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About S.G. Nilsson

International Conference on Finite Fermionic Systems
Nilsson Model 50 Years
June 14-18 2005, Lund, Sweden


A portrait of Sven Gösta Nilsson
Torsten Gustafson, Kungliga Fysiografiska Sällskapet i Lund, Annual Report 1980

Sven Gösta Nilsson was born in 1927. His farther was a well-known preacher in the Swedish Evangelical Mission, active in the northern part of the province of Scania. His mother died early, and at the age of 12 he also lost his father.

Very early he displayed those characteristics which would later make him a great scientist and teacher. Both in Ängelholm, and later in Helsingborg, he had schoolmates who were destined to achieve important things for society later in life, and he stayed in touch with them throughout his life. In this inspiring circle he became the foremost, admired for his manyfaceted gifts, his joy in penetrating intellectual problems and his helpfulness towards his fellows, when they asked him to clarify difficult lines of reasoning. His physics teacher has described him as the greatest talent in physics that he has met in his teaching career. His teacher of Christian religion and philosophy says: "Sven Gösta Nilsson gave the impression of a brilliant intelligence and a remarkably fine human being. After thirty years of teaching, I must admit that no other student has made such a strong impression on me as Sven Gösta Nilsson."

Upon graduating from secondary school, he studied technical physics at the Royal Institute of Technology in Stockholm. During these years he wrote papers in physics for Lamek Hulthén and Kai Siegbahn. At that time he studied for one year in Pasadena and received a Bachelor of Arts degree. In his last year of study there he stated, in a conversation with his former physics teacher in Helsingborg, that he thrived at the Royal Institute of Technology but nevertheless felt that a career in engineering was not the right thing for him. Among other things, he expressed a strong desire to "work together with people". His teacher advised him to switch to the study of theoretical physics in Lund. He had some anxiety about starting in a new field, but having entered the department in 1950, he was quickly fascinated by the new physics.

The interests of the department at that time included both elementary particle physics, where especially Gunnar Källén was active, and nuclear physics where Sven Gösta Nilsson came to make his great contributions. The atomic nucleus attracts a great deal of purely physical interest as a many-body problem of great richness and variety. The shape of the nucleus can vary from spherical to ellipsoidal, ´pear-shaped´, etc. Also its constitution in terms of protons and neutrons can vary considerably.

The first theory of the atomic nucleus came from Niels Bohr in 1936, when he showed that in energetic reactions it behaves in analogy with a liquid drop, the reason being the very short range of the nuclear forces.

Around 1949 it was discovered that the nucleus in its ground state and near-lying excited states exhibits a new aspect. Surprisingly, it was found that the individual nucleons are not much influenced by their nearest neighbours, but appear to move in a potential made up as the sum from the other nucleons (the shell model or the independent particle model). There is a clear analogy with the motion of the electrons around the atom. In that case there are particularly stable configurations, the inert gases. The addition of an electron to neon gives sodium, the addition of two electrons gives magnesium. It is the additional electrons which essentially determine the chemical properties of the elements.

The analogies of the inert gases were found in nuclei, namely the so-called magic nuclei with 2, 8, 20, 28, 50, 82, ... protons or neutrons. If, for example, the number of protons is 20 and the number of neutrons is 28, the nucleus is even ´doubly magic´. The shell model explains this, and if for example a nucleon is added to a doubly magic nucleus, there is a good agreement with the data if it is assumed to move in a spherical potential.

However, it turned out that nuclei in the regions between the magic nuclei could not be regarded as spherical. This is apparent from their special electrical properties, among other things. Aage Bohr, together with Ben Mottelson, showed that large groups of nuclei were strongly ellipsoidal. This raised the fundamental problem of how to determine eigenfunctions and eigenenergies for protons and neutrons in an ellipsoidal potential. We were in longstanding close contact with the Bohr Institute, where in the beginning of the fifties important progress was started. Sven Gösta Nilsson's capacity, which was immediately noticed in Lund, was also clear to Aage Bohr and Ben Mottelson. They suggested that he should work on this broad problem. The results that he achieved turned out to be highly remarkable.

The eigenfunctions and energy for all of these nucleons had to be calculated, and this must be done for different values of the eccentricity. Sven Gösta Nilsson carried out these complicated calculations with the utmost elegance and precision and he chose the approximations for the nuclear field with the greatest care. Although others also tried to solve the same problem, it was Nilsson's work that came to be of lasting value. The reason is his deep penetration and broad understanding of the experimental facts, and the rarely seen mathematical elegance which characterizes his treatment of physical problems. Through the skillful mathematics, the results in this classic piece of work emerge with unusual clarity.

