Effects of Nuclear Shells and Angular Momentum in Evaporative Deexcitation

Abstract

A detailed statistical-model analysis has been carried out of recently reported proton and $\ensuremath{\alpha}$ spectra for the complex nuclear reactions $^{63}\mathrm{Cu}$ + $^{12}\mathrm{C}$ (55 MeV, lab) and $^{64}\mathrm{Zn}$ + $^{11}\mathrm{B}$ (43 MeV, lab). In both systems the compound nucleus $^{75}\mathrm{Br}^{*}$ is formed with the same excitation energy of 50 MeV, but the distribution of angular momentum is expected to be significantly different. Observed differences in the experimental spectra were accordingly interpreted in terms of assumed differing angular momentum distributions. In our calculations it was found possible to achieve agreement with the data within experimental error for plausible but widely differing sets of important but unknown systemic properties, viz., the distribution of angular momentum in the $^{75}\mathrm{Br}^{*}$, and the level densities to high excitation of the several nuclei involved. However, it was always found necessary to include the effect of the proximity of the closed proton shell at $Z=28$. The behavior of the calculated $\ensuremath{\alpha}$ emission for individual nuclei shows important differences of detail between reasonable sets of input data, although for all such sets the production ratio [(total protons) / (total $\ensuremath{\alpha}$ particles)] decreases with increasing angular momentum of the compound nucleus. We feel it is significant that one of the data sets giving satisfactory agreement with experiment included level densities calculated numerically up to the high energies involved using a realistic shell model. These calculations have already been shown to give values in agreement with reliable experimental level densities, which are, however, only available for lower energies. Since additional data on the same system are needed to reduce the ambiguities, specific suggestions for further experiments are offered, and examples of how such experiments can be useful are worked out.