly on the anode, but form a cloud circling in the space between the cathode and the anode. The anode of the magnetron is not a simple cylinder, but it consists of a metal block containing several (mostly 8) peripheral cavity resonators - Fig.1.5.8 at the top left.
   Electrons, during their circular motion as they pass around resonant cavities, release some of their energy and cause electromagnetic oscillations in the cavities. The most efficient transfer of energy to the electromagnetic field in resonators occurs at such a speed of electron movement that during its transition from one circumferential slit to another, the polarity of the field in the slit changes to the opposite; then the electron at each slit is braked and transfers energy to the field in the resonator. This synchronization (called
p- mode) is achieved by a suitable choice of anode voltage. Overall, the motion of electrons is quite complex. The oscillating electromagnetic field density modulates the rotating electron cloud - there is a clustering of electrons into bent rays in the shape of a "wheel with spokes" (the number of louvers is half that of the circumferential anode resonators) which rotate about an axis; it is only symbolically drawn in Fig.1.5.8 at the top left. It can be said that the whole magnetron system is put into a state of intense high-frequency oscillations (whose frequency is given by the mechanical dimensions of the resonators), in which the electrical energy of the flowing anode current is converted with high efficiency into oscillating field energy. The generated high-frequency signal is then output by antennas or waveguides for external use.

Fig.1.5.8. Physico-electronic principle of magnetron, klystron and gyrotron operation.
Top left: Cross section of a magnetron with the indicated movement of electrons between the cathode and the anode in a crossed electric and magnetic field. Bottom left: Connection and placement of the magnetron in the magnetic field - longitudinal section. Top right: A two- circuit klystron as an RF signal amplifier. Bottom right: Reflective single-circuit klystron as an oscillator and RF signal generator. Bottom center: Gyrotron with an indicated spiral motion of electrons in a strong magnetic field and the formation of electromagnetic oscillations in a cavity resonator.

Klystron (Greek klys = surf, waves crashing into the shore)
is also a vacuum tube in which electrons emitted by a heated cathode are accelerated and focused into a narrow linear beam by a hollow anode connected to a positive voltage. The kinetic energy of an electron beam (electron clusters) is converted into electromagnetic oscillations in resonant cavities. Klystrons are divided into two basic types :
A two-circuit klystron ,
where electrons from the cathode on their way to the anode first pass through one resonator, which modulates their speed, then the formed clusters of electrons pass through a second cavity resonator, in which oscillations are aroused when resonance is reached - Fig.1.5.8 top right. In the area between the two resonators, a magnet is sometimes placed around the tube to hold and focus the electron beam in the center of the tube. Electrons that have already transferred their kinetic energy are captured in the collector
(the rest of their energy is converted into heat there; in large devices, these electrons are returned to the space in front of the resonators to increase efficiency). If we supply the first (input) resonator with an external RF signal, then the oscillations excited in the second (output) resonator have a larger amplitude than the oscillations supplied to the input resonator - in Fig.1.5.8 on the right it is sybmolically indicated by an amplifying wavy line. This type of klystron serves as an amplifier of the RF signal. By introducing feedback (by electrically connecting the cavities of both resonators of a two-circuit klystron) it is possible to construct a generator of self-excited oscillations with high power, similarly to the reflex klystron below. For special purposes of RF technology, klystrons with a larger number of resonant cavities are also constructed - this achieves greater amplification and the possibility of tuning in a wider frequency range.
Reflective klystron ,
in which after acceleration and focusing of electrons by the anode into a linear beam, these electrons at the opposite end of the tube are reflected by a negative reflective electrode (repeller) and returned to the working space of the tube. The speed of the electrons inside the klystron is modulated by their interaction with a cavity resonator, in which the passing electrons evoke electromagnetic oscillations. Each electron passes through the resonator twice. In the forward direction, the electron flow is velocity- modulated, the electron clusters continue toward the reflecting electrode, where they stop, reverse, and in the opposite field move rapidly back to the resonator into which the electron clusters enter and excite this resonator. With the correct setting of the voltage on the reflecting electrode with respect to the geometric dimensions, the electron clusters enter the resonator always at the moment when the RF field has the maximum value of the opposite polarity and give it energy - resonance is achieved and, the oscillations are permanently maintained (Fig.1.5.8 at the bottom right). The electromagnetic RF signal is output from the cavity resonator by an antenna or a waveguide.
Comparison :

