PERSONALIA

In Memory of S. Z. Belenky

On September 21, 1956, in the forty-first year of his life, Semen Zakharovich Belenky died—a prominent theoretical physicist, widely known chiefly for his work in the field of cosmic-ray physics.

S. Z. Belenky was born in Moscow on June 14, 1916. After completing the seven-year school in 1931, Semen Zakharovich studied for two years and worked at the factory-training school of the Moscow Electric-Lamp Plant. In 1933 he entered the physics faculty of Moscow University, from which he graduated with honors in 1938 and was retained for postgraduate study. From 1941 to 1943 S. Z. worked at the Central Aerohydrodynamic Institute (TsAGI), and then transferred to the doctoral program of the Physics Institute of the Academy of Sciences of the USSR. There, in 1946, he defended his doctoral dissertation and continued to work as a senior research associate; from 1948 Semen Zakharovich was head of one of the sectors of the theoretical department.

Semen Zakharovich’s first scientific work was carried out in his final year at the university and was devoted to the theory of the scattering of X-rays[^1]. In this work it was shown that a certain scattering of electromagnetic waves and, in particular, of X-rays can be regarded as scattering by fluctuations of the density of electrons. Such an interpretation of the general quantum-mechanical formula for the scattering intensity is close to the well-known classical interpretation of the scattering process and has undoubted methodological value. The application of such a method of calculation to the case of the scattering of X-rays in a Fermi gas makes it possible simply and clearly to arrive at the final formulas for the scattering intensity[^1][^2]; the same also applies to the case of light scattering in a Bose gas[^2].

These first scientific results had, of course, a much greater, indirect significance: they showed S. Z. that he could successfully engage in theoretical physics, and showed him how interesting and absorbing independent work could be. Very soon, already at the end of 1938, S. Z., as a postgraduate student of the Institute of Physics of Moscow State University, had the full opportunity to concentrate all his attention on solving a difficult and, at the same time, very important theoretical problem. This problem, posed to him by his postgraduate supervisor I. E. Tamm, belonged to the field of the theory of cascade showers in cosmic rays. It was a period when only the $\mu$-meson had been discovered in cosmic rays, and when the study of cascade (electron-photon) showers was only beginning. In the works of Bhabha and Heitler, Carlson and Oppenheimer, Landau and Rumer, the equations of the shower theory had been formulated, but they had in fact been solved only with ionization losses neglected. Meanwhile, taking ionization losses into account is extremely essential, and without it comparison of the theory with experiment is in most cases simply impossible. On the other hand, to take ionization losses into account is far from simple, as a result of which at first attempts were made to do this by approximate methods. S. Z. showed that these methods were unsatisfactory and gave a complete solution of the problem. In his first paper on this subject (jointly with I. E. Tamm)[^3], the equations of the cascade theory with allowance for ionization losses had not yet been completely solved, but a very substantial quantity for comparison with experiment was found—the integral characteristic, the so-called “equilibrium spectrum” of cascade electrons. When an electron (or photon) of a given energy $E_0$ enters a layer of matter, then, as it moves away from the boundary of the medium, the spectrum of secondary electrons is constantly changing and, thus, the number of electrons $P$ is a function of the path length $t$ traversed by the cascade and of the electron energy $E$. The equilibrium spectrum is the integral of $P$ over $t$, i.e., it determines the dependence of the number of electrons only on energy. In experiment such a spectrum can be observed when the soft component (electrons, positrons, and photons) is in equilibrium with the $\mu$-meson component of cosmic rays that generates it. The “Tamm–Belenky equilibrium spectrum” became well known and widely used. However, finding the equilibrium spectrum solves, evidently, only part of the problem; its complete solution—i.e., finding the cascade-electron spectrum itself with allowance for ionization losses—was carried out by S. Z. in a subsequent work[^4], which served as the basis for his candidate dissertation[^5], defended in 1941. The same problem was subsequently studied by other authors as well,

but in doing so not only was nothing new obtained, but in some cases unnecessary complications and superfluous approximations were introduced (see ^15,22,23,25).

