Statistics of Excited Energy States of Nuclei

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Abstract
The spacing of nuclear energy levels at excitation energies of about 8 Mev is calculated by numerical summation over the individual particle states, thus avoiding the use of the asymptotic Sommerfeld formulas whose validity in nuclear considerations is far from exact. The model used as basis is that of free particles moving in a spherical well. The results indicate that deviations from Bethe's formula for the level density, which represents correctly the mean trend with both excitation energy and atomic number, can be very great indeed. The group structure introduced by the free particle model has a strong effect on the spacing. The fluctuations thus shown to exist permit an explanation of the fact that heavy nuclei, which according to current theory should be strong absorbers of slow neutrons, do not as a rule possess this property.