As noted in § 184, the laws of the photoelectric effect were explained in 1905 by A. Einstein using the concept of light quanta (photons). According to these ideas, the energy of the electromagnetic field cannot be divided into arbitrary parts, but is always emitted and absorbed in certain portions equal to . Here is the oscillation frequency for the radiation, and is Planck’s constant. It is these portions of the energy of the electromagnetic field that are called light quanta or photons.
The quantum nature of electromagnetic radiation usually manifests itself in such experiments when the energy of each photon is sufficiently high and the number of photons is not too large. But in many optical experiments in which the wave properties of light are clearly observed, we encounter the opposite situation, when the photon energies are small and their number is very large (see example in § 184). That is why the quantum nature of light has long eluded the attention of researchers.
As mentioned earlier, in experiments on the photoelectric effect on conductors, it was discovered that the maximum kinetic energy of electrons emitted under the influence of light (the so-called photoelectrons) is related to the work function and the frequency of electromagnetic waves irradiating the conductor by the relation
This relationship was confirmed in 1916 by the American physicist R. Millikan. Millikan's subtle and careful measurements, carried out according to the experimental scheme described in § 183, made it possible to establish a linear relationship between the maximum energy received by an electron from light and the frequency of this light, to determine the universal nature of Planck's constant and to measure this value 
. In further experiments, the frequency of radiation incident on the metal surface varied over a wide range - from visible light to X-rays, and throughout the frequency range studied, the measurement results turned out to be in excellent agreement with the theory.
In experiments with X-ray radiation, ideas about quanta were subjected to particularly thorough and comprehensive testing. Indeed, visible light quanta (photons) have very low energy - for example, for yellow light and 
. Therefore, to register such light in most experiments one has to deal with a large number of photons per unit time. In accordance with this, the action produced by randomly distributed light quanta flying in all directions is difficult to distinguish from the action of a wave spreading uniformly in all directions. The greater the energy of the quanta, the easier it is to observe the action of an individual quantum and, therefore, it is easier to carry out an experiment to observe the spread of radiation energy not evenly in all directions, but in flashes in one direction or another. The energy of photons in the X-ray region of the spectrum significantly exceeds the energy of photons of visible light. In addition, in experiments with X-ray radiation, it is easier to implement the conditions for the emission of a small number of quanta per unit time.
To obtain x-ray radiation, it is necessary to bombard the anode of the x-ray tube with electrons (see §§ 151, 153). Any stopping (braking) of electrons in the anode substance is accompanied by the emission of X-rays. The theory of light quanta predicts that in the most favorable case, the entire kinetic energy of the electron after it stops will be completely converted into a single photon, the energy of which is determined from the condition. If the electron was accelerated by a potential difference, then.
So, the maximum frequency of X-ray radiation is given by the relation
Indeed, measurements confirmed that the X-ray spectrum in such experiments is characterized by a short-wavelength boundary
where is the speed of light, and the maximum frequency of radiation is consistent with condition (209.2). Shorter waves (higher frequency values) are never observed, but more long waves correspond to the transformation of only a part kinetic energy electron into x-rays. Determination of the short-wavelength boundary of the X-ray spectrum can be performed very reliably. Therefore, such experiments were used to determine the value of Planck’s constant (in accordance with (209.2)). The best measurements made by this method gave . These data are consistent with the measurement results in experiments on the photoelectric effect. Thus, the quantum theory is well confirmed not only by experiments on the absorption of radiation energy (photoelectric effect), but also by experiments on its emission.
By adjusting the number of electrons bombarding the anode of the X-ray tube, we can change the number of X-ray photons emitted. If we now expose a metal plate to X-ray radiation, thereby causing the release of photoelectrons, then, as experiments show, the kinetic energy of these electrons will be equal to the energy of X-ray quanta (since the energy of electrons and X-ray quanta in such experiments is tens of kilovolts, then the work function of electrons from metal - a few electron volts - can be neglected).
