A simple model for two-proton radioactivity

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