Despite the great success achieved, the construction of the cascade theory of showers had not yet been completed in full, all the more so since the development of experiment posed new problems. The literature lacked a shower theory suitable for heavy elements, for example for the especially frequently used lead. Nor had questions about the angular distribution of shower particles, about the role of scattering in cascade processes, and certain others been sufficiently fully considered. Therefore S. Z., in close connection with the problems arising in experiment, undertook a whole series of further investigations in which all the questions listed were solved and the development of the theory of cascade (electron-photon) showers was practically completed. This cycle includes the papers ^6,7,9,10 that went into his doctoral dissertation ^14, as well as a number of subsequent articles ^16,18,19,20,21,23,24,25,26. Also belonging here are several works carried out under the direction of S. Z., by V. Ya. Fainberg, P. S. Isaev, and I. P. Ivanenko.

In 1948 S. Z. Belen'kii’s monograph Avalanche Processes in Cosmic Rays appeared in print; it was awarded the N. D. Papaleksi Prize in physics. The results of subsequent investigations in the field of shower theory were presented in a review ^39 written jointly with I. P. Ivanenko, which was completed shortly before S. Z.’s death and had not yet appeared in print.

S. Z. Belen'kii’s works on the cascade theory of showers are of fundamental importance for this field and for cosmic-ray physics as a whole. These investigations received high appraisal and recognition in the world literature.

The study of electromagnetic processes at high energies and, in particular, of cascade showers, although they pass like a red thread through all of S. Z.’s activity, is by no means the only direction of his investigations. He also worked in two other fields. The first of these is hydrodynamics, which S. Z. began to study upon entering TsAGI in 1941. In addition to solving a number of practical problems, over the next several years, often in parallel with his work in the field of cosmic-ray physics, S. Z. successfully considered several interesting hydrodynamic problems. Thus, he was the first to prove a very general and elegant theorem relating the wave resistance of a body in a supersonic flow to the increase of entropy in compression shocks ^8. This theorem not only simplifies in a number of cases the consideration of the resistance of bodies of a given shape, but also has fundamental significance. Then S. Z. gave the theory of so-called “condensation” shocks, arising as a result of the sudden condensation of water vapor when bodies are flowed around by moist air or, for example, when such air is passed through a Laval nozzle ^11,13,17. The theory of condensation shocks developed by S. Z. found experimental confirmation ^13. S. Z.’s hydrodynamic works also include two articles ^12,27, which remained unpublished *).

The third circle of questions with which S. Z. Belen'kii was occupied is the hydrodynamic and statistical theory of multiple particle production at high and ultrahigh energies.

In recent years, as is known, the center of gravity in cosmic-ray physics and, in general, in high-energy particle physics has shifted to the study of nuclear interaction, to the field of production of various mesons and hyperons. A large role in this field was played by the statistical theory of multiple particle production put forward by Fermi in 1950. Fermi’s original idea that at high energies the probability of a process is determined chiefly by the statistical weight of the final state was correct and very fruitful. But Fermi’s theory in its initial form did not take into account the stage of expansion of the composite system formed after the collision of two high-energy nucleons. L. D. Landau showed that this stage can be considered by hydrodynamic methods and solved the equations of relativistic hydrodynamics describing the expansion of the composite system. However, for comparison with experiment it was very important to generalize Landau’s theory to the practically important cases of the collision of a nucleon with a nucleus and of the collision of two nuclei. This very difficult problem, in mathematical terms, was solved by S. Z. Belen'kii (together with G. A. Milekhin) ^30,32,34. Further, S. Z. analyzed in detail the question of the number of particles of various types formed in the expansion stage following the hydrodynamic stage ^28—30,32—34. In particular, S. Z. indicated an ingenious method for determining the temperature of the system in the expansion stage on the basis of experimental data.

