by Luisa Bonolis
J. Hans D. Jensen
Nobel Prize in Physics 1963 together with Eugene Wigner and Maria Goeppert Mayer
"for their discoveries concerning nuclear shell structure".
The theoretical formulation of the nuclear shell model, which Hans Jensen published in 1949 in collaboration with Haxel and Suess, and independently from Maria Goeppert-Mayer, offered the first coherent explanation for a variety of properties and structures of atomic nuclei. In particular, it explained quite naturally the existence of the “magic numbers” of protons and neutrons, which had been determined from experiments on the stability properties and from observed abundances of chemical elements both for terrestrial and non-terrestrial sources. Atomic nuclei consisting of such a magic number of nucleons are more stable against nuclear decay and thus play a decisive role in the synthesis of the elements in stars, as well as in the artificial synthesis of the heaviest elements, at the borderline of the periodic table. The element abundances are mainly determined by nuclear structure, and hence, by the shell model. Since then the nuclear shell model has remained one of the cornerstones of modern nuclear physics, becoming an important guide in the interpretation of nuclear phenomena and stimulated deep work in the many-body problem, later providing the intellectual background for the quark model.
First Visits to Niels Bohr in Copenhagen
Johannes Hans Daniel Jensen was born in Hamburg in 1907 and was, from a very early age, a brilliant student. After graduating in 1926, he went on to study physics, mathematics, physical chemistry, and philosophy at the Universities of Freiburg and Hamburg. He earned his Ph.D. in physics in 1932, and remained at the University of Hamburg as a scientific assistant. His early research, there, concerned quantum-mechanical studies of ionic lattices and in general the properties of materials under extremely high pressures. During the 1930s, Jensen's scientific interests were also especially focused on the Thomas-Fermi statistical model of the atom, one of the most powerful means of studying the system of many electrons in an atom, treating them as if they were a collection of weakly interacting fermions, moving independently in an effective potential.
From the outset of his career, Jensen also became familiar with the emerging field of nuclear physics; in particular the many models for a nuclear structure of protons and neutrons proposed after Chadwick demonstrated the existence of the neutron in 1932 - the first uncharged subatomic particle to be identified. A vigorous development of experimental nuclear physics was beginning at that time. It was in part due to the possibility of performing experiments with neutrons, as well as to the completion of the first accelerators and to great improvements in measuring and counting techniques. For Jensen these were the years of his first visits to Copenhagen, at Niels Bohr's Institute for theoretical physics. During his sojourns there, he participated in the stimulating discussions on the latest results and witnessed many attempts at a theoretical interpretation of the rapidly accumulating experimental data, trying to gain some understanding of the background from which the first concepts of nuclear structure were emerging. As many others, Jensen was especially influenced by Bohr, whom he always considered as one of his teachers.
“Magic Numbers” and Early Models of Nuclear Structure
The periodic table shows that similarity of chemical behaviour recurs in cycles, or periods, as the atomic number increases. The recurring stability at certain atomic numbers was explained on the basis of a system of energy levels, each identified by a set of four quantum numbers, to which the restriction of Wolfgang Pauli's exclusion principle is to be added: only one electron can occupy a quantum state of a given set of quantum numbers. The large energy steps related to the principal energy levels occur in clusters of smaller steps. Such clusters were called shells, and each of them can contain only a fixed number of electrons. The electronic shells in the atom are the K shell with 2 electrons, the L shell with 8 electrons, the M shell with 18 electrons, and so on. Each shell is composed by one or more subshells related to the azimuthal quantum number, determined by its orbital angular momentum l. Each subshell is constrained to hold 2(2l+1) electrons at most, so that the recurrence of chemical properties related to the filling of shells and the beginning of new ones follows naturally from the principles of quantum physics applied to electronic energy levels. The chemical element, in whose atom the outermost electron occupies the last level before a large energy step, is said to “close the shell.” The element of next higher atomic number (one more electron + one more proton) starts the next shell. Open shells are valence shells, being not completely filled. Likewise, a closed shell configuration, containing the maximum number of electrons permitted by the Pauli exclusion principle, means chemical stability, since chemical reactions are associated with the loss, gain, or sharing of electrons. These particular atoms are the noble gases, such as helium, neon, argon, xenon, and radon, which are chemically almost inert, as their closed shells contain as many electrons as possible. They have very special properties, that is: particularly small atomic radii and of course very high ionisation energies.