The magnetron achieves a relatively high efficiency of about 60-70% of the conversion of power supply to a high-frequency signal. Klystron, whose efficiency is somewhat lower (about 30-40%), but generates RF oscillations with a more stable frequency, with the possibility of its precise tuning and modulation. Magnetrons and klystrons are widely used in high-frequency technology - in UHF television broadcasting, satellite communication, radar technology, microwave heating (eg in microwave ovens, microwaves are excited by magnetrons); for us is important here its application in particle accelerators. They often work in pulse mode, achieving a respectable performance of up to hundreds of megawatts! In the area of lower powers, magnetrons and klystrons have recently been replaced by semiconductor components.
The so-called gyrotrons
(Greek gyros = turning, rotation, rolling, machining; also a rotating grill ) were constructed for the areas of the highest frequencies, Fig.1.5.8 in the middle at the bottom. They are vacuum tubes in which the electrons emitted from the cathode are accelerated in an "electron gun" by a voltage of tens to hundreds of kV and concentrated in a linear beam. There is a cavity resonator in the working space of the gyrotron and a very strong magnetic field is applied (approx. 3-8 T), excited mostly by a superconducting electromagnet. When moving in this strong magnetic field, the electrons circle in a spiral with a Larmor frequency f = e.B/(2p.me) depending on the intensity B of the magnetic field. As this electron spiral passes through the cavity resonator - if cyclotron resonance occurs - intense electromagnetic oscillations of high frequencies 20-250 GHz are evoked in it (resonance can occur at the fundamental frequency given by the dimensions of the resonator, or at higher harmonics). After passing through the resonator, the electrons that have already transferred most of their energy are absorbed in the collector. Electromagnetic waves are at the output by the waveguide for external use. In addition to microwave RF electronics, gyrotrons are so far rarely used for RF plasma heating in the most demanding applications, eg in the field of thermonuclear fusion in tokamaks (1.3, part "Fusion of atomic nuclei"; more than 20 powerful gyrotrons for deuterium-tritium plasma heating in a working toroidal tube are planned in the ITER tokamak under construction).
Note: The formation of electromagnetic oscillations in the cavity resonators of a magnetron and a klystron is sometimes explained simplified from an electronic point of view as follows: Individual chambers or cavity resonators can be imagined as small oscillating circuits - LC connected in parallel. The gap between the edges of the chambers acts as a small "capacitor" C (capacitance of pF units), the conductive inner sheath of the resonator represents a "coil" L. The generated magnetic field induces the opposite current, charging the "capacitor" to the opposite polarity ... etc ... - in the chamber there is an alternating current of high frequency f = 1/L.C, similarly as in the oscillating circuit LC.
Although this comparison is illustrative, it is not very suitable for accurate analysis, it is necessary to use the methods of wave behavior of the electromagnetic field.

Electromagnets in accelerators and other nuclear devices
An important part of most accelerators are electromagnets, which are generally used to shape the path of accelerated charged particles by applying a Lorentz force perpendicular to the speed of motion. These are dipole electromagnets for the basic curvature of the path, quadrupole electromagnets for focusing individual particles into a defined beam, sometimes even more complex shapes of pole pieces are used. In the classic design, the electromagnets are formed by coils wound with the required number of turns by insulated wire from a good conductor, mostly copper, on a suitable ferromagnetic core (forming a "pole pieces "). The strength of the excited magnetic field (magnetic flux density) is proportional to the electrical current through the coil. It is supplied either by direct current - a permanent electromagnets, or a variable or alternating current - gives the time varying or alternating magnetic field. The "auxiliary"coil for beam focusing, its corrections, output or separation, have this classic design for all accelerators. For smaller and older devices, this conventional electromagnets are also used for basic curvature of the particle beam in circular accelerators - cyclotrons and synchrotrons.
   In the case large high-energy cyclotrons and synchrotrons,
a very strong magnetic field is required to keep the particles in circular orbits, for the excitation of which an electric current of many tens to several thousand amperes must flow through the coils. When using conventional electromagnets, it is energy-consuming, heat is generated, the electromagnets must be cooled. For newer large accelerators, therefore, superconducting coils are often used in strong electromagnets :
Superconducting electromagnets
The physical principles of superconductivity have been briefly discussed above in the passage "Fermions as bosons. Superconductivity.". Let us recall only the basic fact that when some conductors cool to a sufficiently low temperature - lower than the so-called critical temperature Tc - their specific electrical resistance drops to zero ( ohmic resistance for direct current drops to practically zero; inductive component of resistance, impedance, for alternating current remains unchanged). In this situation, even a strong electric current flows through the superconductor with absolutely no heat loss. The most used superconducting material for electromagnets is the alloy niobium (53%) - titanium (47%) working up to 9 Tesla, resp. Nb3Sn, usable even above 9 T. So-called high-temperature superconductors have also been developed, which have a critical temperature higher than -196 C and can work instead of liquid helium even when using liquid nitrogen. However, it is not yet suitable for strong electromagnets, it is not possible to create long thin wires from them.
Material note :  
It is interesting that copper, which is one of the best electrical conductors at normal temperatures, can serve as a suitable insulating material for superconducting windings ! In the Kelvin units, however, copper does not go into the superconducting state, it has a resistivity many billions of times greater than the superconducting Nb-Ti, so it acts as an insulator relative to the superconductor. Superconducting wires are usually made up of a large number (at least several tens, but sometimes several thousand) of thin NbTi fibers embedded in a copper matrix (or suitable alloys of copper, nickel).

