Dates of Life and Activity
Awards and Prizes
About A.I. Akhiezer
In memorium Isaak Yakovlevich Pomeranchuk (A tribute on the 80th anniversary of his birth)
A. I. Akhiezer
Isaak Yakovlevich Pomeranchuk
Isaak Yakovlevich Pomeranchuk was a leading theoretical physicist with an astonishing range of interests covering a wide circle of problems associated with the most important aspects of modern physics. Fundamental research in the field of low temperature physics formed a significant part of his scientific activity. His publications in this field cover the theory of metals, physics of insulators, and the theory of Bose and Fermi liquids. Hence it is appropriate that these reminiscences about Isaak Yakovlevich Pomeranchuk are being published in this journal.
I first met Isaak Yakovlevich early in the autumn of 1935, when he came to Kharkov to work with L. D. Landau in the Physicotechnical Institute (UPTI). At that time, Landau was obsessed with the idea of expanding his theoretical physics department by inviting talented young people from anywhere as long as they were really worthy of being a part of his collective. Lev Vasil'evich Shubnikov, the head of the cryogenics laboratory at UPTI and a close friend of Landau, was also pursuing the same goals. Through their combined efforts, they were able to lure four graduate students from Leningrad to UPTI. Pomeranchuk was one of them.
I saw the graduate student Pomeranchuk for the first time in the library of UPTI. It was perhaps the first library in our country with an open-shelf system, and we got acquainted near one of the shelves. I instantly took a liking towards him. He had a charming personality and a pleasing disposition. Even the strong myopia imparted a characteristic trait to his person. Thus began a friendship that lasted until his death. I became fond of him and quickly understood that he was a specially talented person whose main aim in life was the pursuit of knowledge.
Landau at once gave due recognition to Pomeranchuk or Chuk, as he called him. It was impossible to deny Chuk such an appreciation after he passed Landau's dreaded theoretical minimum in just a few months a rare accomplishment that no one has been able to repeat.
Once a student had passed the theoretical minimum, he earned the right to address Landau familiarly as "tu". He also received his first independent research work. Chuk was assigned the task of studying the electrical conductivity of metals and determining their thermo-emf at very low temperatures. This required a consideration of electron-electron interaction with an arbitrary energy-momentum relation in addition to the traditional interaction of electrons with lattice vibrations. Later, the concept of electrons with an arbitrary dispersion relation was as if rediscovered. But in those distant times, it was perilous to present any calculations to Dau in which the electron energy had a quadratic dependence on the quasimomentum.
Pomeranchuk solved this problem brilliantly. This work, which was later published, formed the material of his graduate thesis that he defended in Leningrad. After this, he finally returned to Kharkov to work with Landau at UPTI.
There were five of us in Landau's section at that time. Landau exerted an enormous influence on us. We literally worshipped him and were afraid to miss even a single word spoken by him. Chuk and I even went to Dau's lectures on general physics which he delivered at the university. We usually returned together to UPTI. On the way back, Landau would buy a large cake which we later ate in his study. We adored Landau and were utterly devoted to him. Chuk once remarked that he was even prepared for penal servitude for Landau's sake.
Afterwards, Chuk was "transferred" from the theory of metals to quantum electrodynamics. He and I were assigned the task of studying scattering of light by light. It did not matter to Landau that we were not conversant with the quantum electrodynamics concepts prevailing at that time. He posed the problem in a very simple form: "Do you know Dirac's equation? What, then, is the matter? Go ahead and solve your problem!"
Matters were made worse by the fact that Landau was deprived of half (and better half at that!) of the problem by Heisenberg and Euler. They used an original approach to consider the scattering of light by light at low frequencies before Landau, and even obtained the Lagrangian of the field, taking nonlinear effects into account. All Landau was left with was the high-frequency part of the problem, which was also quite complicated because no suitable perturbation theories like the present one were available at that time, and it was impossible to carry out gradient-invariant calculations. However, Landau invariably demanded the gradient invariance condition to be satisfied at all stages of calculations. This turned out to be impossible, and we even had serious altercations with Landau which held up the work. Finally, Dau retracted from his stand on gradient invariance and said: "Go ahead and carry out the calculations as you wish. Ultimately, it (gradient invariance) will have to show up."
We obtained our first result, according to which the scattering amplitude component not containing four-momenta was found to be equal to zero as 144 terms completely canceled out. This meant that we had not lost gradient invariance. Landau was ecstatic. Soon after, we found the amplitude for large momenta and small scattering angles. Dau was happy with the results and together we sent this paper for publication in "Nature."
