A simple model for the two-proton radioactivity

In this work, considering the preformation factor of the emitted two protons in parent nucleus S2p \replaced{and the effect of the parent nucleus deformation}{}, based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition, we \added{improve} a simple phenomenological model proposed by Bayrak [J. Phys. G: 47, 025102 (2020)] to systematically study the 2p radioactivity half-lives. \added{In this model, it contains two adjustable parameter V0 and aβ, which are related to the depth of nuclear potential obtained and the effect of deformation. } The calculated results show that this model can effectively reproduce the experimental data with a corresponding root-mean-square (RMS) standard deviation sigma = \replaced{0.683 }{0.700}. For comparison, the Gamow-like model (GLM) proposed by Liu et al. [Chin. Phys. C 45, 044110 (2021)], the generalized liquid drop model (GLDM) proposed by Cui et al. [Phys. Rev. C 101, 014301 (2020)], \replaced{effective liquid drop model (ELDM) proposed by M. Gonalves et al. [Phys. Lett. B 774, 14 (2017)], the two-potential approach with Skyrme-Hartree-Fock (TPASHF) proposed by Pan et al. [Chin. Phys. C 45, 124104 (2021)], the phenomenological model with a screened electrostatic barrier (SEB) propoesed by Zou et al. [Chin. Phys. C 45, 104101 (2021)], the unified fission model (UFM) proposed by Xing et al. [Chin. Phys. C 45, 124105 (2021)] ,the Coulomb and proximity potential model for deformed nuclei (CPPMDN) proposed by Santhosh [Phys. Rev. C \textbf{104}, 064613 (2021)],}{} a two-parameter empirical formula proposed by Liu \emph{et\ al}. [Chin. Phys. C \textbf{45}, 024108 (2021)], and a four-parameter empirical formula proposed by Sreeja et al. [Eur. Phys. J. A \textbf{55}, 33 (2019)] are also used. In addition, we use this model to predict the 2p radioactive half-lives of some possible potential nuclei whose 2p radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020.