   Therefore, if we wind a coil made of superconducting material, when an electric current passes through its turns, a magnetic field is excited without heat loss in the winding - a superconducting electromagnet is created.. It can work in two modes :
l Continuous mode of power supply from an external current source - constant or time-varying, analogous to conventional coils. However, the advantage is the possibility of achieving a very strong magnetic field with low electrical consumption. Strong current is generated even at very low source voltage, without heat loss. Continuous mode is used especially where it is necessary to operatively change the intensity of the magnetic field - for example in a synchrotron or tokamak.
Persistent mode - in a closed superconducting winding, the electric current is excited once and then spontaneously maintained permanently, due to the absence of losses in the winding in the form of heat production. The lossless current circulating in the winding cannot decrease or increase unless electromagnetic energy is supplied or consumed from the outside. Of course, this also maintains a strong magnetic field - it is a persistent superconducting electromagnet with a short-closed winding in a very stable current and energy state. For superconductivity, however, the winding must be kept permanently at a low subcritical temperature of approx. 3 K in a cryostat using liquid helium *). Electricity is thus only needed to drive the cooling system. To create a magnetic field of about 3 Tesla, a superconducting coil with about 20,000 turns (with an inductance of several tens of Henry) with a current of about 500 amperes is typically needed. Persistent mode is used where we need it long-term stable magnetic field, eg in MRI nuclear magnetic resonance imaging.
*) This continuous cooling of the superconducting coil must be carefully monitored ! If, as a result of evaporation, the coolant level dropped so much that part of the winding warmed above the critical temperature, the superconductivity would suddenly disappear - the so-called quench (see below). At this point in the winding, an ohmic resistance would arise, the current through the winding would decrease rapidly, and the magnetic field would disappear. This would result in an electromagnetic induction of a large electromotive force in the winding. The considerable energy stored in the magnetic field would be quickly converted into induced current a winding that would heat up strongly with ohmic resistance, the rest of the coolant would boil up and the winding could burn out!

Fig.1.5.9. Left: The superconducting electromagnet consists of a coil wound from a superconducting material, placed in a cryostat with liquid helium. When exciting and damping the superconducting current in strong persistent electromagnets, a short-circuit with a temperature-controlled superconducting key (bifilar winding + heating wire) can be advantageously used.
Right: Temperature dependence of ohmic resistance of Nb-Ti superconducting material (for 1 m of wire 0.3 mm) .

"Switching on" (excitation or charging) and "switching off" (damping or discharging)
of a strong electric current in the superconducting winding of a large persistent electromagnet is a delicate matter! Considerable energy is stored in a strong magnetic field, so that due to electromagnetic induction in the winding, the superconducting current appears to have considerable temporal inertia. Therefore, switching on and off the superconducting current here cannot be done at once by a simple switch, as we are used to in conventional electrical circuits.
(this would lead to the induction of high voltage peaks and currents acting against a sudden change which could lead to a violation of the superconductivity), but it must be done gradually - continuously. Superconducting windings do not "tolerate" sudden current changes, which can also induce strong eddy currents in the copper matrix around the superconducting wires, or voltage spikes in other components. The excitation of the current in the closed winding of the superconducting coil requires a specific procedure.
   Current excitation is standardly maked by connecting an external source with a low voltage of about 10 V 
(sufficient to "push" the current increase of several amperes/min. against the inductive resistance of the coil) which is capable of supplying the required rated current (eg 500 A). The inductance of the superconducting winding resists the increase in current, charging takes about 50 minutes at controlled current rise approx. 10A/min. After reaching the required current (magnetic induction), the coil terminals inside the cryostat must be superconductively "short-circuited"; the external current source can then be disconnected (in the specific way described below) and the current through the coil then flows spontaneously "forever" *).
*) It is only approximately, the eternal flow of constant superconducting current is an idealization! In fact, even the superconducting current, and thus the magnetic field B, will decrease over time very slowly according to the usual exponential relation B(t) = B(0) .e- (R / L) .t, with time constant R/L, where R is the residual resistance caused by electrical connections and the effects of the magnetic field on the electron flux in the superconductor. In some devices, such as nuclear magnetic resonance, an appropriate correction (eg a small change in resonant frequency) is introduced for this gradual decrease .
   Disconnection of the external source after superconducting short-circuiting of the coil must also be performed continuously. Immediately after short-circuiting, a relatively small current will flow through the superconducting short-circuit, which will also be in the opposite direction than it is necessary to create a superconducting coil in a closed circuit. Abrupt disconnection of the external source at this stage would lead to a jump in current in the short-circuit line, which could impair its superconducting properties. The current that has flowed into the superconducting coil from the connected external source needs to be "redirected" in a controlled and smooth manner so that it begins to flow through the superconducting short circuit. It is therefore necessary to reduce the current flowing from an external source for a few minutes (which switches to the mode of a controlled current source with a low internal resistance - there is no need for a voltage acting against the inductive resistance of the coil) from face value to zero. The inductance of the main winding maintains the current, so that the superconducting short circuit gradually increases the current (which had a smaller value and originally the opposite direction just after the short-circuit!) up to the nominal value; only then do we disconnect the external source.
   To switch off or discharge the superconducting current, proceed in the opposite way: an external source set to nominal current (eg 500A) is connected to the external terminals, the superconducting short circuit of the coil is interrupted and the current in the source is gradually reduced with electronic control (approx. -50A/min.); after about 10min. is a superconducting electromagnet "discharged", with intensive cooling of the source.
   Superconducting short circuit or disconnection - "keying"- coil leads were previously made electro-mechanically. Now a temperature-controlled superconducting key is used: a longer superconductor
(bifilarly coiled to avoid an unwanted magnetic field) with a piece of resistance heating wire is connected in parallel to the main coil terminals inside the cryostat. If - when charging or discharging - the heating is turned on, the short-circuiting superconductor is swithed to the normal (resistive) state - short circuit is disabled (off). After turning off the heater bifilar coil cooled, to restore superconducting short-circuit and the superconducting current can flow continuously through the closed circuit, without an external source (Fig.1.5.9 on the left).
Quench of a superconducting magnet

