Systematic study of proton radioactivity of spherical proton emitters within various versions of proximity potential formalisms

In this work we present a systematic study of the proton radioactivity half-lives of spherical proton emitters within the Coulomb and proximity potential model. We investigate 28 different versions of the proximity potential formalisms developed for the description of proton radioactivity, $\mathcal{\alpha}$ decay and heavy particle radioactivity. It is found that 21 of them are not suitable to deal with the proton radioactivity, because the classical turning points $r_{\text{in}}$ cannot be obtained due to the fact that the depth of the total interaction potential between the emitted proton and the daughter nucleus is above the proton radioactivity energy. Among the other 7 versions of the proximity potential formalisms, it is Guo2013 which gives the lowest rms deviation in the description of the experimental half-lives of the known spherical proton emitters. We use this proximity potential formalism to predict the proton radioactivity half-lives of 13 spherical proton emitters, whose proton radioactivity is energetically allowed or observed but not yet quantified, within a factor of 3.71.