APPLICATION OF THE CHERENKOV EFFECT TO THE OBSERVATION OF PROTONS AND MESONS

In 1947 a design was proposed[^1] for counters of charged elementary particles of high energy, based on the use of the Cherenkov effect. Among the positive qualities of such counters, called Cherenkov counters, are: their rapid response, the simplicity of distinguishing particles of different energies, and the identical counting efficiency for both positively and negatively charged particles.

Nevertheless, existing Cherenkov counters require improvement of many of their components, especially the radio-engineering parts of the circuits.

As is known, as early as 1934, in the laboratory of S. I. Vavilov, P. A. Cherenkov[^2] discovered a new type of radiation occurring in a liquid when electrons pass through it with velocities exceeding the phase velocity of light in the given medium and possessing a characteristic directionality and polarization. It later became clear that similar radiation is observed not only in liquids but also, in general, in dielectrics. The theory of this phenomenon, from the standpoint of classical electrodynamics, was given by I. E. Tamm and I. M. Frank[^3] in 1937; the quantum theory of the Cherenkov effect was developed by A. A. Sokolov[^4] and V. L. Ginzburg[^5]. Fermi[^6] considered the case of a complex refractive index, which made it possible to describe in a unified way the energy losses of particles moving rapidly in a medium, both to ionization and to Cherenkov radiation. In Bohr’s work[^7] the relation between the microscopic and macroscopic approaches to the consideration of the effect was analyzed. The features of Cherenkov radiation in an anisotropic medium were revealed in the works of V. L. Ginzburg[^8] and A. Kolomenskii[^9].

However, the Cherenkov effect proved to be a phenomenon of a more general character than could at first have been thought. In particular, a number of authors[^10][^11][^12] investigated the radiation of an electron when it passes through the boundary between two media (“transition radiation”) and when it approaches this boundary (“polarization radiation”). It was likewise shown that the radiation of an electron moving in a magnetic field with “superluminal” velocity is not a simple superposition of the radiation of the “glowing” electron and the radiation of the “superluminal” electron, but in a distinctive way combines (in the “superluminal” region) features of both phenomena.[^13] Radiation of the “superluminal” type, but not in a dielectric, rather in a ferromagnet, was considered by D. Ivanenko and V. G. Gurevich;[^14] in this case radiation in a ferromagnet is possible also from uncharged but magnetic particles, such as, for example, neutrons. I. M. Frank[^15] solved the classical problem of the Cherenkov effect for arbitrarily oriented electric and magnetic multipoles.

Figuratively speaking, the Cherenkov effect consists in the detachment of the electromagnetic field from the particle that gives rise to it when the latter moves in a medium with velocity \(v\) greater than the phase velocity of light \(\dfrac{c}{n}\) in this medium (\(n\) is the refractive index of the medium). In this case the front of the radiation waves, formed as a result of the interference of all the waves emitted by the particle, forms a cone with its apex at the point where the particle is located; in all other directions the waves are extinguished. If by \(\theta\) one denotes the angle between the normal to the front and the direction of motion of the particle, then[^3]

\[ \cos \theta = \frac{1}{\beta n}, \tag{1} \]

where

\[ \beta = \frac{v}{c}. \]

Fig. 1.

A detailed theory of the Cherenkov effect is set forth, for example, in [^16].
The Tamm and Frank formula for the number \(N\) of photons emitted by an electron along a path \(L\) with velocity \(v\) in the wavelength interval from \(\lambda_1\) to \(\lambda_2\) gives:

\[ N = 2\pi \alpha \left( \frac{L}{\lambda_2} - \frac{L}{\lambda_1} \right) \left( 1 - \frac{1}{\beta^2 n^2} \right), \]

where

\[ \alpha = \frac{e^2}{\hbar c} \]

is the fine-structure constant, and \(n\) is the mean value of the refractive index of the medium (the radiator) in this spectral region. In general, for a particle of charge \(Ze\) the radiation amounts to

\[ \frac{dN}{dL} = 2\pi \frac{Z^2 e^2}{\hbar c^2} \left( 1 - \frac{1}{n^2 \beta^2} \right) \Delta \nu \simeq 450 \sin^2 \theta \]

quanta per centimeter of path, if for \(\Delta \nu\) one takes the range of frequencies of visible waves \((3 \cdot 10^{14}\ \text{Hz})\). Then, for example, an electron moving with the speed of light in a medium with \(n = 1.5\) would give, in the visible region of the spectrum, 250 photons for each centimeter of path.

