Particle Binding Energies and the Diffuseness of the Nuclear Boundary

Abstract

The approximate eigenvalues for a spherical well with an exponentially diffuse boundary and with spin-orbit splittings are applied to the study of particle binding energies. If the $A$-value locations of the low velocity $3s$ and $4s$ maxima in the neutron cross-section surface are taken at $A=55\mathrm{}$ and $A=150\mathrm{}$, the general trends of experimental binding energies and experimental radii sharply restrict the degrees of diffuseness that can be allowed. It would appear that the general trends of both proton and neutron binding energies as well as their discontinuities can be accounted for if a diffuseness parameter (i.e., tail length to $e^{-1\mathrm{}}$ point divided by inner radius) is chosen which drifts gradually from $\delta =0.3\mathrm{}$ for light nuclei to $\delta =0.2\mathrm{}$ for heavy nuclei. The diffuseness parameter needed goes to somewhat smaller values ($\delta \sim 0.13$) if the critical $4s$ $A$-value is taken at 170. For heavy elements the diffuseness of the potential well obtained here is comparable to the diffuseness of the nuclear charge distribution obtained in recent studies.