# Tamm, Igor Evgenievich

# TAMM, IGOR EVGENIEVICH

(*b*. Vladivostok, Russia, 8 July 1895; *d*. Moscow, U.S.S.R., 12 April 1971)

*physics*.

From 1899 Tamm’s family lived in the city of Elizavetgrad (now Kirovograd), where his father was a civil engineer. After graduating from the Gymnasium there in 1913, Tamm studied for a year at Edinburgh University; at the beginning of World War I in 1914 he returned to Russia and entered the Faculty of Physics and Mathematics at Moscow University. In 1917 he was a member of the Elizavetgrad City Soviet of Worker and Soldier Deputies and was a delegate to the First Congress of Soviets in Petrograd. The following year Tamm graduated from Moscow University, and in 1921 – 1922 he worked at the Odessa Polytechnical Institute, where Mandelshtam, who greatly influenced Tamm’s later scientific career, was a professor.

From 1922 Tamm worked in Moscow. In 1924 he published his first scientific work, on the electrodynamics of anisotropic media in the special theory of relativity, and became head of the department of theoretical physics at Moscow University, which he directed until 1941. In 1934, after the transfer to Moscow of the Academy of Sciences of the U.S.S.R., Tamm was named director of the theoretical section of its P. N. Lebedev Physical Institute: and from then on, his activity was concentrated there.

Tamm’s first scientific research, begun under the influence of Mandelshtam, was devoted to electrodynamics of anisotropic media, crystal optics in the theory of relativity, quantum theory of paramagnetism, and nonrelativistic quantum mechanics. In a major investigation on the quantum theory of the molecular scattering of light in solid bodies (1930) Tamm conducted the first quantification of elastic (sound) waves in solid bodies and introduced the concept of quanta of sound; later called phonons by Y. I. Frenkel, this concept gained wide acceptance in contemporary physics. In this work he also investigated the Rayleigh scattering of light (the Mandelshtam-Brillouin doublet) and combination scattering (the “Raman effect”), discovered in 1930 by Mandelshtam and G. S. Landsberg in crystals and, at the same time, by C. V. Raman and Krishnan in liquids.

In 1930 Tamm published two works dealing with the phenomenon of relativistic quantum mechanics of the electron, formulated by Dirac: “Über die Wechselwirkung der freien Elektronen . . .,” and “Zamechanie dirakovskogo teorii sveta i dispersii” (“A Note on the Dirac Theory of Light and Dispersion”). Dirac’s theory received almost general acceptance when it appeared, since it automatically led to the existence of a spin on the electron and allowed a natural interpretation of the fine structure in the spectrum of the hydrogen atom. But the concepts of negative energy states that were involved in the theory appeared unusual until the discovery of the positron and demanded more detailed study of the conclusions from the theory and their experimental verification.

With the aid of a strictly consistent quantum mechanical method, Tamm confirmed the results obtained earlier by Felix Klein and Yoshio Nishina on the basis of the method of correspondence. He also showed that according to Dirac’s theory, scattering of even more low-frequency quanta of light from free electrons must occur through intermediate states with the negative electron energies. Thus it was shown that the negative energy states cannot be removed from Dirac’s theory. In this work Tamm also proposed a new method of calculation, later developed by H. B. G. Casimir and named for him. Concurrently with Dirac and Oppenheimer, Tamm independently concluded that the fall of the free electron to a negative level was inevitable and determined the probability of annihilation of the electron and “hole.”

In 1931 – 1933 Tamm studied the quantum theory of metals, specifically the external photoeffect in metals and the state levels of the electrons on the surface of the metal. His work with S. P. Shubin was the first to show that the external photoeffect is caused by the presence of a jump in potential on the border of the metal vacuum and is associated with the effect of surface absorption of light, while the optic absorption of light by the metal is associated with the volume effect. In works dating from 1932 – 1933 Tamm was the first to show, on the basis of quantum mechanics, that, along with the known “zone” electron states inside the crystal, there could also be electron states of a completely different type on the surface of the crystal. Further theoretical and experimental research on semiconductors and dielectrics confirmed that these “Tamm surface levels” of electrons are evident in a great many physical phenomena, particularly in semiconductors, and lead to “barrier” layers.