Thus, the entire cycle of energy transformations in these experiments looks like this: 1) transformation of work electric field into the kinetic energy of an electron in an X-ray tube; 2) conversion of the kinetic energy of the electron into the energy emitted by the electron during sharp braking of the X-ray quantum; 3) absorption of a photon by an electron and conversion of its energy into the kinetic energy of a photoelectron:
Such experiments can be greatly diversified by taking advantage of the convenient conditions of experiments with X-ray radiation. All of them show that energy is transferred in these phenomena in concentrated portions, and does not accumulate gradually, as would be the case with a continuous transfer of energy in the form electromagnetic wave. One of the most convincing experiments of this type was carried out by Abram Fedorovich Ioffe (1880-1960). Direct experiments were also carried out to record individual photons, showing that the energy of X-ray radiation propagates from the anode of the tube in different directions not simultaneously, but in the form of portions (quanta) flying in one direction or the other.
Thus, the study of the photoelectric effect and experiments with X-ray radiation have convincingly shown that light behaves in these phenomena not as a wave, but as a certain particle - a photon, which is formed during radiation, flies in some direction and, when absorbed, gives up its entire energy another particle. But if a photon behaves like a particle with total energy, then it must also have a certain momentum. A photon has a speed equal to the speed of light. Therefore, from the general formulas of relativistic mechanics (see §§ 199, 200) it should be expected that it will have momentum
(209.3)
As we have seen before (§200), distinctive feature photon is equal to zero of its rest mass: a photon always moves at the speed of light and cannot exist as a particle at rest.
The fact that photons have momentum follows indirectly from experiments on light pressure (§ 65). The ability of light to exert pressure on a reflecting or absorbing surface should be interpreted as the result of the transfer of momentum by photons, just as gas molecules reflected from the wall of a container transfer momentum to it and exert pressure on it (see Volume I).
A very important role in the development of ideas about photons as some elementary particles was played by the experiments of the American physicist Arthur Compton (1892-1962), in which it was directly shown that photons in collisions with electrons behave like particles with energy and momentum related to each other by the relation (209.3).
While studying the scattering of X-ray radiation in a substance made of light atoms (Fig. 371), Compton in 1923 discovered that in this case a change in the wavelength of X-ray radiation occurs, and he established a connection between the change in wavelength and the scattering angle:
(209,4)
Rice. 371. a) Scheme of Compton's experiment. b) Spectrum of scattered X-ray radiation
Here the constant was originally determined from experience. The results of these experiments contradict the classical ideas about the scattering of electromagnetic waves by atoms, according to which an atom, under the influence of incident radiation, should experience forced oscillations and become a source of scattered waves having the same frequency (i.e., the same wavelength) as the incident wave.
The phenomenon discovered by Compton was, however, perfectly interpreted using the concept of photons. Compton's experiments were carried out with x-ray quanta with energy . This energy is large compared to the binding energy of electrons in light atoms (several electron volts). Therefore, we can assume that in the experiments a collision of a photon with a free electron (and not with an atom as a whole) occurred, reminiscent of the collision of elastic balls. Applying the laws of conservation of energy and momentum (Fig. 372) to this collision, we obtain
(209.5)
Rice. 372. Elastic collision of a photon and an electron. Before the collision, the electron is at rest: - the momentum of the incident photon, - the momentum of the scattered photon, - the momentum of the electron, - the angle of scattering of the photon
When determining, one should take into account the vector nature of the law of conservation of momentum and use the trigonometric theorem on the relationship between the lengths of the sides of a triangle (Fig. 372).
When high-energy X-ray photons are scattered, the recoil electrons that receive momentum from these photons can have speeds comparable to the speed of light. Therefore, one should take into account the relativistic growth of their mass and use the laws of relativistic mechanics (see §§ 199, 200), as was done in (209.5). The solution of the system of equations (209.5) leads, after some transformations, to a quantitative explanation of the relation for the Compton effect (209.4), previously established experimentally (see Exercise 19 at the end of the chapter). Subsequently, in experiments with very high energy quanta, Compton scattering was discovered not only at interactions with electrons, but also with other particles, for example with protons and neutrons. Thus, in these experiments it was directly established that the photon behaves like an elementary particle not only in the phenomena of the photoelectric effect and radiation, but also in the processes of interaction with electrons and other particles.
Subsequent experiments confirmed the idea that a photon is a certain particle. Processes have been found in which a photon, when interacting with atomic nuclei, disappears, and instead a pair of elementary particles is formed: an electron and a positron (a particle having the mass of an electron and a positive charge equal in absolute value to the charge of an electron), and the nucleus remains unchanged (see § 223). In these experiments it was proven that electrons and positrons are not released from the nucleus, because the nucleus remains unchanged, but arise under the influence of light. The scattered electron, positron and nucleus have energies and impulses that they borrow from the disappeared photon.
