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Examining intermediate coupling inside the nucleus
Murray Gell-Mann Scientist
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There was a contradiction between the statistical approach – especially the heavy nuclei based on very strong coupling – and the apparently simple independent particle approach that gave rise to the j-j coupling shell model which seemed to work, at least for the lighter and intermediate nuclei, and maybe even for the heavier ones. So Viki [Victor Weisskopf] had the idea that somebody should look at this very difficult regime of intermediate coupling inside the nucleus and see if these two notions could somehow be reconciled.

Now the strong coupling, especially in heavy nuclei, but even in intermediate ones and a great extent in light ones, was expressed by the fact that there were many, many, many more levels than you would have gotten with an absolutely pure independent particle model. There were many more levels because of the coupling. You coupled to a lot of states that involved other configurations, and the average width of the levels was reduced by the same factor that the number of levels was increased, so that the ratio of the width to the spacing remained roughly the same. So that was sort of constant as you turned on the coupling, but you went to a quite strong coupling regime in which there was a gigantic ratio for heavy nuclei of levels to the number of levels that…  a number of levels to the number of levels  one would have with an absolutely pure independent particle picture, a single particle picture. So somehow, as one turned on the coupling, there was an intermediate regime in which one had some features left of the weak coupling situation and, nevertheless, a lot of features of the strong coupling situation. Well, I looked into that and I constructed a formalism for it which was a generalization of the formalism of [Leonard] Eisenbud and [Eugene] Wigner I think it was... somebody or other and Wigner, I think it was Eisenbud and Wigner. And I made some observations about the situation and about how in weak coupling the levels would not – I mean in intermediate coupling – the levels would not be reduced so thoroughly to a lot of narrow ones.

But I didn't appreciate the main point, which was worked out later by Wigner, [Anthony] Lane, and [Robert] Thomas. What they showed later on, several years later, was that there were traces of the independent particle model if you plotted the widths of these narrow levels as a function of energy. You would find that the widths tended to get broader and narrower, broader and narrower and so on, on average as the energy varied. And that those... that curve of average behavior of the widths of the levels, followed to some extent the weak coupling curve, the curve that would show the weak coupling levels. And that was what was left in nuclear reactions of the… of the weak coupling model. I didn't get that insight in my dissertation and, when it came out I realized that that's what I should have found. I did a lot of very useful things, but I had no idea they were useful. I derived a number of formulae... I derived a number of concepts that actually were not known and... or not well known... and could have been papers and so on, but I had absolutely no idea.

[Q] You wrote no paper based on your thesis?

No. I had no idea what was publishable and what was not. One thing I did was to find some new - what I thought were new - formulae for the Clebsch… no… Clebsch-Gordon coefficients, or the correlation coefficients between angular momenta… yeah, the Clebsch-Gordon coefficients. But then, when I got to the Institute for Advanced Study a little while later, I talked with Giulio Racah or R'cah – depending on whether you use the Italian or the Hebrew form – and he explained that he had found those formulae in 1942 and that they were published in some obscure place, and the reprints were stuck at Mount Scopus where he couldn't get at them.

New York-born physicist Murray Gell-Mann is known for his creation of the eightfold way, an ordering system for subatomic particles, comparable to the periodic table. His discovery of the omega-minus particle filled a gap in the system, brought the theory wide acceptance and led to Gell-Mann's winning the Nobel Prize in Physics in 1969.

Listeners: Geoffrey West

Geoffrey West is a Staff Member, Fellow, and Program Manager for High Energy Physics at Los Alamos National Laboratory. He is also a member of The Santa Fe Institute. He is a native of England and was educated at Cambridge University (B.A. 1961). He received his Ph.D. from Stanford University in 1966 followed by post-doctoral appointments at Cornell and Harvard Universities. He returned to Stanford as a faculty member in 1970. He left to build and lead the Theoretical High Energy Physics Group at Los Alamos. He has numerous scientific publications including the editing of three books. His primary interest has been in fundamental questions in Physics, especially those concerning the elementary particles and their interactions. His long-term fascination in general scaling phenomena grew out of his work on scaling in quantum chromodynamics and the unification of all forces of nature. In 1996 this evolved into the highly productive collaboration with James Brown and Brian Enquist on the origin of allometric scaling laws in biology and the development of realistic quantitative models that analyse the influence of size on the structural and functional design of organisms.

Tags: Institute for Advanced Study, Victor Weisskopf, David Eisenbud, Eugene Paul Wigner, Anthony Milner Lane, Robert Thomas, Giulio Racah

Duration: 4 minutes, 51 seconds

Date story recorded: October 1997

Date story went live: 24 January 2008