From 1934 Tamm devoted his research to the atomic nucleus and cosmic rays. Two of the early works were related to the nature of nuclear forces: “Obmennye sily mezhdu neytronami i protonami i teoria Fermi” (“Exchange Forces Between Neutrons and Protons, and Fermi’s Theory,” 1934) and “β-radioaktivnost i yadernye sili” (“Beta Radioactivity and Nuclear Forces,” 1936). Using Fermi’s theory of beta radiation, Tamm sought to determine whether the nuclear forces could be caused by an exchange between nucleons, electrons, and neutrinos. In the 1934 work he gave a formula for the potential and evaluated the quantity of force arising in this process, but this kind of exchange interaction proved to be too weak in comparison with the observed nuclear forces and consequently could not serve to explain them. Later it was discovered that the exchange nature of nuclear forces corresponds to the activity; but the exchange is realized not by electrons and neutrinos, as Tamm suggested, but by pi-mesons. All later theories of nuclear forces were constructed according to the theoretical scheme developed in these investigations by Tamm but took into account the role of the pi-meson.

At the same time that he was conducting this research. Tamm and S. A. Altshuler published works on the magnetic moment of the neutron. By analyzing the material he had obtained experimentally. Tamm concluded that although the neutron is a neutral particle, it actually has a magnetic moment. He also correctly estimated the negative sign of this moment. These investigations led Tamm to another important conclusion: that despite current opinion, mesons, which carry an interaction between nucleons, do not have stationary levels in the central Coulomb field. This result led to the work (with L. D. Landau) “O proiskhozhdenii yadernykhsil” (“On the Origin of Nuclear Forces,” 1940).

In 1937 – 1939 Tamm and I. M. Frank developed the theory of radiation of the electron, which moves through a medium with a velocity exceeding the velocity of light in that medium. This theory led to an understanding of the nature of the radiation discovered by S. I. Vavilov and P. A. Cherenkov. For this work Tamm was awarded the Nobel Prize (with I. M. Frank and P. A. Cherenkov) in 1958.

During World War II, Tamm carried out a number of complex practical investigations. In 1945 he returned to the interaction of molecules. In the first of these works he formulated a new method of calculating the interaction not dependent on an expansion in terms of a coupling constant, the large size of which makes perturbation theory inapplicable to quantum meson dynamics. This method, applied by Tamm in 1945 and developed by P. D. Dankov in 1950, is known as the Tamm-Dankov method. It is widely used in the theoretical study of the interaction of mesons with nucleons and of nucleons with each other, particularly in the study of the deuteron.

In 1947 Tamm and V. L. Ginzburg formulated a theory of a molecule that can be found in states with various spins. This work contains the first relativistically invariant wave equations for particles with inner degrees of freedom, described by continuous variables. Tamm’s research in the theory of nuclear forces and elementary particles was continued in two directions. One was the construction of a polyphenomenological theory based on the possibility of the existence of isobaric states of nucleons. On this basis Tamm and his colleagues investigated processes of scattering, the photoproduction of pi-mesons by nucleons, and the interaction of nucleons. The other was the development by Tamm, with V. Y. Feynberg and V. P. Silin, of a new form of Tamm’s method, proposed by F. J. Dyson and intended particularly for the study of the interaction of pi-mesons with nucleons.

Tamm worked on other questions, including the investigation, according to cascade theory, of cosmic ray showers (with S. Z. Belenky), which were first considered to be ionization losses of particles. Of very great importance was the theory of gas discharge in a powerful magnetic field developed in 1950 by Tamm and A. D. Sakharov. It was the basis of all subsequent Soviet research on guided thermonuclear reactions and led to important results.

