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, $\mathcalα$ 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.
Proton radioactivity in deformed nuclei with microscopic optical potential: A novel angular-dependent emission mechanism in the nanosecond-lived $^{149}$Lu
University of South China（南华大学）；Chongqing University（重庆大学）；The University of Tokyo（东京大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论数学科学中心）
Systematic Study of Proton, Two-Proton, Alpha, and Cluster Radioactivity Half-Lives based on the Deformed Gamow-like Model and Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$)
College of Physics and Technology, Kunming University（昆明大学物理与技术学院）；School of Physics and Information Engineering, Zhaotong University（昭通大学物理与信息工程学院）；Key Laboratory of Economic System Simulation of Guizhou Province, Guizhou University of Finance and Economics（贵州省经济系统模拟重点实验室，贵州财经大学）
Centrifugal-corrected harmonic oscillator model for spherical proton emitters
School of Mathematics and Physics, University of South China（南华大学数学与物理学院）；School of Nuclear Science and Technology, University of South China（南华大学核科学与技术学院）；School of Physical Science and Technology, Southwest Jiaotong University（西南交通大学物理科学与技术学院）；Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）
