Description of proton radioactivity using the Coulomb and proximity potential model for deformed nuclei

Half-life predictions have been performed for the proton emitters with $Z>50$ in the ground state and isomeric state using the Coulomb and proximity potential model for deformed nuclei (CPPMDN). The agreement of the calculated values with the experimental data made it possible to predict some proton emissions that are not verified experimentally yet. For a comparison, the calculations also are performed using other theoretical models, such as the Gamow-like model of Zdeb et al. [Eur. Phys. J. A 52, 323 (2016)], the semiempirical relation of Hatsukawa et al. [Phys. Rev. C 42, 674 (1990)], and the CPPM of Santhosh et al. [Pramana 58, 611 (2002)]. The Geiger-Nuttall law, originally observed for $\alpha$ decay, studied for proton radioactivity is found to work well provided it is plotted for the isotopes of a given proton emitter nuclide with the same $\ell$ value. The universal curve is found to be valid for proton radioactivity also as we obtained a single straight line for all proton emissions irrespective of the parents. Through the analysis of the experimentally measured half-lives of 44 proton emitters, the study revealed that the present systematic study lends support to a unified description for studying $\alpha$ decay, cluster radioactivity, and proton radioactivity.

Figure 1

The comparison of the CPPMDN and CPPM results with the experimental values for the proton emitters in the ground state.

Figure 2

G-N plots for different cases of proton radioactivity (a) using calculated half-lives and $Q$ values and (b) using experimental half-lives and $Q$ values. The angular momentum values $\ell$ associated with the transitions are given within the parentheses.

Figure 3

A universal curve for experimental and calculated logarithmic half-lives versus a negative logarithm of penetrability for proton emissions from various parent nuclei using the CPPMDN and CPPM.