After completing the assignment, we allowed ourselves the luxury of a short leisure; we went for a walk in the city park, took showers there, and definitely went to free concerts of classical music which Chuk adored. Chuk was an excellent reciter. I remember well his recitation of the "Unfaithful Maiden" from Pushkin's "Black Shawl." We went to the movies infrequently; I recall, for instance, that we saw Chaplin's City Lights together. We were evicted from the showers in the park by menacing knocks at the door and by the long queues. It seems that we would get involved in scientific discussions and, oblivious of the passage of time, thus causing "holdups."
I was fascinated by the inimitable style of Chuk, always marveling at how he could evaluate natural logarithms in his head, and how he could tell the exact time on his watch which had the hour hand only.
Having solved the problem of scattering of light by light, Chuk and I began working on the coherent scattering of γ-rays by the atomic nuclei. We soon realized that the third approximation should not make any contribution to the scattering amplitude since it is independent of the choice of the sign of vacuum electron charge. This is a manifestation of Furry's familiar theorem which was not known at that time. After completing the computations in the fourth approximation, we wrote a paper which was approved by Dau. Later, at the Nuclear Conference in Moscow, Landau introduced us and our work to Wolfgang Pauli himself, whose response was favorable. These papers are interesting not only because of the new physical results contained in them, but also because they contain an interesting result from the methodological point of view. We found that infinities can be certainly eliminated by imposing the requirement of gradient invariance. Our results were also appreciated by Victor Weisskopf who had once worked at UPTI.
In 1937, Landau moved to Moscow to work at Kapitza's Institute of Physical Problems. Chuk also left for Moscow from where he went to Leningrad and then returned to Moscow again. Our meetings became rare, but we were continuously in touch.
Our contact was interrupted by the outbreak of the Second World War. After the War, however, I was again in Moscow, working at the Moscow Power Institute. Chuk introduced me to Igor Vasil'evich Kurchatov and made every effort to secure me a job at Kurchatov's Institute. After a fairly tiring process, I was allowed to join the section headed by Pomeranchuk on a part-time basis. I was very happy to be with Chuk again, and because we were together with Dau and my brother Naum Il'ich, a famous mathematician, and also because Kurchatov needed our services, which mean that our work was important for our country.
Kurchatov treated us very nicely. We often worked in his office in the evenings. Occasionally, when he went to town, he gave us a lift to the Kremlin.
Pomeranchuk's interests were varied and wide-ranged. He worked in all branches of theoretical physics except the theory of relativity. He had an astonishing knack of grasping the essence of each new physical theory and could use it to obtain new results. Hence he left behind a rich literary heritage. The three volumes of his collected works contain papers on low temperature physics, neutron physics, particle physics, as well as physics of fundamental interactions. He worked on the theory of metals, physics of insulators, problems in quantum liquid theory, general theory of scattering, quantum electrodynamics, passage of charged particles through matter, cosmic rays, magnetic Bremsstrahlung, field theory, physics of strange particles, resonances, weak interactions, peripheral interactions, diffraction process, and asymptotic high-energy physics.
Naturally, it is simply impossible to describe in such a brief sketch the results obtained by Isaak Yakovlevich in various branches of physics. I would simply like to mention just a couple of his significant works. According to the first of these works, the physical charge of an electron is equal to zero if we strictly remain within the framework of quantum electrodynamics (zero-charge theorem). In another work, Pomeranchuk proved the equality of total cross-sections of interactions of nucleons and antinucleons at high energies (Pomeranchuk's theorem).
A book by A.I. Akhiezer and I.Ya. Pomeranchuk, written in 1947 and published in 2002
Pomeranchuk always felt what was vital at every stage of development of the physical science. This quality of his was simply astounding, In this essay of mine, it is not possible, and perhaps not even necessary, to present a detailed picture of Pomeranchuk's scientific activity, the more so because this task was eminently fulfilled by V. B. Berestetskii in his article which appeared in Vol. 1 of the Collected Works of Pomeranchuk. I shall simply mention some of his publications in the field of low temperature physics, and then describe in detail our joint activity during Pomeranchuk's stay in Moscow.
In the field of low temperature physics, Pomeranchuk worked on the theory of metals, physics of insulators, theory of Bose and Fermi liquids. The theory of metals involves electrical conductivity studies at low temperatures, formulation of the theory explaining the Shubnikov-de Haas effect in bismuth, investigations of the thermal conductivity of bismuth, isotopic effect in residual electric resistance of metals and, finally, the interaction between conduction electrons in ferromagnets.