Was discovered and reverse process, when an electron and a positron, interacting with each other, cease to exist as elementary charged particles: their charges are mutually neutralized, and their rest energies are converted into the energy of a pair of photons formed in this process, scattering at the speed of light.
As we will see later (Chapter XXV), such mutual transformations of some particles into others are a very important and characteristic property of them, and in this sense, the photon is no different from other microparticles, such as electrons, protons, etc.
Finally, it should be said that photons, like all other particles, can experience the action of a gravitational field. Thus, accurate observations during total solar eclipses of the position of stars, the light from which passes near the Sun, show that this light is subject to the attraction of the Sun and deviates from its original path. This can be understood qualitatively if we take into account that photons have energy, which corresponds to the “mass of motion” up to the level of the Earth’s surface; it was possible to observe a change in the frequency of photons, which perfectly coincided with theoretical predictions:
,
thereby confirming that photons are subject to gravitational influence.
Thus, as we were able to see by considering numerous and varied experiments, in a number of cases light should be considered as a stream of corpuscles - photons that have properties inherent in other microparticles. However, to explain phenomena such as interference and diffraction, one must proceed from the wave properties of electromagnetic radiation. Both aspects of nature - the wave and the corpuscular - turn out to be equally significant. Therefore, to explain all the features of the behavior of radiation, it turned out to be necessary to recognize that electromagnetic waves under certain conditions exhibit the properties of particle flows. With equal right, the opposite statement can be made: particles of the electromagnetic field - photons - exhibit wave properties. Such wave-particle dualism (duality) of photons contradicts the established classical, separate from each other, ideas about waves and particles.
At first it seemed that photons possessing these unusual properties, differ significantly from other particles, such as electrons or protons. However, the further development of the physics of the microworld has made it possible to establish that wave-particle dualism is by no means a specific feature of photons, but is of a much more general nature.
Photon is an elementary particle, a quantum of electromagnetic radiation.
Photon energy: ε = hv, where h = 6.626 · 10 -34 J s – Planck’s constant.
Photon mass: m = h·v/c 2 . This formula is obtained from the formulas
ε = hv and ε = m·c 2. The mass, defined by the formula m = h·v/c 2, is the mass of the moving photon. The photon has no rest mass (m 0 = 0), since it cannot exist in a state of rest.
Photon momentum: All photons move at speed c = 3·10 8 m/s. Obviously the photon momentum P = m c, which means that
P = h·v/c = h/λ.
4. External photoelectric effect. Current-voltage characteristics of the photoelectric effect. Stoletov's laws. Einstein's equation
The external photoelectric effect is the phenomenon of the emission of electrons by a substance under the influence of light.
The dependence of the current on the voltage in the circuit is called the current-voltage characteristic of the photocell.
1) The number of photoelectrons N’ e ejected from the cathode per unit time is proportional to the intensity of light incident on the cathode (Stoletov’s law). Or in other words: the saturation current is proportional to the power of radiation incident on the cathode: Ń f = P/ε f.
2) The maximum speed V max that an electron has at the exit from the cathode depends only on the frequency of light ν and does not depend on its intensity.
3) For each substance there is a cutoff frequency of light ν 0, below which the photoelectric effect is not observed: v 0 = A out /h. Einstein's equation: ε = A out + mv 2 max /2, where ε = hv is the energy of the absorbed photon, A out is the work function of the electron leaving the substance, mv 2 max /2 is the maximum kinetic energy of the emitted electron.
Einstein's equation, in fact, is one of the forms of writing the law of conservation of energy. The current in the photocell will stop if all the emitted photoelectrons are slowed down before reaching the anode. To do this, it is necessary to apply a reverse (holding) voltage u to the photocell, the value of which is also found from the law of conservation of energy:
|e|u з = mv 2 max /2.
5. Light pressure
Light pressure is the pressure exerted by light falling on the surface of a body.