The earliest ideas about nuclear shell structure were advanced in analogy with electron shells in atoms. These were based on early observations showing that nuclei with certain special numbers of protons or neutrons - 2, 8, 20, 28, 50, 82, 126 - appeared to be unusually stable, that is unlikely to change to other nuclei by radioactive emissions or to engage in nuclear reactions. This meant that such nuclei are also relatively abundant, because stable nuclei tend to persist and accumulate. Speculations concerning the possibility of shell structure in nuclei date back to the discovery of the neutron in 1932. In that same year, Heisenberg established a nuclear model of the nucleus as composed of protons and neutrons and James Bartlett immediately introduced the idea of proton and neutron shells in light nuclei (helium-4 and oxygen-16).
By examining nuclear-binding energies and taking Bartlett's suggestion, the German physicist Walter Elsasser, at the time a refugee from Nazi Germany working in Paris, published a series of articles between 1933 and 1934 (“Sur le principe de Pauli dans les noyaux”) presenting a more detailed and extensive study in which neutrons and protons, in analogy with electrons, were supposed to move independently in an average nuclear field defined by all the other nucleons. They could then be assigned an orbital angular momentum as well as spin so that each nucleon would have its own distinct quantum number. Both protons and neutrons, being fermions, obey the Pauli exclusion principle, so that they arrange themselves in shells, following quantum rules, filling up the levels in order of increasing energy. Whenever a shell was completed, a particularly stable nucleus could be expected, closed shells being characterised by great binding energies. When a new shell is started, the binding energy of the newly added particles should be less than for the particles completing the previous shell.
Elsasser's work was also based on systematic work done by the physical chemist Kurt Guggenheimer, who was also a refugee in Paris, and had studied the stability of isotopes as a function of proton number Z and neutron number N, which showed a surprising periodic variability connected with the numbers 28, 50 and 82.
However, as remarked by an authoritative review of 1936 by Bethe and Bacher, even if the level schemes of Elsasser, Bartlett and Guggenheimer, appeared to agree with the experimental results, they definitely lacked “theoretical foundation.” In this review, which together with two following articles published in the Reviews of Modern Physics soon became known as “Bethe's bible”, very convincing arguments were presented to show that nuclear forces display very weak spin dependence; in particular, the spin-orbit coupling should be very weak.
The first phase of the nuclear shell investigations ended in 1936, in connection with Niels Bohr's successful proposal of the compound nucleus model of nuclear reactions, a strong interaction model based on the assumption that all nucleons take part more or less equally in any nuclear process, which seemed to be incompatible with the basic approach of the shell model, based on the idea of free motion of individual nucleons in an average potential. This change of viewpoint was a consequence of experiments on neutron absorption performed in 1934-1935 by Enrico Fermi and his collaborators in Rome, following their discovery of artificial radioactivity produced by neutron bombardment of different elements. Two phenomena, discovered in connection with slow-neutron scattering and capture, were particularly important to the development of concepts on nuclear structure: the relatively high effective cross-sections for nucleon-nucleon scattering, and especially the sharp, closely spaced resonances, i.e., sharply selected energies, for which a neutron was sure to be picked up by the nucleus. On the uncertainty principle a sharply defined energy is associated with a long time. So it follows that once a neutron gets into a nucleus in conditions of resonance it must stay there a long time – much longer than it would take it to cross a region the size of a nucleus. Fermi and his co-workers and Hans Bethe made attempts to understand why slow neutrons could be easily captured by many nuclei. They developed theories based on an independent particle picture that were in agreement with some aspects of the experimental data, but not with other strongly contradicting evidences, so at that time models based on the single-particle picture seemed to be a complete failure.
The way to resolve these apparent contradictions was pointed out by Bohr. He recognized that it was not right to think of a neutron as passing just through a general field of force, since the nucleus is densely packed with particles which each exert strong forces on the extra neutron as well as on each other. The observation that slow neutron absorption was surprisingly strong and that it was strongly energy dependent, led Bohr to recognize that the narrow resonances discovered in nuclear reaction experiments are essentially a many-particle effect. He clearly saw that the experimental discoveries concerning the interactions of neutrons with nuclei demanded a radical revision in the basic picture of nuclear dynamics. By the end of 1935 Bohr had developed his theory of the compound nucleus as a system of strongly interacting particles, where he pointed out that every nuclear process must be treated as a many-body problem, particularly in the case of heavy nuclei. Because of the strong intimate coupling between the nucleons, when an incoming particle impinges on the target nucleus during a nuclear reaction, it shares its energy quickly with the other nucleons, so that a so-called compound nucleus is formed in which the identity of the incoming particle is completely lost. During the second, completely independent stage, once in a while enough energy is concentrated on a particular nucleon or group of nucleons and one or more particles are emitted.
