The Charge Density Distribution with a Non-Local Potential on \\ $^{16}$O, $^{40}$Ca, and $^{208}$Pb Nuclei

Abstract

Using a non-local nuclear potential in a separable form, as suggested by Perey and Buck, we solve the Schr\"{o}dinger equation for all bound states for $^{16}$O, $^{40}$Ca, and $^{208}$Pb nuclei. We obtain binding energies and radial wave functions for a single particle. Moreover, these calculations derived from a non-local nuclear potential are compared with those of a local potential suggested by Shlomo and Bertsch. With the binding energies and the radial wave functions, we extract the point proton, the point neutron, the charge density distributions and their RMS radii and compare them with the experimental data. The point proton, the point neutron, and the charge density distributions obtained by using the non-local potential are pushed outward compared with those obtained by using the local potential due to the non-local effect. In addition, this effect can be seen in the RMS radii extracted from the point proton, the point neutron, and the charge density distributions, which are repulsive and larger than those obtained using the local potential. Finally, our calculations for the RMS radii, which were done using the non-local potential, agree well with the experimental data.