Comparative Analysis of Woods-Saxon and Yukawa Model Nuclear Potentials

Abstract

In this paper, we model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons. The single particle energy states are obtained by solving the time independent Schrodinger wave equation using matrix diagonalization method with infinite spherical well wave-functions as the basis. The best fit model parameters are obtained by using variational Monte-Carlo algorithm wherein the relative mean-squared error, christened as chi-squared value, is minimized. The universal parameters obtained using Woods-Saxon potential are found to be matched with literature reported data resulting a chi-square value of 0.066 for neutron states and 0.069 for proton states whereas the chi-square value comes out to be 1.98 and 1.57 for neutron and proton states respectively by considering Yukawa potential. To further assess the performance of both the interaction potentials, the model parameters have been optimized for three different groups, light nuclei up to 16O - 56Ni, heavy nuclei 100Sn - 208Pb and all nuclei 16O - 208Pb. It is observed that Yukawa model performed reasonably well for light nuclei but did not give satisfactory results for the other two groups while Woods-Saxon potential gives satisfactory results for all magic nuclei across the periodic table.