Method for optical model analysis of alpha-nucleus elastic scattering

Abstract

A new method for analyzing $\alpha$-nucleus optical potentials is presented. It consists of adding to the conventional Woods-Saxon real potential an extra potential given by a Fourier-Bessel series. The coefficients of the series are determined by least-squares fit to experimental cross sections for elastic scattering. A detailed discussion of the uncertainties in the derived parameters is presented, both for the real potential as a function of radius and for integral quantities such as the volume integral and the root-mean-square radius. The method is illustrated using existing data over wide angular range for the elastic scattering of 139 MeV $\alpha$ particles by ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and of 104 MeV $\alpha$ by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, where with the new method ${\chi }^2$ per degree of freedom is reduced by a factor of between 5 and 7 to a value of almost 1. The method is also used for the analysis of data for 104 MeV $\alpha$ particles scattered by ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, which is restricted to the diffraction region of the angular distribution. In that case the new method is capable of uniquely specifying the region where the real potential is well determined. Evidence is presented for saturation effects in the folding model.