pISSN 0374-4914 eISSN 2289-0041

## Research Paper

New Physics: Sae Mulli 2017; 67: 462-469

Published online April 28, 2017 https://doi.org/10.3938/NPSM.67.462

## Relativistic Analyses of Proton Inelastic Scatterings from Silicon Isotopes

Sugie SHIM*, Moon-Won KIM

Department of Physics, Kongju National University, Gongju 32588, Korea

Correspondence to:shim@kongju.ac.kr

Received: December 19, 2016; Revised: January 6, 2017; Accepted: January 12, 2017

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

Relativistic Dirac coupled-channel calculations are performed employing an optical potential model for intermediate-energy polarized proton inelastic scatterings from silicon isotopes, and the results are compared with those of nonrelativistic calculations. By using a sequential iteration method to solve the Dirac coupled channel equations phenomenologically, we obtained and analyzed the optical potential and the deformation parameters. The Dirac equations are reduced to second-order differential equations to obtain the Schroedinger-equivalent effective central and spin-orbit optical potentials, and the obtained effective potentials are analyzed by considering the mass number and the energy dependence. The deformation parameters obtained in the Dirac phenomenological calculations for the lowest-lying excited $2^+$ state are found to agree pretty well with those of nonrelativistic calculations where the same Woods-Saxon shape is used for the optical potentials. The smaller deformation parameters for the $2^+$ excited state are obtained when two neutrons are added to the target nucleus or when the energy of the projectile is decreased, indicating weaker couplings to the ground state.

Keywords: Dirac phenomenology, Optical potential model, Collective model, Inelastic proton scattering