An unplanned and uncontrolled sudden disappearance of a superconductivity, called a quench, is an unpleasant event for a superconducting magnet operating in a high-intensity mode. It can basically occur due to 5 causes :

Cooling fault - the level of the cooling medium drops so much that part of the winding warms above the critical temperature Tc and goes into the normal resistive mode (already mentioned above)...
Fault in the superconducting connection of an electrical circuit - a defect in material or an imperfectly made connection. At this place, a strong electric discharge (arc) occurs with rapid heating and melting of the components. The most serious accident of this type occurred in 2008 at a large accelerator LHC at CERN...
Too strong electric current - the critical current density Ic (approx. 1000-4000 A/mm2) will be exceeded, above which the material used already loses superconducting properties.
Too strong magnetic field - the critical value of magnetic induction Bc is exceeded, above which the used material already loses its superconducting properties and goes into the normal resistive mode.
Too high rate of change of the magnetic field - induced eddy currents in the supporting copper matrix can heat part of the winding above the critical temperature at some point by their thermal effects.
   If superconductivity were lost for any of these reasons, even in a small area of the electromagnet, an ohmic resistance would arise at this point in the winding, the current through the winding would drop rapidly, and the magnetic field would disappear. This would result in an electromagnetic induction of a large electromotive force in the winding. The considerable energy stored in the magnetic field would be quickly converted into an induced current by the winding, which would it warmed heavily with Joule's heat. The loss of superconductivity within a few seconds and the strong heating of the electromagnet has the irreversible nature of a chain reaction in which most of the refrigerant evaporates by boiling. It is very dangerous for workers near the electromagnet, which can be permanently damaged..!..
   Strong electromagnets, often superconducting, are used in addition to accelerators in other devices of atomic and nuclear physics, industry, medicine. The most powerful electromagnets are used in tokamaks to magnetically hold high-temperature plasma for thermonuclear fusion (1.3, part "Tokamak"). Medium - sized superconducting electromagnets (approx. 1-5 T) are routinely used in nuclear magnetic resonance to achieve the basic orientation of the magnetic moments of nuclei (3.4, part "Nuclear magnetic resonance").

Large accelerators
   For research in the field of (elementary) particle physics, large unique accelerators are being built in an effort to achieve the highest possible energies of accelerated particles. Their task is a detailed investigation of the properties of particle interactions - specifying the mechanisms of interactions of already known particles and finding new particles. Large accelerators (especially synchrotrons) were built, for example, in FermiLab near Chicago, in Brookhaven near New York, at CERN, in Dubna or Serpukhov. New discovery results have been or are expected on each of these accelerators. Recently, interactions of accelerated particles in colliders have mostly been used. Here are just a few of the biggest accelerators from recent years in the table :

Accelerator name Laboratory Particle Energy [GeV] Year
SLAC (Stanford Linear Accelerator Center) Stanford e - - e + 50 1966
Tevatron Fermilab p + - p - 980 1987
LEP (Large Electron-Positron collider) CERN e - - e + 100 1989
RHIC (Relativistic Heavy Ion Collider) Brookhaven p - p, Au - Au, ... 200 2000
LHC (Large Hadron Collider) CERN p - p, Pb - Pb, ... 7000 2008
VLHC (Very Large Hadron Collider) - the future ?? p - p, ..... ? >> LHC? ? > 2030?
CLIC (Compact LInear Collider) - the future ?? e - - e + 3000 ??

