An empirical formula for the proton radioactivity

Proton radioactivity is an exotic decay mode of proton-rich nuclei far from the \(\beta \)-stability line and shares the similar decay mechanism theory of barrier penetration as \(\alpha \) decay. In present work, we extend the Hatsukawa formula (Hatsukawa et al. in Phys Rev C 42:674, 1990) for \(\alpha \) decay to proton radioactivity and propose an empirical formula for evaluating the proton radioactivity half-lives of proton nuclei with Z  >  68. Using this formula, we systematically calculate the proton radioactivity half-lives of 33 spherical proton emitters with the corresponding root-mean-square (rms) deviation being 0.391. It is found that the calculated half-lives can reproduce the experimental data well. Moreover, we extend this formula to predict the proton radioactivity half-lives of 18 spherical proton emitters, whose proton radioactivity is energetically allowed or observed but not yet quantified. For comparison, unified fission model (UFM), Coulomb potential and proximity potential model (CPPM), universal decay law for proton emission (UDLP) and new Geiger-Nuttall law (NG-N) are also used. All the predictions are basically consistent with each other.