HUEPHAH 0H3HKA, 2009, moM 72, № 5, c. 932-934
= IN MEMORY OF YAKOV ABRAMOVICH SMORODINSKY =
YAKOV ABRAMOVICH, AS I REMEMBER HIM
© 2009 J. Nyiri*
KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary
Received October 14, 2008
PACS: 01.60.+q
My first acquaintance with the name of Yakov Abramovich was when I, as a student of the Leningrad State University, have read his papers written with Pomeranchuk [1] and Landau [2]. Later, in my last year at the university, thinking about a possible future working place, I met G. Domokos who at that time was a researcher in Dubna. He gave me the advice to go to Dubna for a while and to look for the possibility to work with Professor Smorodinsky who is the broadest minded physicist he has ever met.
As it happened, after four years of work at the Central Research Institute for Physics in Budapest I went to Dubna. I did not really dare to think about a common work with Yakov Abramovich. From what I knew about his results he seemed to be such a great man that I could not imagine myself in this role. On the other hand, since my diploma work was connected with the dispersion relations, it was natural to continue this topics, so I spent my first year in Dubna working on current algebra.
People unavoidably meet on the narrow corridors of the Laboratory of Theoretical Physics. Yakov Abramovich stopped me several times and we talked about the most different things. His knowledge and the field of his interests were quite amazing — from Hungarian poetry to the last achievements in physics. He followed closely the new results, appreciated their significance, and saw their relevance from the point of view of already known phenomena immediately. His days seemed to be much longer than 24 hours. He was thinking about various problems at the same time, such as nucleon—nucleon interactions, symmetries in physics, nonrelativistic systems with dynamical symmetries, integral representations for relativis-tic amplitudes, unitary representation of the Lorentz group, Poincare and Lorentz invariant expansions of relativistic amplitudes, Regge trajectories, and it was clear that, working on a problem, he knew that there was an answer and he has foreseen what it was.
E-mail: nyiri@rmki.kfki.hu
I feel fortunate that he finally persuaded me to join him in the work on the three-body problem. During those years — from 1968 to 1970 — I learned not only what was possible about the subject, but I got acquainted to a whole new world of physics, where facts of the most different fields were interconnected.
In Budapest I was already working on group theory, but it became a new experience to apply it to the classical and the quantum-mechanical three-body problem. As it turned out, the three-body problem in quantum mechanics in general, and in nuclear physics in particular, provided an extremely interesting field for investigations, and the developed technics were useful for the solution of various, sometimes quite unexpected problems (see, for example, [3—6]).
I defended my PhD thesis on this subject in Dubna in 1970, but continued the common work after returning to Budapest, and later, being again in Dubna, until 1979 [7-11].
In classical mechanics or, more precisely, in celestial mechanics the three-body problem was the subject of several rather successful theories. But, naturally, only systems with Newtonian interactions were considered in detail. The case of other forces was practically not investigated.
In quantum mechanics the three-body problem was almost not taken into consideration at that time, or if, then only for practical purposes — calculations of energy levels in 3He, neutron—deuteron scattering — without formulating the problem in general.
A consequent way to handle the problem was to construct a basis first for noninteracting particles and, after that, develop perturbation theory in the framework of which the functions of the interacting particles could be expanded over this basis.
From a group-theoretical point of view the most interesting questions are related to the fifth quantum number Q. This has to be introduced because the quantum numbers describing rotations and permutations are not sufficient to characterize the states in the three-body system.
YAKOV ABRAMOVICH, AS I REMEMBER HIM
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A complete set of basis functions for the quantum-mechanical three-body problem was chosen in the form of hyperspherical functions, characterized by quantum numbers corresponding to the chain 0(6) D D SU(3) D 0(3). Equations were derived to obtain the basis functions in an explicit form.
The problem of constructing a basis for a system of three free particles, realizing representations of the three-dimensional rotation group and of the permutation group, was quite simple in principle. To solve the problem turned out to be, however, rather hard: it was very difficult to obtain a general solution for the calculated set of equations to determine the eigenfunctions. As it turned out, the eigenvalue equations could be simplified considerably, the solution was derived in a closed form, the coefficients were calculated in different ways, numerical results were obtained.
The developed technics can be applied in a variety of cases. First of all, as soon as the quantum-mechanical problem we have considered has the same symmetry properties as the classical one, it was interesting to investigate the classical problem from this group-theoretical point of view. The equations of motion were obtained very easily for both the case of free particles and that of different potentials.