In his paper on the theory of electrical conductivity of metals at low temperatures which he wrote together with Landau, Pomeranchuk showed that the resistance of metals must change not in proportion to T5, but to T2.
Together with B. I. Davydov, Pomeranchuk studied the effect of magnetic field on the electrical conductivity of bismuth single crystals at low temperatures by investigating the magnetoresistance oscillations in bismuth by taking into account both electrons and holes.
An analysis of the isotopic effect in the residual electrical resistance of metals showed that the presence of isotopes in a crystal without physical defects and chemical impurities is responsible for a finite residual electrical resistance.
In the paper dealing with the interaction of conduction electrons in ferromagnets, which we published together with Pomeranchuk, it was shown that the exchange of spin waves in ferromagnets is responsible for an additional mutual attraction between conduction electrons. It was indicated for the first time that while investigating the mechanism of superconductivity, it is necessary to take into account not only the electron-electron interaction caused by phonon exchange, but also the interactions caused by the exchange of other quasi particles, e.g., magnons, plasmons, etc.
In the theory of insulators, Pomeranchuk published a number of papers on the thermal conductivity of insulators at low as well as high temperatures, in which he demonstrated the necessity of taking into account the four-phonon collisions which are responsible for the emergence of thermal resistance in the crystal.
The paper on the thermal conductivity of paramagnetic insulators was devoted to finding the role of the paramagnetic spectrum. Together with Pomeranchuk, we also studied the thermal equilibrium between spins and the lattice. Our investigations led to the value of the amount of energy transferred from the lattice to the spin system and of the time of relaxation between them.
Together with L. D. Landau, Pomeranchuk made a significant contribution to the theory of a Bose liquid by studying the motion of foreign particles in 3He. They showed that no impurities can participate in the superfluid motion of 3He if their concentration is quite low.
In the paper devoted to the effect of impurities on the thermodynamic properties and second sound velocity in 3He, it was shown that small concentrations of impurities cause significant changes in the thermodynamic properties of 3He as well as in the second sound velocity.
The scattering of neutrons with energy equal to a few degrees in liquid helium 3He was also investigated by Isaak Yakovlevich and myself together. We showed that scattering of slow neutrons with an energy equal to a few degrees at temperatures below the phase transition point is negligibly small.
The Fermi-liquid theory was studied in the papers on Fermi-liquid stability and liquid 3He theory, on the theory of slow-neutron scattering in a Fermi liquid, and on the theory of excitation of zeroth sound in it (these papers were published by Pomeranchuk together with A. I. Akhiezer and I. A. Akhiezer).
However, let us return to the Moscow period in the life of Pomeranchuk and to our meetings.
At that time, Kurchatov was interested in the problem of scattering of slow neutrons. We took to serious investigations of the elastic and inelastic scattering of slow neutrons in crystals involving the absorption and emission of one or more phonons. The capture of slow neutrons in the crystals was studied and the possibility of emergence of "cold" neutrons was established (independently of Fermi). We also showed how a transition to scattering between free nuclei takes place, found the neutron distribution function in crystals, and presented the theory of neutron refraction.
We paid considerable attention to the problem of slowing down of neutrons, obtained the energy distribution function for neutrons, and studied in detail the transition from kinetic to diffusion approximation.
Pomeranchuk and I constructed the theory of resonance absorption of neutrons in homogeneous media. It later turned out that our results are in accord with those obtained later by Wigner.
Together with I. I. Gurevich, Pomeranchuk also constructed the theory of resonance absorption of neutrons in heterogeneous media. All these calculations were found to be necessary for the creation of nuclear reactors.
In 1947, we wrote a fairly large book (over 500 pages) entitled "Theory of Neutron Multiplying Media." Unfortunately, this book could not be published for reasons of secrecy although, strictly speaking, there was nothing secret in it. It was just a normal scientific treatise, although one could find faults with it over trifles. I would like to place on record one such curious trifle.
For family reasons, Pomeranchuk had to shift to Leningrad from Moscow, and I was left alone to handle matters concerning our book in Moscow. Once I was called to a General in the Special Department. He took out a notebook from his pocket and said, "Your manuscript contains the formula Δn = ∂n/∂t, where did you get it?" I explained that this is the standard diffusion equation (with which all physicists are well acquainted) written for the case when the diffusion coefficient is equal to unity. The General asked, "But why did you use the same notation that appears in my materials?" I replied, "Much though I would like to, it is hard to think of any other notation in this equation." We bade farewell to each other, but I could see that the General was not satisfied by my explanation. Perhaps he was afraid that the publication of our book might leak some secret methods worked out by the Special Department.
