Comparing a Local Potential with a Non-Local Potential for the Bound States of ^(16)O and ^(40)Ca

Abstract

Using the non-local nuclear potentials, we calculate the binding energies and radial wave functions of a single particle, and the proton charge density for ^(16)O and ^(40)Ca nuclei. In order to obtain them, we use a matrix equation method generated from the integral form of the Schrodinger equation and find the best parameter set, which includes the potential depth, diffuseness, radius, and non-local parameter, by fitting the experimental data. The proton charge densities for the non-local potential are repulsive in comparison with those for the local potential. It is also found that the radius of the non-local potential is greater than that of the local one due to the non-local parameter (β). In addition, using the trivially equivalent local potential (TELP) method, we compare the local potentials with the non-local potentials and then find that the non-local potentials are repulsive.