Research on convergence of the nuclear matrix elements for 2νββ decays *

Abstract

Abstract In this work, the characteristics of 2νββ decays for six nuclei ( Ar, Ca, Ca, Cr, Zn, and Xe) in a mass range from to are studied within the nuclear shell model (NSM) framework. Calculations are presented for the half-lives, nuclear matrix elements (NMEs), phase space factors ( ), and convergence of the NMEs. The theoretical results agree well with the experimental data. In addition, we predict the half-lives of decays for four nuclei. We focus on the convergence of the NMEs by analyzing the number of contributing intermediate states ( ) for the nuclei of interest. We assume that is safely determined when the accumulated NMEs saturate 99.7% of the final calculated magnitude. From the calculations of the involved nuclei, we discover a connection between and the total number of intermediate states ( ). According to the least squares fit, we conclude that the correlation is .