Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula * *Supported by the National Natural Science Foundation of China (U1731238, 11761161001, 11105079, 11535004, 11375086, 11975167, 12035011), the Science and Technology Development Fund (FDCT) of Macau (020/2014/A1, 008/2017/AFJ, 0042/2018/A2), the Science and Technology Foundation of Guizhou Province ((2016)4008, (2017)5726-37) and the foundation of Guizhou Provincial education Department (KY(2020)003)

Abstract

A systematic analysis on experimental data of the half-lives of nuclear double- decays with two neutrinos ( ) is performed based on the analytical formula proposed by Primakoff and Rosen. We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor. This improved formula can closely describe all available experimental half-lives of decays, both for ground-state transitions and transitions from ground states of parent nuclei to the first excited states of daughter nuclei. The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3. Further predictions are provided for -decay candidates with decay energies above 0.5 MeV. We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double- transitions between the ground state of Ca, Ge, and Xe and the first excited states of their corresponding daughter nuclei, which will be very useful for understanding the underlying mechanisms of double- decays and for further studying the shell effects on nuclear transition matrix elements.