Alpha-Cluster Model, Charge Symmetry of Nuclear Force and Single Particle Bound State Potential in Symmetrical Nuclei

TL;DR

This paper introduces a phenomenological alpha-cluster model that leverages charge symmetry to estimate nuclear parameters and improve the accuracy of single particle potential models in symmetrical nuclei, impacting DWBA analysis.

Contribution

It presents a novel approach combining alpha-cluster modeling with charge symmetry to refine nuclear potential parameters and assess errors in DWBA spectroscopic factors.

Findings

R_C and R_p values are effective for nuclei with Z<=16.

Standard Woods-Saxon potentials are inadequate for Z>16.

Using asymptotic wave function coefficients reduces spectroscopic factor errors.

Abstract

A phenomenological alpha-cluster model based on np-pair interactions and the charge symmetry of nuclear force allows one to estimate the Coulomb energy, the Coulomb radius R_C, the Coulomb energy of the last proton interaction with the residual nucleus and the radius of its position R_p in a symmetrical nucleus. The values R_C and R_p obtained for the symmetrical nuclei with 5<= Z<=45 are used in a long standing task of determination of the parameters of the Woods-Saxon potential of neuton/proton bound state used in DWBA analysis of direct one nucleon transfer reactions. According to the charge symmetry of nuclear force a requirement of equality of the nuclear potentials of the last neutron and the last proton in a symmetrical nucleus is added to the standard well-depth procedure in solving the Shr\"{o}dinger equation, which makes R_C the crucial parameter to determine the parameters of the nuclear potential and the value of the last proton rms radius <r_p^2>^{1/2} in the wave representation. Comparative analysis of the radii <r_p^2>^{1/2} and R_p, R_C, the experimental radii and the nuclear potential radii obtained at the calculations shows that for the nuclei with Z>16 it is inappropriate to represent a single particle bound state by the Woods-Saxon potential. Using asymptotic coefficient of wave function allows one to estimate error in obtaining spectroscopic factor caused by using the standard parameters in DWBA analysis of pure peripheral reactions. It is shown that using these may bring an error up to 48%.