Large Hadron Collider (LHC)
  The largest accelerator so far has currently been built at the Central European Nuclear Laboratory CERN (Centre Europeen pour Recherche Nucleaire)
*) on the Swiss-French border under the name LHC - Large Hadron Collider in 2008.
*) The
name "nuclear research", coined when the institute was founded in 1954, is no longer entirely apt. The original field of nuclear research has long been transformed. CERN's main focus has been research in the deep subnuclear field and mainly in particle physics for several decades, often without direct connection to atomic nuclei. The name "European" has also been extended, and experts from non-European countries are also collaborating on many projects.
   The LHC is a synchrotron (the principle of operation was described above, Fig.6.6.5 on the right), whose ring is located in the tunnel after the previous electron accelerator LEP about 100m underground (50-150m below ground), its circumference is 26.66 km long. The system of magnets along the path of the accelerator is very complex. The circular path of the accelerated particles with high accuracy is ensured by more than 1200 superconducting dipole electromagnets around the circumference of the tube. Furthermore, there are almost 900 quadrupole magnets even more complex shapes, for focusing the beam of accelerated particles, correction and modification of the path shape. The conductors of the superconducting electromagnets are made of niob-titanium alloy and operate at a temperature of 1.9 K. The actual acceleration of protons or heavier ions occurs in one segment of the ring, where a system of radio frequency resonant cavities is located, powered by an intense high-frequency voltage of 400 MHz . The magnetic field curves the paths of the charged particles exactly along the central circumference of the tunnel and returns them periodically to the acceleration cavities. In one cycle, the kinetic energy of the proton increases by 480 keV.
   The LHC, as a synchrotron, needs particles already pre-accelerated for its operation (see Fig.1.6.5 on the right). In the case of such high energies, the protons are even 4-degree pre-accelerated, for which the previously constructed accelerators at CERN are used, arranged in series according to the size of the achieved energies. The protons obtained by hydrogen ionization are first accelerated in a linear accelerator (LINAC) to an energy of 50 MeV, from where they are fed to a circular accelerator PS "booster", where they obtain an energy of 1.4 GeV. They are then routed to the Proton Synchrotron Ring (PSR) with an output energy of 25 GeV and finally to another Super Proton Synchrotron (SPS synchrotron), which gives them an output energy of 450 GeV. With this initial energy, they are injected for final acceleration into the LHC ring, where they will be accelerated to an output energy of 7 TeV during many cycles, wherein the magnetic field in the electromagnet segments changing from an initial value of 0.5 T (at 450GeV) to 8.3 T (at 7 TeV) during each cycle, the current in dipole electromagnets reaches more than 10000 A. The increase in kinetic energy in the LHC from the initial 450GeV to 7TeV takes about 30 minutes. Since synchrotron operates in pulsed mode, the protons are accelerated in groups or clusters (bunches). Protons accelerate in two tubes (rings) in opposite directions for interactions in the colliding beams. At speeds approaching the speed of light (99.999995% c), the proton in the LHC will make more than 11,000 circulations/second. In colliding beams, 1 collision per 10 billion particles is produced, at full power there is more than 30 million collisions per second. The total energy of the proton beam reach up to 350 MJ. In addition to protons, the LHC can accelerate also heavier nuclei, especially lead nuclei (for the ALICE experiment, mentioned below).

