Potentials for the α– 40,44,48Ca elastic scattering

Abstract

The differential cross sections for the elastic scattering of α particles by 40,44,48Ca, over a wide range of incident energies, have been analyzed using a deep as well as shallow non-monotonic optical potential and compared with those using a squared Woods–Saxon (SWS) potential. The shallow non-monotonic potential exhibits a volume integral for the real part, characteristic of a molecular potential. The parameters of the SWS potential have also been obtained for α– 48Ca scattering. The parameters of the shallow non-monotonic potential calculated from the energy-density-formalism provide a satisfactory description of the elastic scattering data. The non-monotonic potentials, both deep and shallow, are found to yield consistently a lower value of the radius parameter of the real potential for 48Ca than that for 40Ca, in conformity with the observed magnitudes of the root-mean-square radii for the two nuclei. Both the potentials indicate that the semi-magic 44Ca behaves differently from the doubly-magic 40,48Ca, in agreement with the findings from the folding potentials. The dispersion effect arising from the causality principle has been investigated for the shallow non-monotonic α– 40Ca potential and is found to play a rather minor role in describing the elastic scattering data.