This work determined the different eigenfunctions and their eigenenergies as a function of the nuclear eccentricity. Then it was possible to place for example the protons in the respective energy levels, from the deepest, i.e. the most strongly bound, up to the highest. In every energy level there is room for two nucleons of opposite spin, so outwardly many of their properties cancel - total spin, magnetism etc. In an odd nucleus a single nucleon occupies the highest level. This nucleon essentially determines the external properties of the entire nucleus.

Sven Gösta's calculations give the properties of every single nucleus, and in particular the highest one, which is so important for the properties of the nucleus.

The energy levels proved to be surprisingly sensitive to the eccentricity. In a spherical nucleus, one particular eigenfunction might come highest, but for a certain eccentricity it could be a completely different one, giving the nucleus completely different properties. Furthermore, since he was able to determine the eccentricity from the calculations, he could predict theoretically for all nuclei, with their different sets of protons and neutrons, what their properties should be. How did this relate to experimental facts? In an extensive paper, Mottelson and Sven Gösta Nilsson compared theory and experiment over a wide range of nuclei. Also the theory was tested in many other parts of the world.

As a rule, the agreement between theory and experiment is only fragmentary and scanty. But in this case there was an incredible, astounding agreement with nature. For one nucleus after another it turned out that the calculations described the nuclear properties well, its spin, rotational states, magnetism etc. And if, initially, there was a lack of agreement with the experiments, it turned out later, in an amazing way, that the calculations were right and the earlier experiments were wrong.

Thus the so-called Nilsson model was created. The leading nuclear physicist Victor Weisskopf, at that time the managing director of CERN, dwelt on it in his summary at the international conference on nuclear structure in 1960. There he discussed ´the independent particle model´. "I think it is the impression of most of us that this model works surprisingly well ... . Another equally impressive indication of the validity of the independent particle model is the immense success of the Nilsson scheme. When I speak of the independent particle model, I do not restrict myself to the spherical potential well, but I include also the deformed potential well which Nilsson has calculated. We know the famous level scheme, and the popularity of his paper - I am sure this is the one paper which one finds on the desk of every nuclear physicist - is a proof of the fact that this independent particle model works surprisingly well. I remind you of many reports and in particular of the report of dr. Perlman who saw how far one really can go with the Nilsson level scheme."

Let me quote also the article ´Swedish Nuclear Physics´ in Kosmos, 1976, by Ingmar Bergström and Arne Johansson. "Sven Gösta's calculations are usually expressed in diagrams, where the sequence of levels is drawn as nuclear eccentricity. These diagrams are called Nilsson diagrams. No other Swedish physicist in recent years has had his name as firmly implanted in the international consciousness as Sven Gösta Nilsson."

He continued to study a rich variety of fresh problems in nuclear physics and published over 70 papers, which continued to make him a leading researcher on the international level in nuclear physics. He retained his close ties with Aage Bohr and Ben Mottelson. Furthermore, in 1956-57, 1960-61 and 1972-73 he was a visiting professor at the University of California in Berkeley, where he participated in very significant investigations.

In 1963 he became professor of mathematical physics in Lund, and there he gathered a group of students and coworkers. One of his great attributes as a scientist was an outstanding ability to lead such a united group and inspire it to intense scientific activity. His merry smile lighted up the department and characterized the atmosphere among his disciples during their work with him.

Among his important papers, those should be mentioned on the consequences of the pairing forces, together with Owe Prior, and the effects of single-particle states on the fission process. The problem at hand had been considered since the beginning of research on fission, namely why a uranium nucleus decays into two fragments of unequal size.

In particular, I would like to mention his work over a period of several years, together with his group and physicists from different parts of the world, concerning the possible existence of so-called superheavy nuclei.

Since the 1940's there has been an intensive search for elements with a charge exceeding that of uranium. Neptunium, plutonium, americium, curium etc. have been discovered. A struggle against even shorter life-times has lead to the element 106, which decays in 0.1 s. At best, it is possible to continue on this path to 107. But there is another possibility. No. 114 is a magic nucleus, and if its neutron number is 184, it is even doubly magic. Thus it should be more stable than ordinary nuclei, and the major question is if it is sufficiently stable to be observed. Thus, on the other side of the sound after 106-107, there is a ´magic island´, around 114, where there exist once again observable elements? The difficulty is that the nucleus can be ellipsoidal to a varying degree, pear-shaped, thin or bulging at the ´waist´ etc. What happens then?

