Empirical constraints on theO16+Ca40optical potential

Abstract

The angular distribution between $20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}180\ifmmode^\circ\else\textdegree\fi{}$ of $^{16}\mathrm{O}$ + $^{40}\mathrm{Ca}$ elastic scattering at ${E}_{\mathrm{c}.\mathrm{m}.}=35.7$ MeV has been analyzed in terms of the optical model. For both the real and imaginary parts, the standard Woods-Saxon and spline-function parametrizations of the optical potential have been investigated. In the angular region ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}112\ifmmode^\circ\else\textdegree\fi{}$, Woods-Saxon---Woods-Saxon potential combinations suffice to describe the data; however, no fit could be obtained either by Woods-Saxon---Woods-Saxon or by Woods-Saxon---Spline-function potentials for the complete angular distribution (${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}180\ifmmode^\circ\else\textdegree\fi{}$). In contrast, the Spline-function---Woods-Saxon combination reproduces the experimental data well. No further improvement of fit quality is obtained by parametrizing both the real and imaginary parts in terms of spline functions. The best-fit Spline-function---Woods-Saxon potential is found to consist of a real part, having significant wiggles in the interior, coupled to a shallow imaginary part with a depth $W\ensuremath{\sim}2$ MeV and a large radius ${R}_{i}=1.60({{A}_{P}}^{\frac{1}{3}}+{{A}_{T}}^{\frac{1}{3}})$ fm.NUCLEAR REACTIONS $^{16}\mathrm{O}$ + $^{40}\mathrm{Ca}$ elastic scattering, ${E}_{\mathrm{c}.\mathrm{m}.}=35.7$ MeV; optical model analysis including a model-independent potential parametrization by spline functions.