Exploring the competition between $\alpha$-decay and proton radioactivity: A comparative study of proximity potential formalisms

We have conducted a comprehensive and systematic study of the proton radioactivity and $\alpha$-decay half-lives of neutron-deficient nuclei. This investigation involved the utilization of various Proximity potentials and also considered the incorporation of thermal effects. For the half-life calculations, we employed both temperature-independent and temperature-dependent interaction potentials. We observed that proton radioactivity serves as the dominant mode of decay for nuclides situated very close to the proton drip-line. We explored a universal curve that examines the correlation between the decimal logarithm of experimental half-lives and the negative decimal logarithm of the penetrability for both proton radioactivity and $\alpha$-decay.