Investigation of two-proton decay using modified formation probability

Abstract

In this study, we investigated two-proton radioactivity using the two-potential approach with a cosh-type potential to calculate the half-lives. The depth parameter V0 = 58.405 MeV and diffuseness a = 0.537 fm in the cosh-type nuclear potential show the lowest standard deviation between the calculated and experimental half-lives. We proposed a linear formula for the formation probability using the linear relationship between log10S2p and A1/3d for the angular momentum state l = 0, 2 and 4. The model achieved the lowest standard deviation (σ = 1.09) using this linear formula compared to previous models and empirical formulas. The proposed formula significantly improved the accuracy of half-life predictions by reducing the standard deviation from 1.73 to 1.09. The predicted half-lives exhibit a hindrance factor in the range of -1.62 to 2.42, which is the lowest compared to earlier theoretical predictions. These results indicate that the proposed linear formation probability formula is suitable for reproducing experimental half-lives. The linear formula for formation probability was generalized for different angular momentum states by conducting least squares fit. We extended the half-life and formation probability predictions to 48 nuclei, and the predicted half-lives are in good agreement with the previous five theoretical models and two empirical formula predictions.