Theories for Angular Distributions in Low Energy Nuclear Reactions : A Series of Six Lectures Presented at the Lawrence Radiation Laboratory, Livermore, California, in 1958 Page: 4
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feature is that there are strong interactions and that the energy is quickly
shared among many nucleons. It is the very opposite of independent particle
motion. I will say more about this later.
In the last 10 years, the shell model has had a dramatic revival. It
really dates back to the time Maria Mayer discovered the magic numbers.
The revival of the shell model has had a tremendous effect on our under-
standing of the theory of nuclear reactions, for it appeared that the simple
compound nucleus picture was not quite adequate.
It is well known that the nucleons in the nucleus must obey the ex-
clusion principle, that the complete nuclear wave function must be anti-
symmetric with respect to interchange of any two nucleons. The effect of
the exclusion principle is considerable. It essentially prevents the inter-
actions which would like to take place from exerting their full effect. In
other words, the exclusion principle drastically cuts down correlations
between particle motions in nuclear matter. This leads one to believe that
the independent particle model is actually a much better approximation
than one might have thought, certainly than one thought at the time the
compound nucleus .model was developed. This will also influence any model
of nuclear reactions. The beginning of this was seen in the late 1940's
when it proved possible to fit the total cross sections for interactions of
rather high energy neutrons with nuclei on the basis of an optical model in
which one assumed that the particles are scattered by a potential well which
may contain an absorptive part. One very remarkable feature is that if one
considers the scattering of low energy nucleons by nuclei, then the optical
potential is rather close to an ordinary real potential. In other words, at
low incident particle energy, the imaginary part of the potential is rather
small. This implies that the mean free path for nucleons of low energy in
nuclear matter is really quite large; in fact, it is of the order of 10 fermis
or even as high as 20 fermis if the incident energy is low enough. This is
of the order of, or even Larger than, the nuclear diameter. On the other
hand, the mean free path for particles in nuclear matter in the compound
nucleus picture would be extremely small compared to the nuclear diameter.
So these are the things which lead one to believe that a kind of independent
particle model is really not a very bad approximation, though it is clearly
not the whole story. This is because on the basis of an independent particle
model, one could never expect to find closely spaced resonances with large
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Moszkowski, Steven A.; Benveniste, J. & Schwarcz, E. H. Theories for Angular Distributions in Low Energy Nuclear Reactions : A Series of Six Lectures Presented at the Lawrence Radiation Laboratory, Livermore, California, in 1958, report, 1958; (https://digital.library.unt.edu/ark:/67531/metadc783793/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.