If we consider light as a stream of photons, then, according to the principles of classical mechanics, particles upon impact with a body must transfer momentum, in other words, exert pressure. This pressure is sometimes called radiation pressure. To calculate light pressure, you can use the following formula:
p = W/c (1+ p), where W is the amount of radiant energy incident normally on 1 m2 of surface in 1 s; c is the speed of light, p- reflection coefficient.
If light falls at an angle to the normal, then the pressure can be expressed by the formula:
6. Compton effect and its explanation
The Compton effect (Compton effect) is the phenomenon of changing the wavelength of electromagnetic radiation due to its scattering by electrons.
For scattering by a stationary electron, the frequency of the scattered photon is:
where is the scattering angle (the angle between the directions of photon propagation before and after scattering).
Compton wavelength is a length dimension parameter characteristic of relativistic quantum processes.
λ С = h/m 0 e c = 2.4∙10 -12 m – Compton wavelength of the electron.
The Compton effect cannot be explained within the framework of classical electrodynamics. From the point of view of classical physics, an electromagnetic wave is a continuous object and, as a result of scattering by free electrons, should not change its wavelength. The Compton effect is direct evidence of the quantization of an electromagnetic wave; in other words, it confirms the existence of a photon. The Compton effect is another proof of the validity of the wave-particle duality of microparticles.
In its modern interpretation, the quantum hypothesis states that energy E vibrations of an atom or molecule can be equal to hν, 2 hν, 3 hν, etc., but there are no oscillations with energy in the interval between two consecutive integers that are multiples of . This means that energy is not continuous, as was believed for centuries, but quantized , i.e. exists only in strictly defined discrete portions. The smallest portion is called quantum of energy . The quantum hypothesis can also be formulated as a statement that at the atomic-molecular level, vibrations do not occur with any amplitudes. Valid values amplitudes are related to the vibration frequency ν .
In 1905, Einstein put forward a bold idea that generalized the quantum hypothesis and laid it as the basis for a new theory of light (the quantum theory of the photoelectric effect). According to Einstein's theory , light with frequencyν Not only emitted, as Planck assumed, but also spreads and is absorbed by the substance in separate portions (quanta), whose energy. Thus, the propagation of light should be considered not as a continuous wave process, but as a stream of discrete light quanta localized in space, moving at the speed of light propagation in vacuum ( With). The quantum of electromagnetic radiation is called photon .
As we have already said, the emission of electrons from the surface of a metal under the influence of radiation incident on it corresponds to the idea of light as an electromagnetic wave, because electric field The electromagnetic wave affects the electrons in the metal and knocks out some of them. But Einstein drew attention to the fact that the details of the photoelectric effect predicted by the wave theory and the photon (quantum corpuscular) theory of light differ significantly.
So, we can measure the energy of the emitted electron based on the wave and photon theory. To answer the question of which theory is preferable, let us consider some details of the photoelectric effect.
Let's start with wave theory and assume that the plate is illuminated with monochromatic light. The light wave is characterized by the following parameters: intensity and frequency(or wavelength). Wave theory predicts that when these characteristics change, the following phenomena occur:
· with increasing light intensity, the number of ejected electrons and their maximum energy should increase, because higher light intensity means greater amplitude of the electric field, and a stronger electric field ejects electrons with more energy;
knocked out electrons; kinetic energy depends only on the intensity of the incident light.
The photon (corpuscular) theory predicts something completely different. First of all, we note that in a monochromatic beam all photons have the same energy (equal to hν). Increasing the intensity of a light beam means an increase in the number of photons in the beam, but does not affect their energy if the frequency remains unchanged. According to Einstein's theory, an electron is knocked off the surface of a metal when a single photon collides with it. In this case, all the energy of the photon is transferred to the electron, and the photon ceases to exist. Because electrons are held in the metal by attractive forces; minimal energy is required to knock an electron out of the metal surface A(which is called the work function and, for most metals, is on the order of several electron volts). If the frequency ν of the incident light is small, then the energy and energy of the photon is not enough to knock out an electron from the surface of the metal. If , then electrons fly out from the surface of the metal, and energy in such a process is preserved, i.e. photon energy ( hν) is equal to the kinetic energy of the emitted electron plus the work of knocking the electron out of the metal:
| (2.3.1) |
Equation (2.3.1) is called Einstein's equation for the external photoelectric effect.
