Dirac Coupled Channel Analyses of Proton Inelastic Scatterings from s-d Shell Nuclei

Sugie Shim,Young-You Kim,Moon-Won Kim

doi:10.4236/jamp.2015.34056

Sugie Shim, Young-You Kim + Show 1 more

Open Access

https://doi.org/10.4236/jamp.2015.34056

Copy DOI

Abstract

Proton inelastic scatterings from several s-d shell nuclei are analyzed using optical potential model and collective model in Dirac coupled channel formalism. The optical potential parameters obtained phenomenologically for the scatterings from the s-d shell nuclei are compared with each other for systematic Dirac analysis. Dirac equations are reduced to the second-order differential equations in order to obtain the Schroedinger equivalent effective central and spin-orbit optical potentials, and the surface-peaked phenomena are observed at the real effective central potentials for the scatterings from 22Ne, 20Ne and 24Mg. By analyzing the obtained effective spin-orbit potentials, it is confirmed that the spin-orbit interaction is a surface-peaked interaction. The first-order rotational collective models are used to describe the low-lying excited states of the ground state rotational bands in the s-d shell deformed nuclei, and the obtained deformation parameters are analyzed by comparing with each other, and compared with those obtained by using the nonrelativistic calculations. The obtained deformation parameters of Dirac phenomenological calculations for the s-d shell nuclei are found to agree pretty well with those of the nonrelativistic calculations using the same Woods-Saxon potential shape, even though the theoretical bases are quite different.

Highlights

Relativistic approaches based on the Dirac equation as the relevant wave equation have been remarkably successful in treating nuclear structure and nuclear reactions
It should be noted that one of the merits of the relativistic approach based on the Dirac equation instead of using the nonrelativistic approach based on the Schroedinger equation is that the spin-orbit potential appears naturally in the Dirac approach when the Dirac equation is reduced to a Schroedinger-like second-order differential equation, whereas the spin-orbit potentials should be inserted by hand in the conventional nonrelativistic Schroedinger approach
In order to compare the calculated results with those of the previous nonrelativistic calculations, we reduce the Dirac equation to a Schroedinger-like secondorder differential equation by considering the upper component of the Dirac wave function to obtain the effective central and spin-orbit optical potentials [4]

Summary

Introduction

Relativistic approaches based on the Dirac equation as the relevant wave equation have been remarkably successful in treating nuclear structure and nuclear reactions.

Results

Conclusion