By virtue of (1), the direction of the radiation depends on the velocity of the particle, which, in turn, depends on its energy. This is the mechanism for distinguishing particles by energy in Cherenkov counters.

DESIGN FEATURES OF CHERENKOV COUNTERS

Good radiators, having a wide operating range, for Cherenkov counters[^1] should meet the following requirements: 1) a sufficiently small ordinal atomic number of the radiator substance, so that there is no appreciable ionizing effect of the medium on the motion of the particle; 2) a large value of \(n\) and high transparency, including in the ultraviolet region; 3) optical homogeneity of the radiator material; 4) low dispersion. In experiments of recent years[^1][^17]–[^25], organic glass, known under the name “plexiglas” or “lucite,” with refractive index \(n = 1.50\) and low dispersion, has most often been used (\(n\) changes by 0.01 from \(\lambda = 5850\ \text{Å}\) to \(4400\ \text{Å}\)); in addition, distilled water (\(n = 1.33\)) has been used, which makes it possible to investigate particles with \(\beta > 0.76\), cubic (\(1 \times 1 \times 1\ \text{cm}^3\)) transparent crystals of sulfur chloride (\(n = 2.07\)), and transparent anthracene plates.

Usually, in experiments of this kind, a cylinder of organic glass[^1][^17][^18][^25] is used, along the axis of which the particles under investigation are directed. In other variants[^21], radiators and optical systems with cylindrical symmetry are also often used. For the most complete transmission of the radiation to the measuring instruments and for the preservation of directionality, total internal reflection of the Cherenkov radiation from the walls of the cylindrical radiator is employed.

Subsequently the radiation is either observed directly or focused onto as small an area as possible. Focusing is made difficult by the fact that most particles do not travel strictly along the optical axis of the system, but at some distance from it (the beam of particles is assumed to be parallel to the axis). As a result, the photons acquire a certain moment with respect to the axis, which they retain thereafter and, consequently, cannot be focused exactly on the continuation of the axis of the system.

Labels in the diagram: particle trajectory; lucite cylinder; Cherenkov-radiation ray; lens; photomultiplier.

Fig. 2.

In view of the fact that Cherenkov radiation is polarized so that the electric vector lies in the plane of incidence on the reflecting surface (under conditions of cylindrical symmetry), at angles close to Brewster’s angle the light passes completely through the boundary between the two media. This circumstance was proposed for separating radiation produced by particles of different energies[^25].

Despite the use of extended radiators (cylinder length 15–20 cm), the radiation obtained is insufficiently intense, and in recording it one must resort to amplification. Schemes with photomultipliers[^17][^19][^20][^21][^25] are usually used (Fig. 2). In particular, a type 5819 photomultiplier was used[^25], having a sensitivity at maximum of 0.065 electron per photon (at \(\lambda = 4700\ \text{Å}\)) and a convenient arrangement of the photocathode.

Such devices ensure the registration of practically every particle that gives Cherenkov radiation and penetrates into the radiator to a depth of several millimeters.

Fig. 3.

Labels in the figure: photomultipliers; lens-radiator of plexiglas; cylindrical mirror; plane mirrors.

To eliminate noise caused by fluctuation currents, etc., coincidence circuits are widely used^21,25 (Fig. 3). However, in the radio-engineering part of the apparatus we encounter difficulties arising from the very short duration of the pulse \((10^{-11} \div 10^{-9}\ \text{sec.})\) and from the impossibility of transforming, without distortion, pulses shorter than \(10^{-9}\ \text{sec.}\)^19,20,25

Fig. 4.

