  Proton radioactivity is an important and common process of the natural
radioactivity of proton-rich nuclei. In our previous work [J. H. Cheng et al.,
Nucl. Rhys. A 997, 121717 (2020)], we systematically studied the proton
radioactivity half-lives of 53< Z <83 nuclei within the two-potential approach
with Skyrme-Hartree-Fock. The calculations can well reproduce the experimental
data of spherical nuclei. The present work is an extension of the previous
work. We systematically study 32 proton radioactivity half-lives of spherical
nuclei with the two-potential approach with Skyrme-Hartree-Fock (TPA-SHF)
within 115 different versions of the Skyrme interactions. The calculated
results indicate that the SLy7 Skyrme interaction gives the lowest r.m.s.
deviation in the description of the experimental data of the spherical proton
emitters among all the different versions of the Skyrme interactions. In
addition, we use this model with the SLy7 Skyrme interaction to predict the
proton radioactivity half-lives of 7 spherical nuclei in the same region, whose
proton radioactivity is energetically allowed or has been observed but is not
yet quantified.