The application of Fermi’s statistical theory is restricted to the region of very high energies. Meanwhile, the region of comparatively low energies (of the order of several Bev) is also of great interest, since it is precisely such energies that are encountered in work with modern cosmotrons. S. Z. successfully generalized

*) Both of these works will appear posthumously in the Proceedings of the Lebedev Physical Institute, USSR Academy of Sciences.

the Fermi theory and thereby extended it to the case of small energies, when the number of particles produced is small. He showed that in the statistical theory one can introduce, in a purely phenomenological way, the interaction of a $\pi$-meson with a nucleon, assuming the presence of a virtual or real level in the meson–nucleon system with ordinary and isotopic spins equal to $3/2$ (see $^{31,36}$). Subsequently S. Z. showed$^{38}$ that the introduction into the statistical theory of an isobar state is equivalent to taking into account the interaction between $\pi$-mesons and nucleons, leading to resonant scattering of $\pi$-mesons by nucleons (as is known, precisely this is what takes place in experiment). If the former Fermi statistical theory gave, for proton energies of about $2\,Bev$, a discrepancy with experiment by a factor of 20, then Belenky’s theory, taking into account the interaction of the meson with the nucleon, agrees quite satisfactorily with the experimental data.

Belonging to the same cycle of investigations is the work of S. Z., together with N. M. Gerasimova,$^{37}$ on the theory of the nuclear-cascade process produced by particles with energies $10^{14}$—$10^{18}\ ev$.

Another direction in which S. Z. worked in recent times was the phenomenological theory of the scattering of nucleons by nucleons and of $\pi$-mesons by nucleons at high energies$^{35}$.

S. Z. had many ideas and plans for further investigations in the field of multiple particle production and the theory of particle collisions at high energies. He worked on these questions up to the last days of his life.

Over a long period S. Z. also devoted much effort to the solution of important applied problems. In this field he obtained very substantial results. His services were recognized with the Order of Lenin and the Stalin Prize.

S. Z. devoted much attention to scientific education and to the upbringing of young people. Under his direction a group of graduate students worked, and a number of dissertations were prepared. As a supervisor S. Z. was characterized by great exactingness and, at the same time, by the ability to give independence in work.

Characteristic features of S. Z.’s scientific style are a clear physical formulation of the problem, profound analysis of the problem under study, the application of rigorous and the most effective mathematical methods, and the carrying of calculations through to numerical results allowing direct comparison with experiment.

S. Z. was not only a talented physicist; he was a truly exceptional and integral person. He possessed a sharp, incisive, and original mind and the ability to analyze reality soberly and precisely. He was marked by independence, complete definiteness of judgment, and organic adherence to principle. He disliked half-hearted people and half-hearted opinions. Any empty phrase or pose was alien to him; he never chased after cheap success. S. Z.’s directness sometimes bordered on sharpness. It was not without reason that he was feared by those who, in life and in science, prefer not direct but roundabout paths. Together with this S. Z. was a reliable, devoted friend and a caring, benevolent supervisor for younger comrades.

S. Z. was always deeply concerned with public questions; he was active in public life. From 1931 he was a member of the VLKSM, and from 1939 a member of the CPSU.

The range of his interests was very broad. He was a person of many-sided education, had an excellent knowledge of literature and history, possessed good literary taste, and was a witty and resourceful conversationalist.

Semen Zakharovich truly loved science, worked with all his strength, and few knew how seriously ill he had been in his last years.

The untimely death of Semen Zakharovich Belenky is a grievous loss for theoretical physics and for all who knew him well and worked with him.

B. T. Geilikman and V. L. Ginzburg

LIST OF SCIENTIFIC WORKS OF S. Z. BELENKY

1. “On the theory of X-ray scattering,” ZhETF 10, 617 (1940).
2. “Fluctuations of the density of light and scattering of light in the Bose—Einstein and Fermi—Dirac gases” (together with V. S. Fursov and A. D. Galanin), Jorn. of Phys. 4, 349 (1940).
3. “On the soft component of cosmic rays at sea level” (together with I. E. Tamm), Journ. of Phys. 1, 177 (1939).
4. “On the avalanche theory of showers,” DAN 30, 603 (1941).
5. “Avalanche theory of showers,” dissertation for the degree of Candidate of Physical and Mathematical Sciences, Moscow State University, 1941.
6. “Distribution of shower particles by angles,” DAN 36, 106 (1942).
7. “On the width of a shower,” ZhETF 14, 129 (1944); Journal of Phys., 8, 9 (1944).
8. “On the wave resistance of bodies in a supersonic flow,” Applied Mathematics and Mechanics 8, 84 (1944).
9. “On the theory of showers in heavy elements,” ZhETF 14, 384, (1944); Journ. of Phys. 8, 305 (1944).

