Quantitative Nuclear Evaporation Theory and the Nuclear Potential

The energy level densities of nucleons in a diffuse nuclear well are calculated using an Eckart-Bethe (Woods-Saxon) potential and shown to be a more sensitive function of energy than the calculated densities of nucleons in a square well having the same volume. The particle spectra of 16-MeV ($p, n$) reactions and 14-MeV inelastically scattered neutrons are computed including multiple neutron emission. Using realistic values for the effective nucleon mass, the nuclear radius, and the diffuseness parameters we find that the theoretical spectra fit the experimentally observed spectra well within the experimental error. This fit is obtained without the usual experimental parameter fitting of theoretically undetermined constants. Methods of obtaining single-particle emission spectra from experimentally determined particle spectra when multiple-particle emission occurs are discussed. Our work suggests that a careful analysis of precisely measured evaporation spectra will give some information about the dependence of the diffuseness of the nuclear potential on excitation energy.