Research on convergence of the nuclear matrix elements for 2νββ decays * *Supported by National Natural Science Foundation of China (11647086, 11647085), Shanxi Province Science Foundation for Youths (201901D211252), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2019L0554, 2019L0505), and the Natural Science Research Fund of North University of China (XJJ201811)

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 .