There is four places around the perimeter of the LHC, where the tubes connect and the opposing beams of particles intercect - there are interactions in the colliding beams. These places are surrounded by large and complex detection systems (cf. 2.1, passage "Arrangement and configuration of radiation detectors"), by means of which six main experiments are performed :
ATLAS (A Toroidal LHC ApparatuS )
is the largest detection system (weighs about 7000 tons), the main carrier program of the LHC. Comprehensively measure and analyze particles arising from proton collisions with an energy of 14TeV. The ATLAS detection system (and also the CMS below, partly ALICE) has a cylindrical coaxial arrangement similar to that in model figure 2.1.2 in 2.1, passage "
Arrangement and configuration of radiation detectors"), but much more complex, it is the most complex and expensive detection device in history !
   The inner part of the detector, which records the trajectories of charged particles flying out of the collision site, consists of three coaxial layers ("shells") of trajectory detectors (trackers): the lowest are pixel semiconductor detectors, then strip detectors and transient radiation detectors. The whole system is located in a strong longitudinal magnetic field 2 Tesla of a superconducting solenoid electromagnet; from the curvature of the particle paths in the magnetic field, the charge and momentum of the particles can be determined.
   Another layer of the detection system is a spectrometer, called a "calorimeter", whose task is to absorb the energy of the flying particles and quantify it (its "sample") using output electrical pulses. It consists of two parts: electromagnetic calorimeter for measuring the energy of photons and electrons and hadron calorimeter ....
   Last, the outer layer of the ATLAS detector consists of a muon spectrometer, designed to detect high-energy muons that are able to pass through the calorimeter layer. By analyzing the orbits of muons curved by a strong toroidal magnetic field, their momentums and signs of electric charges can be determined. Drift tube and multi-wire ionization chambers are used to detect muon trajectories.
CMS (Compact Muon Solenoid) detector ,
optimized for detailed analysis of muons, cooperates with the ATLAS system for comprehensive analysis of high-energy interactions. Its structure is similar to ATLAS. For the analysis of trajectories of fast muons, the detection system includes a large cylindrical electromagnet (solenoid), creating a magnetic field with a force of 4 Tesla.
The ATLAS and CMS detection systems serve primarily for study of new particles, especially the Higgs bosons (discussed in more detail above in the section "Hypothetical and model particles"). If its decay went electromagnetically directly to the high-energy pair g, or (via W-bosons) to electrons and positrons, these secondary particles would be captured in an ATLAS or CMS electromagnetic calorimeter. When decaying into muons (via Z-bosons), the muon detection part of the CMS would come into play. And all charged particles can leave their traces in the intrinsic trajectory detectors (trackers) of both systems.
ALICE ( A Large Ion Collider Experiment )
is another experimental system whose task is to study the collisions of nuclei ("heavy ions"), especially lead, at center of gravity energies up to 5 GeV/nucleon and to investigate the properties of the resulting quark-gluon plasma
(see above "Quark -gluon plasma"). Like ATLAS and CMS, ALICE has a cylindrical coaxial arrangement of a large number of detectors, designed to register and reconstruct the parameters of mainly charged particles arising from nuclear collisions. It is used to study extreme states of matter (nuclear, hadron) under similar conditions as in the universe at the beginning of the hadron era, in the first microseconds of the universe (see 5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe.", in "Black Holes and the Physics of Spacetime", part "Stages of the evolution of the universe - Hadron era").
TOTEM ( Total Cross Section, Elastic Scattering and Diffraction Dissociation )
serves to accurately measure the effective dimensions of protons - effective cross sections - for different types of interactions. Is also used for calibration measurements of LHC properties (such as "luminosity" - the efficiency of collision production in the accelerator). It is consist of 8 detectors, located very close to the colliding beams at the CMS detector.
LHCb ( Large Hadron Collider beauty )
has a task to study the violation of CP symmetry in the decay of B-mesons containing a heavy (second heaviest) b-quark. During high-energy proton collisions in the LHC, a large number of pairs of b-b' quarks-antiquarks are formed, and their hadronization results in B-mesons and baryons. The mode of decomposition of these particles is sensitive to the disruption of CP symmetries - if matter behaves slightly differently than antimatter. The particles are first localized by a VELO detector (VErtex Locator), located near the collision site. Identification of particles before and after passing through a dipole magnetic field is performed using two ring imaging Cherenkov detectors RICH (Ring Imaging Cherenkov detectors)
- see 1.6, passage "Cherenkov radiation" and 2.4, passage "Cherenkov detectors". The RICH1 chamber is located just behind the VELO detector, behind the magnet is a particle traces detector, followed by the RICH2 chamber for the identification of particles with high momentum. Also included are electromagnetic and hadron calorimeters for measuring particle energies. Finally, the muon chambers are located. These results could be interesting in terms of the imbalance of matter and antimatter (baryon asymmetries) in the early stages of the evolution of the universe - why there was an excess of matter over antimatter (5.4 "Standard Cosmological Model. Big Bang.", passage "Baryon asymmetry of the universe" book "Gravity, black holes and space - time physics").
LHCf ( Large Hadron Collider forward )
study high-energy particles generated "forward" in the direction of the proton beam. The LHCf spectrometer (calorimeter) focuses mainly on neutral energy particles (
g photons, neutral pions, neutrons) emitted at small angles; charged particles can be registered by trackers in ATLAS and CMS, particles emitted at large angles in addition by calorimeters and muon spectrometers of both systems. These complex measurements simulate cosmic radiation and study the cascades of particles arising from its interactions (cf. Fig.1.6.7 in the passage "Cosmic radiation", 1.6).
  Already during the planning and construction, physicists promised, among other things, this large accelerator that the energy of collisions in in the LHC could be sufficient to experimentally find the so-called Higgs bosons, so far hypothetical model particles, generating the masses of some elementary particles - quantum fields, especially bosons W and Z of electroweak interaction (mentioned above in the passage "Hypothetical and model particles"; see also B.6 "Unification of fundamental interactions. Supergravity. Superstrings" in book "Gravity, black holes and space-time physics", part "Global and local symmetry; Calibration fields"). This is truly fulfilled !
Also the lightest supersymmetric particle (LSP - Lightest supersymmetric particle), when perhaps these interactions could be detected. The possibility of obtaining circumstantial evidence for extra-dimensions is also discussed assumed by some unitary field theories (see a few lines above B.6 ) - that has not yet been fulfilled...
Discovery of the Higgs boson 
At the ICHEP2012 conference in Melbourne, Australia, on July 4, 2012, the discovery of a new boson whose properties are consistent with the Higgs boson was announced based on data from ATLAS and CMS experiments at CERN. Careful analysis of about 60,000 cases of photon pair detection (derived from high-energy proton collisions) found a small
(but significant, about 160 photon pairs) peak on the curve [number of photons -to-energy], in the energy range around 126 GeV. This peak should probably come from the 2-photon decay of the Higgs bosons. The level of reliability of detecting a new particle by detecting its decay products is 5s. Further experiments are needed to make sure it is a Higgs boson and not another unknown particle. For this discovery, the Nobel Prize was awarded to P.Higgs and F.Englert in 2013.

Source: CERN-LHC
Discovery of the Higgs boson at the LHC great accelerator by detecting its decay products - here two opposite photons of gamma specific energies on the ATLAS detection system.

