Spacings of Nuclear Energy Levels

The distribution of spacings of nuclear energy levels in many heavy nuclei at an excitation energy of 5 to 9 Mev is obtained by careful correction of the observed distributions for the effect of failure to observe all levels. Results of transmission measurements on ${\mathrm{U}}^{234}$ and ${\mathrm{U}}^{236}$, as measured with the Brookhaven fast chopper, are presented. The experimental spacings of the zero-spin nuclides are considered first since all the levels from slow neutron capture have the same spin. The results show a deficiency of small spacings relative to the exponential distribution, which corresponds to a random occurrence of levels. In the analysis it is shown that there is no local correlation of neutron widths and level spacings. The "level repulsion" effect is also found for the nuclides of nonzero spin, for which the data are more abundant but the analysis is complicated by the presence of two spin systems. The distribution obtained is in agreement with one suggested by Wigner based on a probability of level occurrence proportional to the spacing $S$. The corrections here developed are also applied to the reduced neutron width distribution and this corrected distribution is in good agreement with the Porter-Thomas distribution.