Investigation of Alignment Effects of Neutron and Proton Pairs in High Spin States of Band Crossing for &amp;lt;sup&amp;gt;159,160&amp;lt;/sup&amp;gt;Sm Isotopes Using Projected Shell Model (PSM)

Mohammad Reza Pahlavani,Malihe Teimoori

doi:10.11648/j.ns.20210603.11

Abstract

Energy spectrum of nucleus is one the important information for better recognition of nuclear force and interaction of nucleon inside of the nucleus. Energy levels of nucleus are measured by detecting gamma- ray energy spectrum when a target nucleus bombarded with a special projectile to excite it in to levels higher than ground state. On the other hand, there are several models to calculate nuclear energy levels. Solution of the Schrödinger equation by considering a suitable potential is direct method to obtain energy levels of a quantum mechanical system like nucleus. Projected shell model is a model of this type that is developed by solving the Schrödinger equation for a set of potentials along with role of spin. Band structure and yrast bands for even-even and odd-even isotopes of Samarium (159,160Sm) are calculated using a Fortran code founded based on the projected shell model (PSM). Energy levels of negative and positive parity bands of 159Sm and 160Sm isotopes of Samarium nucleus are obtained separately for each spin. Kinetic and dynamic moments of inertias are also calculated for these isotopes. The acquired results are compared with the experimental data. The electromagnetic reduced transition probabilities, B(M1)/B(E2) the behavior of dynamic moment of inertia J2, rotational kinetic energy and moment of inertia J1 as a function of spin have also been investigated and proper comparison is made between the calculated results and the experimental data. The alignment phenomena of neutron-proton pairs in view of the rotational movement in high spin states has also been studied with reference to band crossing.

Highlights

The projected shell model that has been applied in recent years to study the structure of nuclei, especially the nuclei in the lanthanide region, has achieved some success [1]
In 1995, the Nilsson model was developed by Hara and San to describe the deformation characteristics of the axial symmetry of deformed nuclei, and a notion of this new model was recognized as the projected shell model [18]
The calculation results are related to the ground-state band structure of 160Sm isotopes and 159Sm odd-even and even-even isotopes which were carried out using Fortran code based upon the projected shell model

Summary

Introduction

The projected shell model that has been applied in recent years to study the structure of nuclei, especially the nuclei in the lanthanide region, has achieved some success [1]. Topics discussed in this paper include yrast spectrum changes, structures and configurations of quasiparticle bands, band crossing and variation in moments of inertia, excitation of the neutron i13/2 orbital and the proton h11/2 orbital as the shell model intruder. The calculation results are related to the ground-state band structure of 160Sm isotopes and 159Sm odd-even and even-even isotopes which were carried out using Fortran code based upon the projected shell model. The obtained results of the calculations for quasiparticle alignments in the band crossing are compared with each other by examining the moments of inertia and ratio of electromagnetic reduced transition probabilities for these two isotopes None of these studies thoroughly elucidate the structural properties of the whole isotopic chain of odd-mass or even-mass Sm nuclei.

Brief Overview of the Theory

Result and Discussion

Conclusion