1. “On the influence of scattering in cascade processes,” ZhETF 15, 7 (1945); Journ. of Phys. 8, 347 (1944).

2. “On condensation jumps,” DAN 48, 173 (1945).

3. “On the theory of the flow around a wedge by a supersonic gas flow,” 1945.

4. “The influence of water-vapor condensation on supersonic flows” (with V. A. Andreev), Proceedings of TsAGI, No. 579, 1946.

5. “Shower processes.” Dissertation for the degree of Doctor of Physico-Mathematical Sciences, FIAN, 1946.

6. “The energy spectrum of cascade electrons” (with I. E. Tamm), Phys. Rev. 70, 660 (1946).

7. “Ionization showers produced by mesotrons,” ZhETF 16, 465 (1946); Journ. of Phys. 10, 144 (1946).

8. “Stability of condensation jumps,” Technical Reports of TsAGI, No. 84, 1947.

9. “Large collisions and mesotron spin,” ZhETF 17, 204 (1947).

10. “Cascade theory with allowance for ionization losses,” ZhETF 17, 189 (1947).

11. “Large ionization collisions,” in the collection Meson, Gostekhizdat, 1947.

12. “Penetrating showers in cosmic rays” (with L. E. Lazareva), in the collection Meson, Gostekhizdat, 1947.

13. “Shower processes in cosmic rays,” monograph, 243 pp., Gostekhizdat, 1948.

14. “On the comparison of spectra of shower electrons,” DAN 61, 621 (1948).

15. “On the calculation of moments of the distribution function of shower particles,” ZhETF 19, 940 (1949).

16. “Some questions of cascade theory,” Izvestiya AN SSSR, physical series, 14, 95 (1950).

17. “Scattering of shower particles in heavy elements” (with B. I. Maksimov), ZhETF 22, 102 (1952).

18. “On the equations of hydrodynamics with allowance for radiation” (1948).

19. “On the formation of heavy particles in collisions with high energy,” DAN 99, 523 (1954).

20. “Toward the theory of multiple production of particles at high energies,” ZhETF 28, 111 (1955).

21. “Multiple production of particles in collisions of high-energy nucleons with nuclei” (with G. A. Milekhin), ZhETF 29, 20 (1955).

22. “On the multiple production of mesons at energies 1–2.2 Bev” (with A. I. Nikishov), ZhETF 28, 744 (1955).

23. “The hydrodynamical theory of multiple particle production” (with L. D. Landau), UFN 56, 309 (1955). Abridged version: Nuovo Cimento Supplemento 3, No. 1, 15 (1956).

24. “On the annihilation of antinucleons with the formation of stars” (with I. L. Rozental), ZhETF 30, 595 (1956).

25. “Toward the theory of multiple particle production,” Izvestiya AN SSSR, physical series, 19, 611 (1955).

26. “On the diffraction scattering of high-energy π-mesons by nucleons,” ZhETF 30, 983 (1956).

27. “Statistical theory of multiple particle production” (with V. M. Maksimenko, A. I. Nikishov, and I. L. Rozental). Report at the Conference on the Physics of High-Energy Particles, May 1956. (Prepared for publication as a review for UFN.)

28. “On the absorption of high-energy nuclear-active particles” (with N. M. Gerasimova), ZhETF (in press).

29. “The connection between scattering and multiple particle production,” Nuclear Physics 2, 259 (1956), ZhETF (in press).

30. “Cascade theory of showers” (with I. P. Ivanenko). (Prepared for publication in UFN.)