A Comparison of Shell Model Results for Some properties of the Even-Even Ge Isotopes

TL;DR

This paper compares two shell model interactions, JUN45 and JJ4B, for predicting properties of Ge isotopes, revealing discrepancies with experimental data and analyzing the models' effectiveness in describing nuclear quadrupole moments and excited states.

Contribution

It provides a comparative analysis of JUN45 and JJ4B interactions for Ge isotopes, including predictions of quadrupole moments and B(E2) values, and explores their limitations against experimental results.

Findings

Discrepancies in quadrupole moments between models and experiments.

JJ4B and JUN45 show different predictions for excited state properties.

Single-j shell model offers insights into complex shell-model calculations.

Abstract

In this work we examine two recent effective shell model interactions, JUN45 and JJ4B, that have been proposed for use in the $f_{5/2},p_{3/2}, p_{1/2}, g_{9/2}$ model space for both protons and neutrons. We calculate a number of quantities that did not enter into the fits undertaken to fix the parameters of both interactions. In particular we consider static quadrupole moments (Q's) of excited states of the even-even $^{70-76}$Ge isotopes, as well as the B(E2) values in these nuclei. (We have previously studied $^{70}$Zn isotopes using JJ4B.) Some striking disagreements between the JUN45 prediction and the experimental results had already been noted for the quadrupole moments of the $2_1^+$ states of these nuclei. We investigate whether these discrepancies also occur for the JJ4B interaction. Subsequently, we also apply both interactions to calculate the Q's of some more highly excited states and compare the two sets of predictions regarding the nature of the nuclear states under consideration. In order to gain insight into these more complex large-scale shell-model calculations, we examine the corresponding and much simpler single-j shell model calculations in the $g_{9/2}$ neutron shell.