Igor Evgenievich Tamm

(On the Occasion of His Sixtieth Birthday)

V. L. Ginzburg and E. L. Feinberg

On July 8, 1955, sixty years had passed since the birth of the outstanding Soviet theoretical physicist, Academician Igor Evgenievich Tamm. I. E. Tamm was born in 1895 in Vladivostok, but from 1899 he lived in the city of Elizavetgrad (now Kirovograd), where his father was for many years the city engineer. After graduating there from the gymnasium in 1913, I. E. studied for one year in Scotland at the University of Edinburgh, and when the First World War began he transferred to the Faculty of Physics and Mathematics of Moscow University. After graduating from the university in 1918, I. E. taught physics; in 1921–1922 he worked at the Odessa Polytechnic Institute, where L. I. Mandelstam was at that time a professor and exerted a profound influence on all of I. E.’s subsequent scientific development. I. E. maintained close ties with him throughout the following years, right up to L. I. Mandelstam’s death in 1944.

From 1922 onward, Igor Evgenievich’s scientific activity has taken place in Moscow. For many years he headed the chair of theoretical physics of the Physics Faculty of Moscow State University, where he is still a professor. After the USSR Academy of Sciences moved to Moscow in 1934, I. E. became head of the theoretical department of the P. N. Lebedev Physical Institute of the USSR Academy of Sciences, and since then his scientific activity has become increasingly concentrated in this institute. There too, to this day, leading the large collective of theoreticians he has trained, I. E. successfully carries on work on the fundamental problems of theoretical physics.

I. E. began his first scientific investigations under the influence of L. I. Mandelstam. They were devoted to the electrodynamics of an anisotropic medium and to crystal optics in the theory of relativity \(^{1,2}\). He then carried out a number of works in the field of the theory of relativity, the boron-

...quantum theory and the nonrelativistic quantum mechanics that appeared at that time \(^{3-6}\). In 1930 a major work by I. E. appeared, in which he gave a completed quantum theory of the scattering of light in crystals \(^{7}\). In this work, for the first time, the quantization of elastic (sound) waves in a solid was carried out and the concept of sound quanta (phonons) was introduced. As is well known, the concept of phonons is now used in the broadest way. In this elegant and important work not only Rayleigh scattering of light was considered, but also the combination scattering of light in crystals, shortly before discovered by L. I. Mandelstam and G. S. Landsberg. From the quantum point of view, the appearance of the Mandelstam—Brillouin doublet in the spectrum of Rayleigh scattering of light in crystals (the same also applies to liquids) is connected with the emission or absorption of one phonon. In this process the phonon energy is either subtracted from the photon energy (in the case of the red satellite) or (in the case of the violet satellite) added to it. In the case of combination scattering in crystals, a quantum of energy of the Born vibrations in the lattice is emitted or absorbed (disappears).

In the same year, 1930, there appeared a series of works by I. E. devoted to the Dirac relativistic quantum mechanics of the electron, which had just been created. This theory, on its appearance, won sympathy because it automatically gave an explanation of the spin properties of the electron and led to a natural explanation of the fine structure in the spectrum of the hydrogen atom. However, certain unusual elements of Dirac’s theory required careful study of other consequences following from it that admitted comparison with experiment. In this connection I. E. turned to the consideration, within the framework of Dirac’s theory, of the scattering of light by free electrons \(^{8}\), and he investigated this phenomenon by a consistent quantum-mechanical method—the method of the quantum theory of radiation. The result obtained by I. E. coincided with that which had been reached somewhat earlier, using the correspondence method, by Klein and Nishina. Thus the so-called Klein—Nishina formula was confirmed on the basis of a more rigorous and consistent consideration. Such a consideration was of undoubted independent interest and at the same time led to the elucidation of certain important circumstances. Thus, I. E. showed that the scattering even of the softest, low-frequency quanta of light by free electrons in Dirac’s theory proceeds through intermediate states with negative electron energy. Therefore even Thomson’s limiting formula for the scattering of light by a free electron cannot be obtained from Dirac’s theory without taking into account states with negative energy. As a consequence, all attempts that were being undertaken to expel from the theory these negative levels, which at that time (before the discovery of the positron) did not yield to physical interpretation, became hopeless. With this work there is also connected another essential...