These views ruled out any treatment in terms of independently moving particles, so that the concept of nuclear shells seemed to lose its validity. In his paper entitled “Neutron capture and nuclear constitution” published in Nature in early 1936, Bohr himself outlined the fundamental difference between the typical properties of nuclei, for which energy exchanges between the individual nuclear particles is a decisive factor, and atomic electrons, who, in a fairly good approximation, can be treated as weakly interacting particles: “In the atom and in the nucleus we have indeed to do with two extreme cases of mechanical many-body problems for which a procedure of approximation resting on a combination of one-body problems, so effective in the former case, loses any validity in the latter where we, from the very beginning have to do with essential collective aspects of the interplay between the constituent particles.”
Jensen, who was in Copenhagen at the time, has described the great impact of the formula which gave a quantitative account of the variation with energy of the reaction cross section in spite of the complexity of the compound nucleus: “It could soon be seen on every blackboard of Niels Bohr's institute.” Bohr's intuitive, semi-classical picture, was mathematized and brought into agreement with the postulates of quantum mechanics by the so called Breit-Wigner formula for the reaction cross section, a mechanism proposed in 1936 by Gregory Breit and Eugene Wigner, while working at Princeton. This work helped promote Bohr's view of nuclear dynamics, which was soon accepted in the nuclear physics community. Mainly as a result of the success of Bohr's theory, the shell model was abandoned for more than a decade and there was a general tendency to consider “magic numbers” as a curiosity of little significance to the fundamental questions of nuclear structure.
In 1937, together with the brilliant young Danish physicist Fritz Kalckar, Bohr suggested an analogy for nuclei, which was a drop of liquid, adapting in an extended form George Gamow’s idea of 1928 for nuclei built of alpha particles. In envisaging the nucleus as a homogeneous entity, whose behaviour could be understood on a statistical basis with no individual characteristic, the liquid drop model was again an expression of the significance of collective features in a system where the cohesion is a result of the strong mutual attraction of the particles, counter-balancing the repulsive electromagnetic forces between protons.
Three years later, in early 1939, the liquid-drop model was employed by Otto Frisch and Lise Meitner to explain nuclear fission, a term since then used for the phenomenon of splitting of heavy nuclei into lighter elements. Along with John Wheeler, Bohr immediately improved the liquid-drop model providing a quantitative study of the mechanism of fission processes, which changed the static model into a dynamical model capable of surface deformation, which eventually led to important later developments.
The Revival of the Nuclear Shell Model
In 1941 Jensen had accepted a professorship at the Technische Hochschule of Hannover and during the war, when German physicists lived in what Jensen himself has described as “stifling isolation,” he began to have many discussions with the experimental nuclear physicist Otto Haxel, and with the geochemist Hans E. Suess, on the empirical evidence which singled out unusually stable nuclei with certain numbers. In his cosmo-chemical studies, Suess was quite familiar with the extraordinary and systematic work of the Norwegian Swiss-born geochemist Victor Goldschmidt, whom he had also personally met during the war. Already in 1932 George Hevesy had emphasised the importance of the study of relative abundance of nuclei in the universe because it might yield information on the stability and structure of nuclei. This view was fully shared by Goldschmidt. By plotting isotopic abundance - both for terrestrial and non-terrestrial sources - as a function of their proton number Z and neutron number N, in addition to the standard classification by mass number A, he had found that maxima in abundance could be seen at specific values: Z= 28, 40, 50, 74, 82, and 90, and N= 30, 50, 82, and 108. The conclusion was that the abundances must be definitely a consequence of nuclear structure itself. After the war, Suess had definitely become convinced that Goldschmidt's isotopic-abundance data showed evidence of some pattern, and began an extensive analysis of such data graphing empirical results in every possible situation, also trying to develop some rules accounting for the phenomenon of nuclear stability. He identified as “special numbers” N=20, 28, 50, 82 and Z=26 or 28, 50, having less compelling evidence for N=58 and Z=20.