The imposing system of the LHC accelerator and detection apparatus is the most complex and sophisticated work that humanity has created in its history! Details of the design, construction progress and results of experiments at the LHC are listed on the official CERN website: http://lhc.web.cern.ch/lhc/.
Dangers from large accelerators ?

In connection with the design and operation of large accelerators, there are occasional speculations and alarming reports in the mass media, that the energy of colliding particles is so great that the interaction may create a "black hole" or even a new "big bang", which could allegedly endanger us, or even devour and destroy the Earth and the whole universe !! These speculations stem from a misunderstanding of the issue, they are physically completely unfounded and erroneous, for at least two reasons :
1. Even if a high-energy interaction created a black hole (which would be very interesting), due to the small total energy, it would be a microscopic black hole that would immediately quantum evaporate and disappear - sending energy particles (less energy than had the original particles). Such a black micro-hole therefore does not absorb anything
(it is not capable of that, cf. 4.7 "Quantum radiation and thermodynamics of black holes" of the above-mentioned book "Gravity ....."), can only be virtual; it would be very difficult to prove it at all.
2. Particles with much higher energies (even 9 orders of magnitude higher!) commonly occur in cosmic rays
(see 1.6 "Ionizing radiation", part "Cosmic rays"), interact and collide with other particles in space and in the Earth's atmosphere for billions of years already, without something "catastrophic" happening.