However, Igor Vasil'evich Kurchatov allowed us to publish some portions of the book which were of general physical nature and contained information which was already well known. These were problems related to the general theory of the nucleus. We started looking for a new name for our publication. We could not call it "Theory of the Nucleus" since the manuscript did not contain the entire nuclear theory. We turned to my brother Naum Il'ich for advice, and he jocularly remarked. "'You need not look far. Take the lead from Stalin. He called his book "Some Problems in Leninism," so you can call your book "Some Problems in Nuclear Theory." We decided to follow his advice. The manuscript was reviewed by Igor' Evgen'evich Tamm and Vladimir Aleksandrovich Fock. They gave an excellent evaluation and our first monograph entitled "Some Problems in Nuclear Theory" appeared in 1948. This book played an important role for preparing theoretical nuclear physicists.
Our work on the scattering of slow neutrons actually served as the starting point for subsequent investigations in which we studied the possibility of reconstructing the phonon spectrum of crystals from the neutron scattering data.
At the recommendation of Lev Davidovich Landau and Mikhail Aleksandrovich Leontovich, the book "Some Problems in Nuclear Theory" was awarded the L. I. Mandel'shtam Prize of the Academy of Sciences of the USSR.
We were also interested in the region of high neutron energies. It was shown by Bohr, Placek, and Peierls that diffraction of neutrons absorbed by heavy nuclei occurs in this region. This phenomenon is analogous to the diffraction of light at an absorbing sphere.
We were able to generalize their theory to the case of fast protons. The resulting diffraction pattern can be called diffraction of charged rays.
The method developed by us was widely used in many works and was called the Akhiezer-Pomeranchuk-Blayer approximation. It can be safely stated that Pomeranchuk played a vital role in the creation of the theory of nuclear reactors.
Diffraction or peripheral interactions were subsequently considered in a cycle of works by Pomeranchuk together with E. L. Feinberg, as well as in the paper in which Pomeranchuk and Landau considered the phonon emission as a result of collision of fast pions with nucleons.
During that (Kurchatov) period, we completed a work in which the possible laws of scattering of slow neutrons by nuclei were obtained for the first time from the most general assumptions concerning the analytical properties of scattering amplitudes.
Those were unforgettable times! As I reminisce all these events now, I feel very sad. The dedication to Gothe's "Faust" comes to my mind: "The urgency recedes, and the remoteness becomes overt on approach."
Chuk called me his brother, and my son his nephew. Many years later, Chuk presented the reprints of his papers to my son with the citation "To my dear nephew."
For a brief period, Landau "isolated" Chuk. In those days, I would return from Landau's seminars to Chuk at Serov Proezd and recount all that had been discussed at the seminar. Only after this would I go back to my residence in Lefortovo. Both Chuk and Dau were quite upset over the break in their relations. Fortunately, it did not last long and everything soon ended peacefully.
When Chuk left Kurchatov to work with Alikhanov, I retained my part-time job with Kurchatov, but returned at his behest to Kharkov to work with K. D. Sinel'nikov at UPTI. I became a regular commuter to Moscow where Chuk and I met frequently and spent the same amount of time together as in Kharkov. In Moscow, we both lived through the tragedy caused by Kurchatov's demise. Chuk and I stood in vigil by the coffin which was placed in the Columned Hall so that people could pay their last respects.
Each of my visits to Moscow at that time and in later years began with a visit to Chuk who was always glad to see me. When Volodya Berestetskii arrived, Chuk would examine us about our awareness of what was being published in "current issues." Our strict examiner frequently held me as an example before Berestetskii. After this Chuk used to serve me tea, very hot and very strong, which he brewed by some special method known only to himself. Each time he would jocularly remark, "Look, I have thoroughly disinfected the glass!"
This was followed by scientific discussions and work which always ended with a visit to Landau so we could appraise him of our results and get them "acknowledged."
I. Ya. Pomeranchuk was a true Knight of science, and his name will always be remembered in the temple of learning about which Einstein once wrote a temple from which many people could be banished without bringing any harm to science, and only a few would be allowed to remain. I. Ya. Pomeranchuk was one of the chosen few.
Translated by R. S. Wadhwa
© 1994 American Institute of Physics