An important place among Tamm’s investigations was occupied by the work (carried out in 1946 with Mandelshtam) on the meaning of the indeterminacy between time and energy in quantum mechanics. Also worth noting is his work, done in 1948 – 1949, on several mathematical methods for the theory of particle scattering. During his last years Tamm searched for ways to remove fundamental difficulties in the theory of elementary particles and often presented survey reports at conferences. For example, at the All-Union Conference on Quantum Electrodynamics and the Theory of Elementary Particles (1955), he presented the survey reports “Metod oberzania uravneny po chislu chastits v teorii mezonov” (“Method of Truncating the Equation According to the Number of Particles in the Theory of Mesons”), written with V. P. Silin and V. Y. Feynberg, and “Polufenomenologicheskaya izobarnaya teoria vzaimodeystvia mezonov s nuklonami” (“Semiphenomenological Isobar Theory of Interaction of Mesons With Nucleons”), written with Y. A. Golfand, G. F. Farkov, and others. At the All-Union Conference on the Physics of High-Energy Particles (1956), Tamm, Silin, and Feynberg delivered the survey report “Sravnenie mezonnoy teorii s eksperimentami” (“Comparison of Meson Theory With Experiments”).

Tamm’s activity was not limited to scientific research. He gave much attention to teaching, to the solution of practical and administrative problems, and to social questions. From 1924 as a docent, and from 1930 as professor and head of the department of theoretical physics at the M. V. Lomonosov Moscow State University, Tamm (in collaboration with Mandelshtam) supervised the orientation and content of all courses in theoretical physics and lectured at the Physics and Mathematics Faculty of the university. During this period he wrote *Osnovy teorii elektrichestva* (“Principles of the Theory of Electricity”), which went through many editions.

The fight for scientific biology, which Tamm led, also is worthy of attention. He maintained the firm conviction that leadership of the natural sciences would pass in the relatively near future from physics to biology. Tamm was active in the Pugwash movement and was awarded the Order of State Prize, First Degree, for his service to science. In 1933 he was elected corresponding member and, in 1953 active member, of the Academy of Sciences of the U.S.S.R.

## BIBLIOGRAPHY

I. Original Works. Tamm’s early writings include “Über die Quantentheorie der molekularen Lichtzerstreuung in festen Köpern,” in *Zeitschrift für Physik*, **60** (1930); 345 – 363; “Über die Wechselwirkung der freien Elektronen mit der Strahlung nach der Diracschen The orie des Elektrons und nach der Quantenelektrodynamik,” *ibid.,***62** (1930), 545 – 568; “Über eine mögliche Art der Elektronenbindung an Kristalloberflächen,” in *Physikalische Zeitschrift der Sowjetunion*, **1** (1932), 733; “Exchange Forces Between Neutrons and Protons, and Fermi’s Theory,” in *Nature*, **133** (1934), 981; “Nuclear Magnetic Moments and the Properties of the Neutron,” *ibid.,***134** (1934), 380; “Kogerentnoe izluchenie bystrogo elektrona v srede” (“Coherent Radiation of Fast Electrons Passing Through Matter”), in *Doklady Akademii nauk SSSR*, **14** , no. 3 (1937), 107 – 112; “Svechenie chistykh zhidkostey pod deystviem bystrykh elektronov” (“Luminenscence of Pure Liquids Under the Influence of Fast Electrons”). in *Izvestiya Akademii nauk SSSR*, Seria fiz. (1938), nos. 1 – 2, 29, written with I. M. Frank and P. A. Cherenkov; “The Transmutations of the Cosmic-Ray Electrons and the Nuclear Forces,” in *Physical Review*, **53** (1938), 1016 – 1017; and “Radiation Emitted By Uniformly Moving Electrons,” in *Journal of Physics of the* U.S.S.R., **1** nos. 5 – 6 (1939), 439.