Conceptual perspectives of large accelerators
Circular or linear accelerators ?
Although the principle of circular acceleration of charged particles is very successful and effective, it seems that circular accelerators have already approached the limits of their possibilities in terrestrial conditions. If we wanted to accelerate charged particles to even significantly higher energies at realistically available circular orbital diameters (ie accelerator tube diameters), the phenomenon of synchrotron radiation *) would be increasingly applied, which would carry away a significant part of the kinetic energy of particles and ultimately prevent further acceleration. Thus, it seems that future accelerators for the highest energies in terrestrial conditions will have to be linear. The length of linear accelerators to achieve high energies is many kilometers. This is also a limiting factor in terrestrial conditions.
*) Synchrotron radiation arises as braking radiation due to the uneven movement of electrically charged particles in a circular orbiting. According to the well-known Larmor formula of electrodynamics, the intensity of this radiation is proportional to the electric charge and the square of the acceleration of the particle motion, here it is a centripetal acceleration of the circular motion. Thus, at a given kinetic energy, the intensity of synchrotron radiation is inversely proportional to the square of the particle mass. This phenomenon therefore applies mainly during the circular acceleration of light particles, electrons, which move at high speeds and with high radial accelerations when high kinetic energies are reached. Due to their high mass, protons emit synchrotron radiation a million times smaller.
  Linear colliders have another disadvantage: while in circular colliders the accelerated particles magnetically return repeatedly to the interaction site and their paths intersect many times, in linear colliders the accelerated cluster of particles meets its opposing cluster only once and most particles flying through away - their energy is lost. Therefore, a certain "recuperation" of the energy carried by the beam of particles passing trought the interaction areras is considered: these particles would, after passing trought the interaction region, can successively transfer their energy to the accelerating structure in opposed linear accelerator. Another option is to use particles that have flown through the interaction region without interaction, for the experiments on fixed targets.
The proton or electron accelerator ?
Protons and electrons (incl. positrons) in terms of its characteristics and structure are very different particles, which manifests itself by different mechanisms of interaction. Protons have a complex internal structure quarks interacting via gluon field. In their high-energy collision, they do not interact as a whole, but the energy of interaction will be divided to individual quarks, while in the gluon field a larger amount of other particles is produced - two- and three-quark combinations, mesons and baryons. Although these processes are important for studying the strong interactions and properties of hadrons, the energy of the interaction is "comminuted" into a large number of secondary particles; energy concentration per small number of particles cannot be achieved. About 1/2 of the proton's momentum is carried by gluons, 3 quarks are bound in the proton. For each quark, there is about 1/6 of the momentum of the proton, so the effective energy of quark interactions is E
ef E/6 (in an electron-proton collision it is roughly Eef E/6). During proton collisions, all quarks enter into interactions, which "infest" the detection space around the interaction site with a number of secondary particles (Fig.1.5.1G, H). In this "ballast" it is very difficult to "find" (separate) rare cases of the desired interaction of one of the quark pairs.
  An electron, on the other hand, is a practically point particle without an internal structure (at least in the spatial scales known and available to us). During a high-energy collision, therefore, the electrons interact as a whole (Eef = E), significantly fewer secondary particles are formed, on which it is concentrated significantly more energy. Therefore, for the search for new massive particles, the interactions of accelerated compact electrons are more advantageous than intricately structured protons. Simply put, at high energies, electron collisions are "harder" than proton collisions. Electron collisions are significantly "purer" than proton collisions, they produce much fewer secondary particles (compare the corresponding Feynman diagrams in Fig.1.5.1). The advantage is therefore the lower radiation background of uninteresting particles, among which it is easier to find the desired massive particles. Thus, it appears that large electron accelerators - opposite-electron-positron collisions - will be more advantageous for achieving the highest actual energy concentrations during interactions.
Note: The designers from LHC accelerator at CERN to date are already designing the construction of a large electron-positron collider called the CLIC (Compact LInear Collider) with 3 TeV energy.
Muon accelerators ?
In order to achieve the highest possible energy that would be available for the creation of new particles during the collision, proton and electron accelerators therefore have certain limitations. Circular electron accelerators at a technically achievable diameter have limitations due to synchrotron radiation. Linear accelerators, in turn, have limitations in the technically achievable length of the acceleration path. Synchrotron radiation is weak for protons and antiprotons, so we can accelerate them to significantly higher energies. However, protons and antiprotons are not basic compact particles, but composite particles with a quark-gluon structure. In a collision, "whole protons" do not collide, but always only one elementary particle inside each proton; others fly by without the direct desired interaction. During the collision, only a fraction of the energy of the accelerated proton is available for the creation of new particles. A large number of particles fly out from the collision site, most of which do not carry information about the direct collision of two quarks.
  A certain potential option to largely bypass these limitations and obtain suitable elementary (structureless) particles accelerated to very high energy, which will be entirely available for the creation of new particles upon collision, is the acceleration of m muons. Muons (mentioned above in the passage "Muons m and tauons t ") are particles very similar to electrons and positrons e. They have the same electric charge, are elementary and behave like point particles. From the electron, the muon differs in mass - it is 206 times heavier than the electron - and it is unstable - with a lifetime of 2.2 microseconds, it decays into an electron and two neutrinos.
  The instability of muons T1/2=2.2 ms is not so extreme (in contrast to pions) that it completely precludes the possibility of their acceleration. In co-production with the relativistic time dilation of the special theory of relativity, it enables multiple movement at speeds close to the speed of light along a circular path in the accelerator for a period of about 0.1 s., sufficient for effective acceleration. The great advantage of muons is their relatively high rest mass, 206 times greater than that of electrons. This makes it possible to accelerate muons in a ring accelerator to very high energies (similar to protons) with almost no unwanted energy loss effect from synchrotron radiation.
  Several steps are required to create a bunch of accelerated muons :
=> Accelerate protons to high energies higher than about 300 MeV. => Let them hit the target
(metal or plastic). => This creates a shower of particles containing fast charged pions. => The pions then rapidly decay into muons and anti-muons. => These are led into the counter-current acceleration rings of the synchrotron - collider, where they are accelerated to high energies and then allowed to collide.
  The result would be net collisions at high energies between point particles where 100% of their energy is available for the creation of new particles. A relatively "clean" signal would arrive at the detectors from the collision site, without excessive contamination by parasitic interactions. The expected disadvantage of this technologically complex process of creating, collecting and collimating muons and antimuons, will be a significantly lower frequency of collisions (about 10-5-x compared to an electron-positron or proton-proton collider), so it will be difficult to accumulate the necessary statistics to prove the discovery of new kinds of particles..?..
  Muon accelerators - colliders - can be promising for obtaining high energies due to minimal synchrotron radiation and for the realization of "clean" collisions, in which all the energy is available for the creation of new secondary particles.
Space accelerators
These technical problems and limitations are mostly due to the terrestrial conditions in which the accelerators are constructed. Many of these problems would automatically eliminated, if we installed accelerators outside the space of our Earth. The design of accelerators in universe has several principal advantages :
Plenty of free space
for the installation of even the largest accelerator systems.
Weightless condition
There is no need for robust constructions ensuring mechanical strength. It is also possible, without structural interventions, to make changes to the position and reconfiguration of individual parts of the acceleration system in space.
High vacuum ,
which is available everywhere, throughout the space, "free". Thus, there is no need to design accelerating tubes in which it is difficult to maintain the necessary vacuum in terrestrial conditions. Accelerated particles can move in free space along paths precisely determined and shaped by the magnetic field.

Low temperature (when shielding from sunlight, or in outer space) ,
which automatically ensures superconductivity with suitable materials. Coils of electromagnets therefore it is not necessary to cool, the once excited current will be permanently maintained and excite a permanent magnetic field for the necessary curvature of the paths of the accelerated charged particles. Even electromagnets with a time-varying magnetic field will work without energy losses by heat.
  However, in the current state of our technology, the real use of these fundamental advantages is hindered by technical problems that are very difficult to solve. It is primarily the transport of heavyweight construction material (hundreds of thousands of tons) from the Earth's surface, against gravity, into orbit around the Earth, or even into outer universe. We do not yet have the technical means to do so, the current rockets are too weak, slow and inefficient. Furthermore, it is a question of remote power supply and also ensuring the exact position of the individual parts of the acceleration system with submillimeter accuracy. Only the area of transmission of measured data from particle interactions would be solvable by means of our current electronics (which in recent decades - as the only technical discipline - has made significant qualitative progress!).
  In the future, experiments with particles accelerated to the highest energies can be expected to move from Earth to universe ...

1.4. Radionuclides   1.6. Ionizing radiation

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Vojtech Ullmann