Based on these considerations, the photonic (corpuscular) theory of light predicts the following.
1. An increase in light intensity means an increase in the number of incident photons, which knock out more electrons from the metal surface. But since the photon energy is the same, the maximum kinetic energy of the electron will not change ( confirmed I photoelectric effect law).
2. As the frequency of the incident light increases, the maximum kinetic energy of electrons increases linearly in accordance with Einstein’s formula (2.3.1). ( Confirmation II photoelectric effect law). The graph of this dependence is presented in Fig. 2.3.
 ,
|
Rice. 2.3
3. If the frequency ν is less than the critical frequency, then electrons are not knocked out from the surface (III law).
So, we see that the predictions of the corpuscular (photon) theory are very different from the predictions of the wave theory, but coincide very well with the three experimentally established laws of the photoelectric effect.
Einstein's equation was confirmed by Millikan's experiments performed in 1913–1914. The main difference from Stoletov’s experiment is that the metal surface was cleaned in a vacuum. The dependence of the maximum kinetic energy on frequency was studied and Planck’s constant was determined h.
In 1926, Russian physicists P.I. Lukirsky and S.S. Prilezhaev used the method of a vacuum spherical capacitor to study the photoelectric effect. The anode was the silver-plated walls of a glass spherical cylinder, and the cathode was a ball ( R≈ 1.5 cm) from the metal under study, placed in the center of the sphere. This shape of the electrodes made it possible to increase the slope of the current-voltage characteristic and thereby more accurately determine the retardation voltage (and, consequently, h). Value of Planck's constant h, obtained from these experiments, is consistent with the values found by other methods (from black body radiation and from the short-wavelength edge of the continuous X-ray spectrum). All this is proof of the correctness of Einstein’s equation, and at the same time his quantum theory of the photoelectric effect.
To explain thermal radiation, Planck proposed that light was emitted by quanta. Einstein, when explaining the photoelectric effect, suggested that light is absorbed by quanta. Einstein also suggested that light propagates by quanta, i.e. in portions. The quantum of light energy is called photon . Those. again we came to the concept of corpuscle (particle).
The most direct confirmation of Einstein's hypothesis was provided by Bothe's experiment, which used the coincidence method (Fig. 2.4).
Rice. 2.4
Thin metal foil F was placed between two gas-discharge meters SCH. The foil was illuminated by a weak beam of X-rays, under the influence of which it itself became a source of X-rays (this phenomenon is called X-ray fluorescence). Due to the low intensity of the primary beam, the number of quanta emitted by the foil was small. When quanta hit the counter, the mechanism was triggered and a mark was made on the moving paper tape. If the emitted energy were distributed evenly in all directions, as follows from wave concepts, both counters would have to operate simultaneously and the marks on the tape would be opposite each other. In reality, there was a completely random arrangement of marks. This can only be explained by the fact that in individual acts of emission light particles appear, flying in one direction or another. This is how the existence of special light particles – photons – was experimentally proven.
A photon has energy
. For visible light, wavelength λ = 0.5 µm and energy E= 2.2 eV, for X-rays λ = µm and E= 0.5 eV.
The photon has inertial mass , which can be found from the relation:
| ; |
| (2.3.2) |
Photon travels at the speed of light c= 3·10 8 m/s. Let's substitute this speed value into the expression for the relativistic mass:
 .
|
A photon is a particle that has no rest mass. It can only exist by moving at the speed of light c .
Let's find the connection between energy and photon momentum.
We know the relativistic expression for momentum:
| . | (2.3.3) |
And for energy:
| . | (2.3.4) |
Photon is an elementary particle, a quantum of electromagnetic radiation. Quantum energy (that is, discretely), where is Planck’s constant. momentum. If we attribute to the photon the presence of the so-called. “relativistic mass” based on the relationship, it will be There is no rest mass for the photon. The photo effect is the emission of electrons from a substance under the influence of light (and, generally speaking, any electromagnetic radiation). Einstein’s formula for the photo effect:
hν = A out + E k
Where A out- so-called work function (minimum energy required to remove an electron from a substance), E k is the kinetic energy of the emitted electron (depending on the speed, either the kinetic energy of a relativistic particle can be calculated or not), ν is the frequency of the incident photon with energy hν, h- Planck's constant.
