An empirical formula for the half-lives of one- and two-proton radioactivity

Abstract

We have proposed an empirical formula for one- and two-proton decays, including the angular momentum term. While investigating the first term in the Viola–Seaborg formula, we found a linear relationship between the logarithmic half-life and the expression [Formula: see text] for each angular momentum state. Furthermore, we obtained a linear relationship between the slope and intercept as functions of the angular momentum (l). Using these relations, we proposed a generalized empirical formula for the half-lives of one- and two-proton radioactivity for all angular momentum states. We analyzed the accuracy of the formula predictions by computing the standard deviation between the predicted and experimental decay half-lives. For the decay of one proton, the standard deviation of the proposed formula is 0.389, while that of the generalized formula is 0.400. These values represent the lowest standard deviations compared to previous models and the empirical formula. In the case of two-proton decay, the standard deviation for the current formula is 1.31, and the generalized formula also exhibits a lower standard deviation of 1.32. This lowest standard deviation value indicates that the proposed formula is suitable for reproducing the experimental half-life. We extended the half-life predictions to another 207 nuclei for one-proton decay and 42 nuclei for two-proton decay cases, which are energetically possible. The estimated half-lives for both one- and two-proton decays agree well with other theoretical predictions.