Investigating the impact of nuclear surface energy coefficients on one-proton radioactivity

The influence of different nuclear surface energy coefficients $\gamma$ on the process of proton radioactivity is systematically studied within the Coulomb and proximity potential formalism. We investigate the proximity potential Guo 2013 formalism with 13 different versions of the coefficient $\gamma$ for the description of 44 experimental half-lives of proton emitters in the ground and isomeric states. It has been observed that the four versions, namely Guo 2013 (original), Guo 2013 (set 1), Guo 2013 (set 2), and Guo 2013 (set 3), exhibit the lowest rms deviations (approximately $\sigma =0.4733$) when compared to the experimental data. The detailed investigation of the known proton decay processes indicate that the decrease in the strength of nuclear surface tension improves the agreement between the experimental data and the calculated values of proton radioactivity half-lives. In addition, our results reveal that the apparent deviation does not follow a continuous behavior around $Z=68$. In fact, by decreasing the strength of the surface energy coefficient $\gamma$ compared to its calculated value from the original proximity potential (Guo 2013) for lighter mass regions $(Z<68)$ and increasing it for heavier ones $(Z>68)$, we observe significantly improved agreement with experimental data $(\sigma =0.453)$. A discussion about the role of nuclear surface tension coefficients in the experimental information of proton emitters in the ground state and the isomeric state is also presented.