External photoelectric effect (photoelectron emission) is the emission of electrons by a substance under the influence of electromagnetic radiation. 1) The maximum initial speed of photoelectrons does not depend on the intensity of the incident light, but is determined only by its frequency. 2) There is a minimum frequency at which the photoelectric effect is possible (red border) 3) The saturation current depends on the intensity of light incident on the sample 4) The photoelectric effect is an inertia-free phenomenon. To stop the photocurrent, a negative voltage (turn-off voltage) must be applied to the anode. 
Internal photoelectric effect is a change in the electronic conductivity of a substance under the influence of light. Photoconductivity is characteristic of semiconductors. The electrical conductivity of semiconductors is limited by the lack of charge carriers. When a photon is absorbed, an electron moves from the valence band to the conduction band. As a result, a pair of charge carriers is formed: an electron in the conduction band and a hole in the valence band. Both charge carriers, when voltage is applied to the semiconductor, create an electric current.
When photoconductivity is excited in an intrinsic semiconductor, the photon energy must exceed the band gap. In a doped semiconductor, the absorption of a photon can be accompanied by a transition from a level located in the bandgap, which allows the wavelength of light that causes photoconductivity to be increased. This circumstance is important for detecting infrared radiation. A condition for high photoconductivity is also a high light absorption coefficient, which is realized in direct-gap semiconductors.
16. Light pressure.
Light pressure is the pressure produced by electromagnetic light waves incident on the surface of a body. The quantum theory of light explains light pressure as a result of photons transferring their momentum to atoms or molecules of matter. Let N photons fall on the surface of an absolutely black body with area S perpendicular to it every second: . Each photon has momentum. The total impulse received by the surface of the body is equal. Light pressure: 
.
- reflection coefficient, - volumetric radiation energy density. Classical theory 
17. Bremsstrahlung and characteristic X-ray radiation.
X-rays are electromagnetic waves, the energy of photons of which lies on the scale of electromagnetic waves between ultraviolet radiation and gamma radiation, which corresponds to wavelengths from 10 −2 to 10 3 Å (from 10 −12 to 10 −7 m). 
Schematic illustration of an X-ray tube. X - X-rays, K - cathode, A - anode (sometimes called anticathode), C - heat sink, U h- cathode filament voltage, U a- accelerating voltage, W in - water cooling inlet, W out - water cooling outlet. When the energy of the electrons bombarding the anode becomes sufficient to tear electrons out of the inner shells of the atom, sharp lines appear against the background of bremsstrahlung characteristic radiation. The frequencies of these lines depend on the nature of the anode substance, which is why they are called characteristic.
Bremsstrahlung is electromagnetic radiation emitted by a charged particle when it is scattered (braked) in an electric field. 
dp/dλ hv cannot be greater than the energy eU. from the law of conservation of energy The most common source of X-ray radiation is an X-ray tube, in which electrons strongly accelerated by an electric field bombard the anode (a metal target made of heavy metals, such as W or Pt), experiencing sharp deceleration on it. In this case, X-ray radiation appears, which is electromagnetic waves with a wavelength of approximately 10 -12 -10 -8 m. The wave nature of X-ray radiation is proven by experiments on its diffraction, discussed in § 182.
A study of the spectral composition of X-ray radiation shows that its spectrum has a complex structure (Fig. 306) and depends both on the energy of the electrons and on the anode material. The spectrum is a superposition of a continuous spectrum, limited on the short wavelength side by a certain boundary min, called the boundary of the continuous spectrum, and a line spectrum - a collection of individual lines appearing against the background of the continuous spectrum.
Research has shown that the nature of the continuous spectrum is completely independent of the anode material, but is determined only by the energy of the electrons bombarding the anode. A detailed study of the properties of this radiation showed that it is emitted by electrons bombarding the anode as a result of their deceleration during interaction with target atoms. The continuous X-ray spectrum is therefore called the bremsstrahlung spectrum. This conclusion is in agreement with the classical theory of radiation, since when moving charges are decelerated, radiation with a continuous spectrum should actually arise.
The classical theory, however, does not imply the existence of a short-wavelength boundary of the continuous spectrum. From experiments it follows that the greater the kinetic energy of the electrons causing X-ray bremsstrahlung, the less min. This circumstance, as well as the presence of the boundary itself, is explained by quantum theory. Obviously, the limiting energy of a quantum corresponds to the case of braking in which all the kinetic energy of the electron is converted into quantum energy, i.e.