Quite independently, Haxel had observed unusual nuclear behaviour in the same isotopes, encountering the same numbers. Through discussing the issue together they remarked how abundance and nuclear stability coincided in nuclei that had magic numbers of protons or neutrons. As Suess later recalled, “I was so impressed I couldn't sleep for many nights.”
They tried hard to convince Jensen that these numbers might be a key to the understanding of nuclear structure. At the time, however, Jensen did not know what to make of this idea, even if he thought the name “magic number” to be very appropriate. A few years after the war he was able to visit Copenhagen for the first time. There, in a recent issue of the Physical Review, he found a paper by Maria Goeppert-Mayer, “On closed shells in nuclei”, submitted in April 1948, where she, too, had collected wide empirical evidence showing that, “nuclei with 20, 50, 80 or 126 neutrons or protons are particularly stable.” Around 1947 Maria Goeppert-Mayer had worked in Chicago with Edward Teller on the origin of elements and thus had started from analysing data on isotopic abundances, discovering the phenomenon of magic numbers. At that time there was much more information available than there had been in the early 1930s and the picture was clearer. Nuclear physics had advanced to a stage where a more detailed picture of the structure of the atomic nucleus was beginning to emerge and it was becoming possible to calculate its properties in a quantitative way. Like Haxel and Suess, Goeppert-Mayer became intrigued by regularities repeating in a wide variety of different isotopes and collected every possible piece of evidence by analysing nuclear-binding energies, radioactive-decay energies, and especially isotopic abundances provided by Goldschmidt's monumental work. In continuing the arguments of Guggenheimer and Elsasser, she also pointed out new data obtained from fission and neutron physics. This pattern suggested that nucleons fill nuclear-energy levels similar to the way in which electrons fill atomic-energy levels. She concluded by saying that the situation was of course very different even if it appeared that the effect of closed shells in the nuclei seemed very pronounced. In her first paper Goeppert-Mayer emphasised the particular stability for the numbers 20, 50, 82 and 126, also based on the small neutron absorption cross sections for targets with 82 and 126 neutrons as measured by D. J. Hughes at Argonne Laboratory.
The paper, which showed impressive evidence in favour of magic numbers, rekindled Jensen's interest in the topic and he discussed the paper, as well as results coming from Suess and Haxel, in a theoretical seminar at Bohr's Institute in Copenhagen. The lively discussions with Bohr remained in his mind for the rest of his life. From that afternoon on, Jensen “began to consider seriously the possibility of a 'demagification' of the 'magic numbers'.”
All this happened during the summer 1948. The well-founded establishment of the particular values of numbers indicating closed shells had been the first major contribution of Goeppert-Mayer to the nuclear shell model. The overwhelming evidence convinced even the sceptics, but yet there was no theory that explained why one got those particular values for the closed shell numbers. The identification of the shell structure itself, based on the evidence for nuclear stability, had led to the basic assumption that a single-particle model can describe the nucleus. The lowest values 2, 8 and 20 could be obtained by putting nucleons into a reasonable single particle potential due to the other nucleons, in which they move nearly independently, and that - in an extremely oversimplified form - can be represented by a rectangular well. The infinite square well potential has unevenly spaced levels each with 2(2l+1) nucleons, which, according to quantum rules, predicts closures at the total particle numbers (neutrons or protons): 2, 8, 18, 20, 34, 40, 58, ... These are not the nuclear magic numbers. If the nucleons are filled in a harmonic oscillator potential well, the smaller magic numbers 2, 8, 20 can be reproduced. The magic number 8 corresponds to filling all levels up to the oscillator shell n=1; and the magic number 20 is still explained as filling the oscillator shell up to n=2. But beyond that the system breaks down and there is no trace of a gap indicating shells in the level system at 28, 50, or 82. This simple model does not work for the higher magic numbers, because for higher A one actually gets 40, 70, 112 and 168, which are not magic.
The case of closed shells in nuclei certainly shows similarities to those of atoms, and several groups worked on this problem in 1948, trying to modify the nuclear potential so that the closed shells would appear for 28, 50, 82 and 126. However, the higher numbers continued to be a real challenge to explain. It became clear that a change in the shape of the potential could not explain the magic numbers, but the general attitude was that “so little is known about nuclear forces...”
However, the magic numbers, as well as many other pieces were there, forcefully demonstrating the independent movements of individual nucleons, but one more key piece was needed to solve the puzzle.
