An empirical formula for the two-proton decay half-lives in the ground and excited states

Abstract

We proposed an empirical formula for the half-life of two proton emissions in the ground and excited states. The proposed empirical formula has a half-life dependence on the Q-value and the atomic number of the parent, similar to the Geiger-Nuttall law and the Viola and Seaborg formula. The half-lives of 6Be, 12O, 16Ne, 19Mg, 45Fe, 48Ni, 54Zn, and 67Kr nuclei are calculated using the present empirical formula. The empirical formula has the lowest standard deviation with experimental data (σ=1.39) compared to previously predicted formulas, indicating that the formula can reproduce the experimental half-lives well. The predictions of the half-lives are made for another 56 nuclei whose two-proton emission is energetically feasible (Q2P>0). These half-life values are compared with five theoretical models and two empirical formulas. The predicted half-lives are in good agreement with other theoretical predictions. The predicted half-lives of two-proton emission in the excited states of 14O⁎, 17,18Ne⁎, 22Mg⁎, 29S⁎, and 94Ag⁎ nuclei are compared with the experimental half-lives and also with different models' and formulas' predictions. The experimentally observed half-lives of the excited states are better reproduced using the proposed formula compared with previous theoretical predictions. Only the proposed formula can reproduce the experimental half-lives of 94Ag⁎ in excited states.