Two-proton radioactivity within a Coulomb and proximity potential model for deformed nuclei

Abstract

The half-lives of two-proton $(2p)$ emitters $^{6}\mathrm{Be}$, $^{12}\mathrm{O}$, $^{16}\mathrm{Ne}$, $^{19}\mathrm{Mg}$, $^{45}\mathrm{Fe}$, $^{48}\mathrm{Ni}$, $^{54}\mathrm{Zn}$, and $^{67}\mathrm{Kr}$ have been predicted using the Coulomb and proximity potential model for deformed nuclei (CPPMDN) incorporating ground-state deformation (${\ensuremath{\beta}}_{2}$) and orientation effect, and the predicted values are compared with experimental data. As predicted values are in agreement with experimental data I extended my studies to 51 nuclei, whose decay are energetically possible with released energy ${Q}_{2p}>0$ for which $2p$ radioactivity is not yet experimentally detected, and the predicted half-life values are compared with other theoretical models/formulas. I hope the future experimental investigations will be guided by these predictions. The new Geiger Nuttall plot connecting ${log}_{10}[{T}_{1/2}(s)]$ computed using the CPPMDN versus $[{Z}_{d}^{0.8}+{\ensuremath{\ell}}^{\ensuremath{\beta}}]{Q}_{2p}^{\ensuremath{-}1/2}$ is found to be linear which shows the reliability of my calculations. It is found for the first time that $2p$ radioactivity also obeys the linear nature of a universal curve connecting ${log}_{10}[{T}_{1/2}(s)]$ versus $\ensuremath{-}lnP$ as that of the proton, $\ensuremath{\alpha}$, and cluster radioactivity.