The classification of a three-body system can be used also for the analysis of three-particle decay processes. For example, dealing with a Dalitz plot for decay processes, it turned out to be useful to expand the point density inside the physical region into a series of orthonormal functions. (Such an expansion is similar to the usual phase analysis for two-particle decays. It was helpful in analyzing experimental data, for the calculation of different correlation functions etc.) The set of basis functions chosen as K-harmonics was especially suitable for the description of correlations between the momenta of particles. Also, from a practical point of view it was essential to develop a method to calculate matrix elements of two-particle interactions introducing different potentials and to obtain a proper approximation for bound states as well.
It was not only the physics which was interesting and beautiful. I think the most important fact for me was, especially in the first years in Dubna, that with the help of Yakov Abramovich I got a feeling about a country and about a culture I did not know. At Smorodinsky's place it was always interesting, friendly and warm, the food was nice, and I had the opportunity to meet remarkable people — not only physicists. And, of course, there was the fantastic library of Yakov Abramovich which gave me a lot of pleasure and knowledge.
Our connection remained quite close for many years when I already switched to the quark model and
to high-energy physics. Yakov Abramovich visited us often in Moscow; to our delight, he dropped in every time when he had something to do in the vicinity of our apartment. We — he, my husband V.N. Gribov, and me — had long discussions on new achievements in physics and astronomy, on literature and art, and on events in the world around.
My little son Pali had a very nice company in his early childhood: Masha, Yakov Abramovich's granddaughter, and Seryozha Filippov(the parents of both are my close friends up to now). Pali enjoyed the toys and puzzles invented by Yakov Abramovich — as he remembered in his article in the book containing Smorodinsky's selected papers [11], he often had the feeling that they were of the same age. Growing up, when my son began to study chemistry, he was amazed by the fact that Yakov Abramovich seemed to know everything also about the last research results in chemistry.
It is, in a way, significant for me that the article of Yakov Abramovich which was the first I got acquainted with [1] influenced the only paper on which I was working together with my husband [12]. I regretted deeply that I could present this work [13] only after the death of Yakov Abramovich, at the conference which was devoted to his memory in 1993. This was 15 years ago, and we are at a Smorodinsky conference again; remarkably, these conferences continue to take place regularly. Yakov Abramovich remains with us who were fortunate to know him, and I am sure that his personality and his results will inspire generations of physicists to come.
REFERENCES
1. I. Ya. Pomeranchuk and Ya. A. Smorodinsky, J. Phys. USSR 9,97(1945).
2. L. D. Landau, Ya. A. Smorodinsky, Zh. Eksp. Teor. Fiz. 14,269(1944).
3. J. Nyiri and Ya. A. Smorodinsky, Preprint No. E4-4043, JINR (Dubna, 1968); Yad. Fiz. 9, 882 (1969); in Materials of Symposium on the Nuclear Three-Body Problem and Related Topics (Budapest, 1971); in Selected Papers of Ya. A. Smorodinsky (Moscow, 2001), p. 380.
4. J. Nyiri and Ya. A. Smorodinsky, Preprint No. E2-4809, JINR (1969); Yad. Fiz. 12, 202 (1970); in Selected Papers of Ya. A. Smorodinsky (Moscow, 2001), p. 393.
5. J. Nyiri and Ya. A. Smorodinsky, in Materials of the Second Problem Symposium on Nuclear Physics (Novosibirsk, 1970).
6. J. Nyiri and Ya. A. Smorodinsky, in Materials of the XV International Conference on High Energy Physics (Kiev, 1970).
7. J. Nyiri, Preprint KFKI-72-3 (1972).
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NYIRI
8. J. Nyiri, Acta Phys. Hung. 32, 241 (1972).
9. J. Nyiri, Acta Phys. Slovaca 23, 81 (1973).
10. J. Nyiri, Ya. A. Smorodinsky, Yad. Fiz. 29,833 (1979); in Selected Papers of Ya. A. Smorodinsky (Moscow, 2001), p. 431.
11. P. Nyiri, in Selected Papers of Ya. A. Smorodinsky (Moscow, 2001), p. 535.
12. V. N. Gribov and J. Nyiri, Perturbative QCD Workshop Meeting, Lund Preprint LU-TP-91-15 (1991); V. N. Gribov, Gauge Theories and Quark Con
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