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).
Publisher: Nilsson 2005
Download the conference poster in pdf-format here!
E-mail: Nilsson2005@matfys.lth.se
Last modified: June 22, 2005
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