Systematic study of even-even $^{20-32}$Mg isotopes

TL;DR

This paper systematically investigates the energies and transition probabilities of even-even magnesium isotopes using large-scale shell model calculations, achieving good agreement with experimental data but highlighting limitations in transition strength predictions.

Contribution

It provides a comprehensive shell model analysis of Mg isotopes with USDB interactions, comparing results with experimental data and previous models, and discusses the limitations in reproducing transition strengths.

Findings

Good agreement with experimental energy levels for Mg isotopes.

Transition probabilities show limitations of current models.

Highlights the need for improved effective charges in calculations.

Abstract

A systematic study for 2$^+_1$ and 4$^+_1$ energies for even-even $^{20-32}$Mg by means of large-scale shell model calculations using the effective interaction USDB and USDBPN with SD and SDPN model space respectively. The reduced transition probability {\em B}({\em E}2;$\uparrow$) were also calculated for the chain of Mg isotopes.Very good agreement were obtained by comparing the first 2$^+_1$ and 4$^+_1$ levels for all isotopes with the recently available experimental data and with the previous theoretical work using 3DAMP+GCM model, but studying the transition strengths {\em B}({\em E}2; 0$^+_{g.s.} \rightarrow2^+_1$) for Mg isotopes using constant proton-neutron effective charges prove the limitations of the present large-scale calculations to reproduce the experiment in detail.