Proton radioactivity within a generalized liquid drop model

Abstract

The proton radioactivity half-lives of spherical proton emitters are investigated theoretically. The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM) including the proximity effects between nuclei in a neck and the mass and charge asymmetry. The penetrability is calculated with the WKB approximation. The spectroscopic factor has been taken into account in half-life calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the BCS method with the force NL3. The half-lives within the GLDM are compared with the experimental data and other theoretical values. The GLDM works quite well for spherical proton emitters when the spectroscopic factors are considered, indicating the necessity of introducing the spectroscopic factor and the success of the GLDM for proton emission. Finally, we present two formulas for proton emission half-life calculation similar to the Viola-Seaborg formulas and Royer's formulas of $\ensuremath{\alpha}$ decay.