The Unexpected: the Role of Spin-Orbit Coupling in Nuclei
On February 4, 1949, Maria Goeppert-Mayer sent a new short letter to the Physical Review, “On closed shells in Nuclei. II” where she presented her solution to the puzzle of the magic numbers. A most important acknowledgement was written at the end of the letter: “Thanks are due to Enrico Fermi for the remark, 'Is there any indication of spin-orbit coupling?' which was the origin of this paper.” At that time Enrico Fermi had become interested in magic numbers, and they often had discussions on this topic in Chicago. Goeppert-Mayer had great skills in quantum mechanics and was extremely familiar with the interpretation of atomic and molecular spectroscopic data in terms of electron shell structures. In particular she was specialist on the individual-orbital approximation that she had used in her calculations on heavy atoms and molecules in which the energy of the spin-orbit interaction for electrons is comparable to that of the Coulomb interaction. In light atoms, the orbital angular momenta of all electrons combine into a total L and all spins into a total S, and L and S combine to form J, because the interactions between the orbital angular momenta of individual electrons is stronger than the interaction of each electron's spin with its own orbital angular momentum, the so called spin-orbit coupling. However, for heavier elements the spin-orbit interactions become as strong as the interactions between individual spins or orbital angular momenta. In these cases, they tend to couple to form individual electron angular momenta given by the sum of the two (j=l+s) so that one has the so called j-j coupling between individual electrons, a small effect which, after the discovery of spin, was able to explain the splitting of the energy levels and the consequent observation of the fine structure in the spectrum of alkali atoms, like the well-known “sodium doublet.”
Goeppert-Mayer immediately recognised that a strong spin-orbit interaction in the same shell, but with no interaction with nucleons in other shells, actually would explain the magic numbers. She immediately answered Fermi's question: “Yes, and it will explain everything.” Fermi was sceptical, but within hours she was able to perform the right calculations and everything fit perfectly.
The key assumption was thus that the spin of any nucleon is strongly coupled to its own orbital angular momentum, leading to a strong splitting of a term with angular momentum l into two distinct terms j=l+1/2 and j=l-1/2, due to differing orientation of the total angular momentum, and invariantly giving the level j=l+1/2 a considerably lower energy, so that it will be filled before that for j=l-1/2. This is because the spin-orbit coupling has the opposite sign to that in atoms. The magic numbers follow at once on the assumption of a particularly marked splitting of the term with the highest angular momentum j=l+1/2, resulting in a closed shell structure in which each group related to the levels characterised by the oscillator quantum number n merges with the highest j-term of the next succeeding n-group.
A strong enough spin-orbit coupling thus overcomes the oscillator spacing of levels and the shells close at the correct magic numbers 2, 8, 20, 28, 50, 82 and 126.
Meanwhile, Jensen had continued to stick to the magic number puzzle. At first he tried to remain as much as possible within the old framework and considered only the spin of the whole nucleus, since there appeared to exist a simple correlation between the magic nucleon numbers and the sequence of nuclear spins and their multiplicities. However, in following earlier suggestions that the spin of a nucleus is due to the spin of the last (odd) nucleon, Suess had plotted the experimental spin-values for odd-even and even-odd nuclei against nucleon number and obtained the right magic numbers in reversing the sequence of spin values and including the highest value j=l+1/2 in the previous shell. When Jensen saw it, things became clear and he was soon able to explain the underlying clue for the obtained scheme: a strong spin-orbit coupling. As Jensen said, fortunately he did not remember the old arguments against a strong spin-orbit coupling described in “Bethe's bible.” During a discussion with Haxel and Suess, they tried to include all available empirical facts in the scheme of the single-particle model with strong spin-orbit coupling. In his Nobel lecture Jensen actually remembered being elated when they found some hints in the still meagre data that were available at that time that the proton- and the neutron-number 28 should also be something like a magic number confirming the spin-orbit explanation.
Their first note was rejected by Nature, stating, “...it is not really physics but rather playing with numbers.” It was only because of the lively interest in the magic numbers displayed by Niels Bohr that Jensen sent the same letter to Victor Weisskopf, who forwarded it to the Physical Review where it was submitted on April 18 and published in the June issue of 1949 with the title “On 'Magic Numbers' in Nuclear Structure.” Two weeks later, Maria Goeppert-Mayer's above-mentioned note independently explaining magic numbers with spin-orbit coupling appeared in the following June issue of the same journal. In the meantime Jensen Haxel and Suess were more successful with Die Naturwissenschaften, where they published a series of three papers on the theory of nuclear energy levels related to orbital angular momenta and the effect of nucleon spin. In their extensive paper sent on 5 May 1950 to Zeitschrift für Physik they clearly provided a theoretical explanation for the numbers 2, 8, 28, 50, 82, 126, initially proposed by Goeppert-Mayer. The spin-orbit coupling sequence is nearly the same for neutrons and protons till N=Z=50 is reached at the level 1g9/2, beyond which the neutrons and protons follow different sequences due to the increasing effect of Coulomb repulsion.
