Nuclear Hulthén potentials for F and G partial waves

Abstract

In the past few decades, several investigation have been made and at the same time a number of theoretical models have also been projected for the nucleon-nucleon scattering in the low and intermediate energy range. These phenomenological models involve large number of free parameters to be fitted to reproduce the physical observables. In contrast to these potentials a two-term four parameter nuclear Hulthén type interaction is proposed to describe the nuclear part of the nucleon-nucleon interaction. The electromagnetic part of the interaction is represented by atomic Hulthén potential. This simple potential model is utilized to reproduce the nucleon-nucleon scattering phase shifts for the F and G partial waves. The phase shifts are computed by exploiting the phase function method. The phase function method is an efficient tool for computing scattering phase shifts for quantum mechanical systems involving both local and nonlocal potentials. In this method the wave function of the radial Schrödinger equation is separated into two parts viz. the amplitude part and phase part. For a local potential the phase function obeys a non-linear differential equation. The scattering phase shift is obtained by solving this equation from the origin to the asymptotic region with the initial condition, the phase shift is zero. The phase equation is solved numerically to compute scattering phase parameters for (n-p) and (p-p) systems and compared them with the standard data to judge the merit of our model. Reasonable agreement in phase shifts is achieved with the results of more sophisticated calculations. Particularly, our models reproduce better results for n-p system over p-p one.