Resolution of Fixed-Geometry Optical-Model Ambiguities

Abstract

In order to test a procedure for resolving the problem of discrete real-well-depth ambiguities found in optical-model analyses, $\alpha$ particles were elastically scattered from ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$, and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ at incident energies from 0.6 to 1.2 times the classical Coulomb-barrier height for each nucleus. The real and imaginary nuclear potential-well radii and the Coulomb radius (assuming a uniformly charged sphere) for each nucleus were taken to be $R=R_C={\gamma }_0(A_{\mathrm{Alpha}}^{\frac{1}{3}}+A_{\mathrm{Target}}^{{}^{\frac{1}{3}}})$, where ${\gamma }_0=1.22\mathrm{}$ F. A diffuseness of 0.57 F was used throughout. For three of the nuclei, only one pair of real ($U$) and volume-imaginary ($W$) potentials was found, with the real-well depth for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ showing a slight energy dependence. The potentials obtained were (in MeV): $U=23.5\mathrm{}$, $W=11.0\mathrm{}$ for ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$; $U\sim 22$, $W\sim 10.3$ for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$; $U=23.5\mathrm{}$, $W=14.5\mathrm{}$ for ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$; and $U=18.0\mathrm{}$, $W=6.0\mathrm{}$ for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$. Analysis of angular distributions taken with 15-18-MeV $\alpha$ particles did not yield evidence of expected ambiguities in the real-well depth, so further calculations were performed in which the effect of absorption was more generally explored. The usefulness of the proposed method was found to be limited to cases where the absorption is either ineffective, or small compared with the average spacing between single-particle levels of the same spin and parity.