Once more, analogy in physics had played a decisive role. The shell model was accepted immediately, in spite of the apparent conflict with Bohr's compound model. It immediately showed itself to be a reasonable model of nuclear structure, being able to explain and predict nuclear properties other than just a half dozen numbers. Not only could it account for many of the recently measured values of nuclear spins and nuclear magnetic moments, it provided wavefunctions for nuclear states, which could be used to make predictions that could be tested by observations using new experimental techniques. The model especially explained several regularities of nuclear spins and parities, and indicated that numerous nuclear isomers should exist for nuclei with large values of angular momentum. Its success demonstrated that knowledge of nuclear structure could advance model by model. Bohr, too, was convinced by the new results and argued that certainly a deeper understanding of the quantum-mechanical many-body problem was needed to reconcile the two points of view.
Goeppert-Mayer and Jensen eventually met in Germany, became very good friends and later collaborated on a book, Elementary Theory of Nuclear Shell Structure, which was published in 1955. By that time, together with Walther Bothe, Jensen had become in Heidelberg a driving force in the rebuilding of physics research after the Second World War. Eight years later, in 1963, he was jointly awarded with Goeppert-Mayer half of the Nobel Prize for Physics “for their discoveries concerning nuclear shell structure.” The other half was awarded to Eugene P. Wigner “for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.” Maria Goeppert-Mayer was at the time the only living woman in the world with a Nobel Prize in science, and she and Marie Curie, who was awarded the Nobel Prize in Physics in 1903 with her husband Pierre Curie, were the only women to have won a Nobel in Physics. Only three years before Goeppert-Mayer had finally become a paid professor at the University of California at San Diego, after many years of discrimination, notwithstanding the longstanding appreciation of prominent physicists for her outstanding work during her whole career.
The shell model represented a great leap forward in the understanding of the nucleus, however, it was very soon found that some properties cannot be explained by this model, the most striking perhaps being the marked deviation of the charge distribution from spherical symmetry, which was observed in several cases. No one was able to give a reasonable explanation of the phenomenon. The solution to such a problem was in accepting the complementary nature of the independent particle and the statistical model, each being able to explain only certain phenomena.
Several attempts were made to develop a collective model which treated the movement of the nucleons as a whole, as well as the movements of individual nucleons outside the closed shells, thus combining the essential characteristics of the two models. A first proposal was presented by James Rainwater in April 1950, and independently, one month later, by Aage Bohr, the fourth son of Niels Bohr, who was soon joined by Ben Mottelson in pursuing the consequences of the interplay of individual-particle and collective motion for the great variety of nuclear phenomena that was then coming within the range of experimental studies. They developed a comprehensive study of the coupling of oscillations of the nuclear surface to the motion of the individual nucleons and were thus able to predict the different types of collective excitations: vibrations and rotations. Their model retained most of the features of the liquid drop model and the shell model, and was also able to explain additional phenomena, such as electric quadrupole moments, transition probabilities of gamma radiation, etc. The explosive development of nuclear spectroscopy in those years rapidly led to an extensive body of data on nuclear rotational spectra and went hand in hand with further clarifications and expansion of the theoretical basis.
Unfortunately Niels Bohr was no longer alive when his son Aage was awarded jointly with James Rainwater and Ben Mottelson the Nobel Prize for Physics in 1975,“for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection.”
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Johnson, K. E. (2004) From Natural History to the Nuclear Shell Model: Chemical Thinking in the Work of Mayer, Haxel, Jensen, and Suess. Physics in Perspective 6: 295-309
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Mladjenovic, M. (1998) The Defining Years in Nuclear Physics 1932-1960s. Institute of Physics Publishing, Bristol and Philadelphia
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Wasson, T. (ed.) (1987) Jensen, J. Hans D. In Nobel Prize Winners, H. W. Wilson Company, New York, pp. 505-507
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