Subsequent works are “O proiskhozhdenii yadernykh sil” (“On the Origin of Nuclear Forces”), in *Doklady Akademii nauk SSR*, **29** (1940), 555 – 556, written with L. D. Landau; “Izluchenie elektrona pri ravnomernom dvizhenii v prelomlyayushchey srede” (“Theory of the Electron in Uniform Motion in a Refracting Medium”), in *Trudy fizicheskago instituta*, **2** , no. 4 (1944), 63, written with I. M. Frank; “The Energy Spectrum of Cascade Electrons,” in *Physical Review*, **70** (1946), 660 – 664, written with S. Z. Belenky; “K teorii spina” (“Toward a Theory of Spin”), in *Zhurnal eksperimentalnogo i teoreticheskogo fizika*, **17** , no. 3 (1947), 227, written with V. L. Ginzburg; and “O nekotorykh matematicheskikh metodakh teorii rasseyania chastits” (“On Certain Mathematical Methods in the Theory of Scattering of Particles”), *ibid.*, **18** , no. 4 (1948), 337 – 345, and **19** , no. 1 (1949), 74 – 77.

Later writings include “K relyativistskoy teorii vzaimodeystvia nuklonov” (“Toward a Relativistic Theory of the Mutual Interaction of Nucleons”). *ibid.*, **24** , no. 1 (1954), 3; “Polufenomenologicheskaya teoria vzaimodeystvia π-mezonov s nuklonami. Rasseyanie π-mezonov nuklonami” (“Semiphenomenological Theory of the Mutual Interaction of pi-Mesons With Nucleons. Scattering of pi-Mesons With Nucleons”), *ibid.*, **26** , no. 6 (1954), 649 – 667, written with Y. A. Golfand and V. Y. Feynberg; “Metod usechennykh uravneny polya i ego primenenie k rasseyaniyu mezonov nuklonami” (“Method of Truncating Field Equations and Its Application to the Scattering of Mesons by Nucleons”). *ibid*., **29** , no. 1 (1955), 6 – 19, written with V. P. Silin and V. Y. Feynberg; “O strukture nuklonov” (“On the Structure of Nucleons”), ibid., **32** , no. 1 (1957), 178 – 180; “Teoria magnitnykh termoyadernykh reaktsy” (“Theory of Magnetic Thermodynamic Reactions”), in *Fizika plazmy i problemy upravlyaemykh termoyadernykh reaktsy* (“Plasma Physics and Problems of Thermodynamic Reactions”), I (Moscow, 1958), 3 – 19, 31 – 41; and *Osnovy teorii elektrichestva*, 7th ed. (“Principles of the Theory of Electricity”; Moscow, 1957).

II. Secondary Literature. *Igor Evgenievich Tamm, Materialy k biobibliografii uchenykh SSSR*. Seria fizik, no. 9 (Moscow, 1959), with introductory articles by V. L. Ginzburg and E. L. Feynberg and a bibliogaphy; V. L. Ginzburg and E. L. Feynberg, “Igor Evgenievich Tamm,” in *Uspekhi fizicheskikh nauk*, **56** , no. 4 (1955), 469 – 475, with bibliography of Tamm’s most important works; V. L. Ginzburg, A. D. Sakharov, and E. L. Feynberg, “Igor Evgenievich Tamm,” *ibid.*, **86** , no. 2 (1965), 353 – 356; I. M. Lifshits and S. I. Pekar, “Tammovskie svyazannye sostoyania elektronov na poverkhnosti kristalla i poverkhnostynye kolebania atomov reshetki” (“Tamm Connected Electron States on the Surface of a Crystral and Surface Vibration of Atoms in a Lattice”), *ibid.*, **56** , no. 4 (1955), 531 – 568; S. V. Vonsovsky, A. V. Sokolov, and A. Z. Veksler, “Fotoeffekt v metallakh” (“Photoeffect in Metals”), ibid., 477-530; and V. P. Silin and V. Y. Feynberg, “Metod Tamma-Dankova” (“The Tamm-Dankov Method”), *ibid.*, 569 – 635.

J. G. Dorfman

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