Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula

A systematic analysis on experimental data of the half-lives of nuclear double-beta decays with two neutrinos (2 nu beta beta) 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 2 nu beta(-)beta(-) decays, both for ground-state transitions and transitions from ground states of parent nuclei to the first 0(+) 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 2 nu beta beta-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-beta transitions between the ground state of Ca-48, Ge-76, and Xe-136 and the first 0(+) excited states of their corresponding daughter nuclei, which will be very useful for understanding the underlying mechanisms of double-beta decays and for further studying the shell effects on nuclear transition matrix elements.

Automated summary

A systematic analysis on the experimental data of nuclear double-beta decay half-lives is performed using an improved analytical formula, showing good agreement with known ground-state transitions. Further predictions are made for decay candidates above 0.5 MeV, emphasizing the importance of experimental measurements for understanding double-beta decay mechanisms and studying shell effects on nuclear transitions.