IGOR EVGEN’EVICH TAMM

an important methodological point: here a method was proposed and applied for computing expressions encountered in the perturbation theory of a Dirac particle, a method that greatly simplified calculations (subsequently this method was developed by Casimir and is known under his name).

Not limiting himself to pointing out the irremovability of negative-energy levels, I. E. also studied other consequences of the theory; in particular—simultaneously with Dirac and Oppenheimer—he pointed to the inevitability of the fall of a free electron to a negative level and calculated the probability of annihilation of an electron with a “hole.”

In the next few years I. E.’s attention was directed to another area of quantum mechanics, which at that time was among the most topical—the quantum theory of metals. Here I. E. and his students carried out a number of works that firmly entered the modern theory of metals. These were, above all, the work that laid the foundations of the theory of the photoelectric effect in metals10, 12, and, secondly, the work13 in which the existence was discovered of levels of a special type, namely such that an electron situated at such a level, being bound to the surface of a crystal, can neither go out nor enter inside. Subsequently these “Tamm levels” played an enormous role in the development of the theory of the surface and contact properties of solids. The surveys included in the present issue give a more detailed idea of the significance of I. E.’s works in the field of the theory of metals and semiconductors.

In 1934 I. E. Tamm began a cycle of works devoted to a central problem of modern physics—the problem of the atomic nucleus and cosmic rays. I. E. continues his work in this direction up to the present time with unflagging persistence and scientific ingenuity. Already the first works of this cycle occupy an outstanding place in the history of the development of the theory of the nucleus and nuclear forces.

Relying on Fermi’s theory of beta decay, I. E. put forward the idea that, as a result of the exchange of particles between nucleons, namely as a result of exchange by electrons and neutrinos, nuclear forces arise. At the same time I. E. did not confine himself to indicating the presence of forces, but in his very first communication gave the formula he had obtained for the potential, estimated the magnitude of the forces, and showed the smallness of these forces in comparison with the observed nuclear forces15, 17, 19. As is known, it subsequently became clear that nuclear forces are indeed due to particle exchange, but that these particles are not the electron and neutrino, but the π-mesons, unknown at the time the beta-force theory was created. However, all subsequent theories of nuclear forces were constructed in general according to the same theoretical scheme as the beta-force theory created by Tamm. Let us note that in this same period, analyzing the experimental material then available, I. E. came (together with S. A. Al’tshuler) to the conclusion14, 16 (coinciding with the conclusions of the experimentalists Bacher and Schuler) that

the neutron must have a magnetic moment, and correctly estimated the sign of this moment. The existence of a magnetic moment in a neutral particle at that time seemed paradoxical. However, this conclusion proved to be entirely correct.

As is known, the theory of nuclear forces is still in a complicated and difficult state. The efforts of numerous theorists have for many years been directed toward the study of subtle questions, often of fundamental methodological significance. Thus, for a long time a theory was developed in which the mesons carrying the interaction between nucleons were considered to have spin equal to unity. Therefore, when I. E. showed^23 that such a particle does not possess stationary levels in the field of a Coulomb center, this was of essential importance for meson theory. In particular, this led to an interesting work^24 carried out by I. E. jointly with L. D. Landau.

I. E. began a new series of investigations on nuclear forces in 1945 with a paper^28 in which a method was formulated for considering the interaction of particles, different from the perturbation-theory method that had until then been used in almost all cases. The “Tamm method” proposed in this paper, or, as it is often called, the Tamm–Dancoff method, gave rise to a stream of investigations, the analysis of which is the subject of a special review in the present issue of the journal.

An attempt to construct a theory of a particle capable of being in states with different spins is represented by a work carried out by I. E. in 1947 jointly with V. L. Ginzburg^31.

At present I. E. is conducting research on the interaction of particles in two directions at once. On the one hand, this is a semi-phenomenological theory based on taking into account the possibility of the existence of isobaric states of nucleons (it is reflected in work^35). On the other hand, jointly with V. P. Silin and V. Ya. Fainberg, I. E. is developing a new form of the Tamm method proposed by Dyson.

Throughout the entire 20-year period of work on the problem of nuclear interactions, I. E. did not leave aside the study of other questions as well. Here one may, with some conventionality, distinguish three groups of works.