Labels in the figure: proton beam; photographic plates; Cherenkov radiation; AgCl crystal; spherical mirror.

Fig. 5.

Labels in the figure: Cherenkov radiation; film camera; proton beam; glass sheet.

There also exist other ways of observing Cherenkov radiation; one of them is based on the property of photosensitive photographic materials to “sum” weak illumination acting on them for a long time \(^{23,24}\) (Figs. 4 and 5). However, such a method is not suitable for observing individual particles or particles present in small quantities. Geiger–Müller counters are also used, sensitive to light in the range \(2000\)—\(3000\) Å \(^{26}\).

Sometimes in a coincidence circuit not two photomultipliers are used, but a photomultiplier in combination with some counter (a Geiger–Müller counter \(^{19,20}\), a scintillating crystal \(^{22}\)), placed in front of the Cherenkov radiator in the path of the particles (Fig. 6).

Fig. 6.

Labels in the figure: Geiger–Müller counters; black paper; cuvette with water; photomultiplier.

APPLICATION OF CHERENKOV COUNTERS

Let us now turn to the results obtained with the aid of Cherenkov counters. As we have already seen, these counters can be used to observe charged particles possessing high energy (velocity greater than the phase velocity of light in the given medium) and sufficient penetrating power. When it is necessary to measure the angle of radiation, it is also important to have a well-collimated beam of particles. Coulomb scattering is reduced by selecting the radiator. The degree of accuracy in measuring the Cherenkov angle varies for different counter designs; it amounts to minutes of arc \(^{23,25}\). In this case the accuracy of determining the particle energy was, for example, \(\pm 0.2\) MeV in estimating an energy of 340 MeV (for protons \(^{23,28}\)).

Fig. 7.

Labels in the figure: Number of pulses; Cherenkov angle.

It is important to note that it proved possible to measure directly the velocity not only of electrons, but also of protons, \(\pi^+\)- and \(\pi^-\)-mesons; moreover, with the aid of the particles produced by them, neutrons, \(\gamma\)-rays (as early as 1934 by Cherenkov), and \(\pi^0\)-mesons were observed.

Cherenkov counters were used to determine changes in the energy of particles as they passed through matter. For example, in one experiment 145-MeV \(\pi^-\)-mesons from the 170-inch synchrocyclotron were passed through a graphite plate \(7.6\) cm thick, which should have caused a decrease in the energy of the \(\pi^-\)-mesons to 121 MeV and changed the Cherenkov angle from \(40.4^\circ\) to \(38.1^\circ\). As can be seen from Fig. 7, the experiment gave a change from \(39.9^\circ\) (curve I) to \(38.0^\circ\)

(curve II). The general lowering of curve II is caused by the scattering of mesons in graphite, as a result of which their number in the beam decreased.

In many other cases, the Cherenkov counter can serve as a simple and convenient instrument for investigating various kinds of interactions of particles with matter; for example, it has been proposed to use it for studying the elastic scattering of particles.

An example of the use of the Cherenkov counter is also provided by an experiment carried out^22,25 with the aid of an unfocused amateur counter: a cylinder of Lucite 3 inches long and 1.5 inches in diameter was brought into optical contact with a type 5819 photomultiplier; the apparatus operated in a coincidence circuit with a crystal scintillator. For protons with energies above 400 MeV the counting efficiency was high, but already at 350 MeV the number of coincidences fell almost to zero. The instrument was used as a detector of neutrons of a definite energy, onto which the protons of the synchrocyclotron with the greatest energy, 450 MeV, were incident. A radiator rich in hydrogen was used, and the energy of the protons knocked out of it by neutrons was measured. The resulting neutron energy spectrum had a maximum at about 406 MeV and fell to zero in the regions of 450 MeV and 360 MeV, with a width at half-intensity level of about 32 MeV.

