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

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${}_{g.s.}^{+}\to 2_1^{+}$) for Mg isotopes using constant proton-neutron effective charges prove the limitations of the present large-scale calculations to reproduce the experiment in detail.

Comments: 3 pages, 3 figures