First, these are studies of individual concrete phenomena, called to life mainly by the needs of the national economy that arose during the period of the Great Patriotic War. Problems of this kind I. E. always solves with ease and great skill. Such, for example, are works^25, ^26, ^30, and others.

Second, these are works on the cascade theory of showers in cosmic rays (jointly with S. Z. Belen’kii)^22, ^29, in which, for the first time, the ionization losses of particles were consistently taken into account.

Third, this is the theory, created by I. E. (jointly with I. M. Frank), of the radiation of an electron moving with superluminal velo-

growth in a medium ^20, ^21. Here the nature of Cherenkov—Vavilov radiation, observed when fast electrons pass through matter, was revealed. This phenomenon, the discovery of which represents one of the outstanding achievements of Soviet physics, acquired special interest precisely after the development of Tamm and Frank’s theory.

I. E.’s interest in fundamental questions is reflected in a paper ^27 (carried out jointly with L. I. Mandelstam) on the meaning of the uncertainty relation between time and energy in quantum mechanics.

Already on the basis of what has been said above, one may draw certain conclusions about the characteristic features of I. E. as a researcher. These are, above all, the striving at every stage in the development of physics to study the most topical, the most important problems. Further, it is a superb mastery of the technique of scientific work, of what is usually called the apparatus of theoretical physics—a mastery of this apparatus in which it is placed at the service of the main goal and does not dominate. Finally, it is a subtle understanding of the physical essence of the phenomenon under study, the ability to proceed first and foremost from the qualitative features of that phenomenon.

Such is a far from complete outline of the intensive and substantial scientific work of I. E. Tamm in past years (and here we have not even touched on some of the studies included in the list of I. E. Tamm’s principal works given below). But the present outline cannot give any exhaustive idea of the full significance of I. E.’s activity for the development of Soviet science, also because this activity is by no means exhausted by purely scientific creativity.

While devoting his chief attention to scientific work, I. E. expends considerable effort on pedagogical activity, and on solving the most difficult and important practical and scientific-organizational questions.

Beginning in 1924 as a docent, and from 1930 as professor at Moscow State University and head of the department of theoretical physics, I. E., in collaboration with L. I. Mandelstam, revised the character and content of the courses in theoretical physics taught in the University’s physics faculty. During this period he also wrote the widely known course Foundations of the Theory of Electricity, which has gone through a whole series of editions. I. E. has always attached, and continues to attach, great importance to the training not only of students but also of postgraduates and young scientific workers. It is therefore no accident that among I. E.’s pupils and collaborators there is a whole series of Soviet theoretical physicists. Among them are: S. A. Al’tshuler, S. Z. Belen’kii, D. I. Blokhintsev, A. D. Galanin, V. L. Ginzburg, A. S. Davydov, S. I. Pekar, A. D. Sakharov, E. L. Feinberg, V. S. Fursov, S. P. Shubin, and many others.

The seminars on theoretical physics, conducted for many years under I. E.’s guidance, bring inestimable benefit to a wide circle

...Moscow physicists, as well as physicists from other cities of the Soviet Union who often attend these seminars.

I. E.’s services to Soviet science and to the Soviet country have been highly appreciated. He has been awarded the title of Hero of Socialist Labor, he has been decorated with two Orders of Lenin and the Order of the Red Banner of Labor. Twice I. E. received the Stalin Prize, First Class. In 1933 I. E. was elected a Corresponding Member, and in 1953 a Full Member, of the Academy of Sciences of the USSR.

I. E. meets his sixtieth birthday not as a jubilarian resting on his achievements, but as a scientist full of energy and creative plans, working with intensity and with inexhaustible energy, enthusiasm, and conviction.