The difficulties can be illustrated by a famous example from astronomy. About 90 years ago, Henri Poincaré showed that a rotating star can have a pear-shaped equilibrium. Is this equilibrium stable, or can the smaller section be strung off to give rise to a double star? It is still not clear, whether this can happen under realistic assumptions about the star.

For the nucleus 114 and its neighbours, it is necessary to investigate, for every significant change of the nuclear shape, what the probability is for decay into two parts. Thence the mean life of the nucleus is obtained.

It was clear that Sven Gösta's exceptional capacity to carry out extensive mathematical computations, and his knowledge about the properties of heavy nuclei, made him particularly suited for this investigation. Together with a prominent group of coworkers he carried out grandly disposed calculations of lifetimes for the relevant nuclei on the ´magic island´, which illustrated well the possibility of finding them. Experimentally, no superheavy elements have yet been found and the question is presently unresolved.

During the last years, Sven Gösta worked on the remarkable conditions in very rapidly rotating nuclei which had recently been discovered by the experimentalists. There, a transition to a new phase of nuclear matter seems to take place.

Through his logical capacity and his fast, penetrating intellect, Sven Gösta was able to attain very deep and extensive knowledge about both experimental facts and theoretical reasoning within the range of problems he treated. He knew every nucleus. He had a masterful ability to find the most adequate mathematical methods, and his results became very clear and illuminating.

He had one more great gift. He was an excellent teacher, who generated enthusiasm among his coworkers. With his warm and generous personality, and his deep insights, he became the leader of a research group in Lund which developed into one of the most active centers of theoretical nuclear physics.

Physicists from different parts of the world were anxious to discuss things with him. He had the ability to talk to experimentalists in their own language, and they felt that even shorter conversations with him could spread new light over the problems. He travelled a great deal, particularly to USA, and lived there for a total of 4 years. He considered himself fortunate to provide his family with this international experience.

Deepest down he seems to have had not only a probing but also a restless soul. His unceasing desire to be active might have been a sign of it. He seems also to have considered searching his way into new fields, perhaps biophysics.

With his manyfaceted gifts, he was greatly interested in literature and philosophy. His teacher of Christian religion and philosophy says: "In his final year of study, Sven Gösta demonstrated his great interest in the human arts by participating beside the regular curriculum in classes on the history of philosophy. He showed his interest, among other ways, by treating in an essay the philosophy of empirism, as always in an excellent manner.I want to add that he appeared to be a devout young man, influenced by 'a Christian home'."

Sven Gösta's religious beliefs followed him through his life. He was "a confessing Christian" and this was a fundamental part of his personality.

He was strongly concerned with the questions of current interest in society like the crisis of international overpopulation, the coming shortage of resources and problems associated with energy and environment. He studied the energy question thoroughly during a stay with his family in USA, 1972-73. In many articles, especially in the daily newspaper ´Sydsvenska Dagbladet´, he tried to give a comprehensive and objective analysis of the problems. It is known that his opinions were widely read and contemplated.

He was also eager to give the interested general public a knowledge about new discoveries of physics. I quote from his article about Penzias' and Wilson's discovery of the cosmic background radiation which is supposed to come from the time of the birth of the universe: "The Cosmos appears to have started at one point and Penzias and Wilson might have beheld the light of dawn from the morning of The First Day".

On the 24th of April, I had half an hour of conversation with him in the morning, as always in an inspired and creative atmosphere. When he walked out through the door, I saw his happy and positive smile. A few hours later, he was dead. - One of his closest collaborators has written: "Swedish and international physics has suffered a great loss. But most of all we miss Sven Gösta as a friend. His boyish smile will never again make life happier for us."

Up to the last day, he led a life of creativity and warm contact with his fellow-beings.

Further reading:
A. Bohr and B. Mottelson, Nuclear Physics A361 (1981) (preface).
R. Sheline, Proceedings Nuclei at Very High Spin - Sven Gösta Nilsson in Memoriam, Physica Scripta 24, 69 (1981).

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Last modified: June 22, 2005