Study of the Electric Quadrupole Moments for some Scandium Isotopes Using Shell Model Calculations with Different Interactions

Baghdad Science Journal

doi:10.21123/bsj.15.3.304-309

Abstract

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the experimental data. The theoretical results of the quadrupole moments for some scandium isotopes performed with FPD6 interaction and Bohr-Mottelson effective charge agree with experimental values.

Highlights

The nuclear electric quadrupole moment, is considered as a probe for the deviation of nuclear charge from spherical symmetry which gives a useful measure of how the core is polarized especially if the valence nucleons are neutrons which do not directly participate to the electric quadrupole moment )1(
Shell-model calculations are performed by using the program NuShellX@MSU (10) to calculate one body density matrix (OBDM) with the fp model space for N 20, where 40Ca nucleus is considered as the inert core for all isotopes under consideration and the other valence nucleons are moving in the fpshell model space within 1f7/2, 2p3/2, 1f5/2 and 2p1/2 orbits
The results that obtained from this work have been deduced by using the shell model calculations, which were successful in describing the quadrupole moment when taking the core polarization effects into account

Summary

Introduction

The nuclear electric quadrupole moment, is considered as a probe for the deviation of nuclear charge from spherical symmetry which gives a useful measure of how the core is polarized especially if the valence nucleons are neutrons which do not directly participate to the electric quadrupole moment )1(. The calculated quadrupole moment for 41Sc (N=20) nucleus with FPD6 effective interaction and by using B-M effective charges for proton ep=1.19e and neutron en=0.85e is Q(B-M)= -13.5 efm[2], which agree with the measured values of Ref.(14).

Results

Conclusion