LIST

OF THE MOST IMPORTANT SCIENTIFIC WORKS OF I. E. TAMM

1. Electrodynamics of an anisotropic medium in the special theory of relativity, ZhRFKhO, Phys. part, 1924, vol. 56, p. 248.
2. Crystal optics of the theory of relativity in connection with the geometry of a biquadratic form, ZhRFKhO, Phys. part, 1925, vol. 57, p. 209.
3. On the quantum theory of paramagnetism, Zs. f. Phys., 1925, vol. 32, p. 582.
4. An attempt at a quantitative formulation of the correspondence principle and the calculation of the intensities of spectral lines, Zs. f. Phys., 1925, vol. 34, p. 58.
5. On the quantum mechanics of the rotator. Ibid., 1926, vol. 37, p. 685.
6. On the electrodynamics of a rotating electron. Ibid., 1929, vol. 55, p. 199.
7. On the quantum theory of molecular scattering of light in solids. Ibid., 1930, vol. 60, p. 345.
8. On the interaction of a free electron with radiation according to Dirac’s theory of the electron and quantum electrodynamics. Ibid., 1930, vol. 62, p. 545.
9. A note on Dirac’s theory of scattering of light and dispersion. Ibid., 1930, vol. 65, p. 705.
10. On the theory of the photoelectric effect in metals. Ibid., 1931, vol. 68, p. 97 (jointly with S. P. Shubin).
11. Generalized spherical functions and wave functions of the electron in the field of a magnetic monopole. Ibid., 1931, vol. 71, p. 141.
12. On the theory of the photoelectric effect in metals, Phys. Rev., 1932, vol. 39, p. 170.
13. On a possible binding of electrons on crystal surfaces, ZhETF, 1933, vol. 3, p. 34.
14. The magnetic moment of the neutron, DAN, 1934, vol. I, p. 455 (jointly with S. A. Al’tshuler).
15. Exchange forces between neutrons and protons and Fermi’s theory, Nature, 1934, vol. 133, p. 981.
16. The magnetic moment of the nucleus and the properties of the neutron. Ibid., 1934, vol. 134, p. 380.
17. Interaction of neutrons and protons. Ibid., 1934, vol. 134, p. 1010.
18. Zero energy and physical properties of H$_2$O and D$_2$O. Ibid., 1935, vol. 135, p. 229 (jointly with J. D. Bernal).
19. β-radioactivity and nuclear forces, Sow. Phys., 1936, vol. 10, p. 567.

1. Coherent radiation of a fast electron in a medium, Doklady Akademii Nauk, 1937, vol. 14, p. 107 (with I. M. Frank).

2. Radiation of a uniformly moving electron, Journ. of Phys., 1939, vol. 1, p. 439.

3. The soft component of cosmic radiation. Ibid., 1939, vol. 1, p. 177 (with S. Z. Belenky).

4. Motion of mesons in electric fields, Doklady Akademii Nauk, 1940, vol. 29, p. 551.

5. On the origin of nuclear forces, Doklady Akademii Nauk, 1940, vol. 29, p. 555 (with L. D. Landau).

6. Theory of electromagnetic processes in a layered core, Izvestiya Akademii Nauk, Physical Series, 1943, vol. 7, p. 30 (with V. L. Ginzburg).

7. On currents in the ionosphere causing variations of the Earth’s magnetic field, Izvestiya Akademii Nauk, Physical Series, 1944, vol. 8, p. 30.

8. The energy–time uncertainty relation in nonrelativistic quantum electrodynamics, Izvestiya Akademii Nauk, Physical Series, 1945, vol. 3, p. 122 (with L. I. Mandelstam).

9. Relativistic interaction of elementary particles, Journ. of Phys., 1945, vol. 9, p. 449.

10. Energy spectrum of cascade electrons, Phys. Rev., 1946, vol. 70, p. 660 (with S. Z. Belenky).

11. On the forced oscillations of an infinite plate in contact with water, ZhTF, 1946, vol. 16, p. 879 (with L. M. Brekhovskikh).

12. On the theory of spin, ZhETF, 1947, vol. 17, p. 227 (with V. L. Ginzburg).

13. On certain mathematical methods in the theory of particle scattering, Part I, ZhETF, 1948, vol. 18, p. 337.

14. On certain mathematical methods in the theory of particle scattering, Part II, ZhETF, 1949, vol. 19, p. 74.

15. On the relativistic theory of the interaction of nucleons, ZhETF, 1953, vol. 24, p. 3 (with V. P. Silin and V. Ya. Fainberg).

16. Phenomenological theory of the interaction of π-mesons with nucleons, ZhETF, vol. 26, 649 (1954) (with Yu. A. Golfand and V. Ya. Fainberg).