Where U- potential difference due to which energy is imparted to an electron E max, max - frequency corresponding to the boundary of the continuous spectrum. Hence the cutoff wavelength
Feynman diagram for photon-photon scattering. Photons themselves cannot interact with each other, since they are neutral particles. Therefore, one of the photons turns into a particle-antiparticle pair, with which the other photon interacts.
Physicists from the ATLAS collaboration have for the first time recorded the effect of scattering of light quanta, photons, on photons. This effect is one of the oldest predictions of quantum electrodynamics; it was described theoretically more than 70 years ago, but has not yet been discovered experimentally. Interestingly, it violates Maxwell's classical equations, being a purely quantum phenomenon. The study was published this week in the journal Nature Physics, however, a preprint of the article was published back in February 2017. Details about it were reported by the portal "Elements.ru"
One of the main properties of classical Maxwellian electrodynamics is the principle of superposition for electromagnetic fields in a vacuum. It allows you to directly add fields from different charges. Since photons are excitations of fields, within the framework of classical electrodynamics they cannot interact with each other. Instead, they should pass freely through each other.
ATLAS detector magnets
Quantum electrodynamics extends the action of classical theory to the movement of charged particles at near-light speeds; in addition, it takes into account the quantization of field energy. Thanks to this, in quantum electrodynamics it is possible to explain unusual phenomena associated with high-energy processes - for example, the birth of pairs of electrons and positrons from a vacuum in high-intensity fields.
In quantum electrodynamics, two photons can collide with each other and scatter. But this process does not occur directly - the light quanta are uncharged and cannot interact with each other. Instead, an intermediate formation of a virtual particle-antiparticle (electron-positron) pair from one photon occurs, with which the second photon interacts. Such a process is very unlikely for visible light quanta. This can be estimated from the fact that light from quasars located 10 billion light years away reaches the Earth. But with increasing photon energy, the probability of the process with the birth of virtual electrons increases.
Until now, the intensity and energy of even the most powerful lasers were not enough to see the scattering of photons directly. However, researchers have already found a way to see this process indirectly, for example, in the processes of decay of one photon into a pair of lower-energy quanta near the heavy nucleus of an atom.
It was possible to directly observe the scattering of a photon on a photon only in the Large Hadron Collider. The process became discernible in experiments after increasing the energy of particles in the accelerator in 2015 - with the launch of Run 2. Physicists of the ATLAS collaboration studied the processes of “ultraperipheral” collisions between heavy lead nuclei, accelerated by the collider to energies of 5 teraelectronvolts per nucleon of the nucleus. In such collisions, the nuclei themselves do not collide directly with each other. Instead, their electromagnetic fields interact, in which photons of enormous energy appear (this is due to the proximity of the speed of nuclei to the speed of light).
Photon-on-photon scattering event (yellow beams)
Ultraperipheral collisions are characterized by great purity. In them, in the case of successful scattering, only a pair of photons with transverse impulses directed in different directions appears. In contrast, ordinary nuclear collisions produce thousands of new fragment particles. Among the four billion events collected by ATLAS in 2015 from the statistics of collisions of lead nuclei, scientists were able to select 13 corresponding to scattering. This is about 4.5 times more than the background signal that physicists expected to see.
Scheme of the scattering process in the collider. Two cannonballs fly close - they electromagnetic fields interact
The ATLAS Collaboration
The collaboration will continue to study the process at the end of 2018, when the collider will again host a session of collisions of heavy nuclei. Interestingly, it was the ATLAS detector that turned out to be suitable for searching for rare events of photon-photon scattering, although another experiment, ALICE, was specially designed to analyze collisions of heavy nuclei.
Currently, the Large Hadron Collider is collecting statistics on proton-proton collisions. Recently, scientists about the discovery of the first doubly charmed baryon at an accelerator, and in the spring, physicists from the ATLAS collaboration about an unusual excess of events in the birth of two weak interaction bosons in the high-energy region (about three teraelectronvolts). It may indicate a new superheavy particle, but the statistical significance of the signal does not yet exceed three sigma.
Vladimir Korolev
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