In another case^25 and others, $\pi^0$-mesons obtained in a synchrocyclotron were investigated; in their decay they gave powerful $\gamma$-rays, which in turn produced fast electrons that created Cherenkov radiation; water was used as the radiator in this case.

Observation of mesons by means of Cherenkov counters is also of special interest because it makes it possible to use Cherenkov counters for the investigation of cosmic rays. It was noted^27 that the Cherenkov effect makes it possible to carry out an accurate measurement of the velocities of individual mesons. Although the first experiments with cosmic rays gave no result^17, subsequently it was possible to construct an instrument that gave a satisfactory result. The initial failures were probably due to radiotechnical shortcomings in the required circuits. By combining, in a coincidence circuit, a Geiger–Müller counter with a Cherenkov counter (Fig. 6), good agreement^19,20 was obtained between the data obtained with the apparatus used earlier and with the Cherenkov counter. On the basis of an experiment in which the number of coincidences was compared for rays that had passed through 10 cm of lead and for rays falling directly on the counter, it was concluded that 80% of the effect registered by the counter was caused by $\mu$-mesons.

When various designs of Cherenkov counters were used, new confirmations of the theory of this effect were, of course, obtained along the way.

In particular, the angular distribution of the intensity of Cherenkov radiation was obtained^23,24, in agreement with theory.

The results set forth above show that counters based on the use of the Cherenkov effect may prove to be an effective means of experimental investigation, especially with further improvement of the radio-engineering parts of their circuits.

N. Mitskevich

CITED LITERATURE

1. I. A. Getting, Phys. Rev. 71, 123 (1947).
2. P. A. Cherenkov, DAN 2, 451 (1934).
3. I. E. Tamm and I. M. Frank, DAN 14, 107 (1937).
4. A. A. Sokolov, DAN 28, 415 (1940).
5. V. Ginzburg, ZhETF 10, 589 (1940).

1. E. Fermi, Phys. Rev. 57, 485, 1940, and the article by P. E. Kunin in the collection Meson, Gostekhizdat, 1947, p. 114.
2. N. Bohr and O. Bohr, The Passage of Atomic Particles through Matter, IL, 1950.
3. V. Ginzburg, ZhETF 10, 601, 608 (1940).
4. A. Kolomenskii, DAN 86, 1097 (1952).
5. V. L. Ginzburg and I. M. Frank, ZhETF 16, 15 (1946).
6. A. I. Rezanov, ZhETF 16, 878 (1946).
7. N. P. Klepikov, Vestnik MGU 8, 61 (1951).
8. V. N. Tsytovich, Vestnik MGU 11, 27 (1951).
9. D. Ivanenko and V. Gurenidze, DAN 67, 997 (1949).
10. Articles by I. M. Frank and V. L. Ginzburg in the collection In Memory of Sergei Ivanovich Vavilov, 1952, p. 172, p. 193.
11. D. Ivanenko and A. Sokolov, Classical Field Theory, 1951, and A. Sokolov and D. Ivanenko, Quantum Field Theory, 1952.
12. R. H. Dicke, Phys. Rev. 71, 737 (1947).
13. V. M. Kharitonov, UFN 39, 402 (1949).
14. J. V. Jelley, Proc. Phys. Soc., L. A64, 82 (1951).
15. V. Vavilov, UFN 44, 443 (1951).
16. J. Marshall, Phys. Rev. 81, 275 (1951).
17. V. A. Nedzela and J. Marshall, Bull. Am. Phys. Soc. 27, No. 1, 29 (1952).
18. R. L. Mather, Phys. Rev. 84, 181 (1952).
19. UFN 46, 413 (1952).
20. J. Marshall, Phys. Rev. 86, 685 (1952).
21. B. Weisz and B. L. Anderson, Phys. Rev. 72, 431 (1947).
22. W. H. Furry, Phys. Rev. 72, 171 (1947).
23. L. N. Bel’, Priroda, 11, 104, 1952.