LAUSR

Half-lives and potential barriers of cluster radioactivity are investigated in the framework of the generalized liquid drop model (GLDM). We focus on the calculation of the preformation factor for heavy and superheavy nuclei within a redefined preformed cluster method, in which the decay constant is the product of the preformation factor, assault frequency, and penetration probability. The preformation factor is obtained from the penetrability of the potential internal barrier. The assault frequency has been estimated using classical methods and the penetration probability is calculated by the Wentzel-Kramers-Brillouin (WKB) method from tunneling through the GLDM potential barrier. The optimal mass inertia was selected for $\ensuremath{\alpha}$ decay and cluster emission by comparison of theoretical half-lives and experimental ones. The calculated preformation factor follows the preformation law formulas $S({A}_{C})=S{(\ensuremath{\alpha})}^{({A}_{C}\ensuremath{-}1)/3}$ [Phys. Rev. Lett. 61, 1930 (1988)], and the theoretical half-lives show better agreement with experimental data, including the new isotopes $^{219}\mathrm{Np}$ [Phys. Lett. B 777, 212 (2018)] and $^{220}\mathrm{Np}$ [Phys. Rev. Lett. 122, 192503 (2019)]. The predictions of cluster radioactivity half-lives are provided for heavy and superheavy nuclei, which will be useful for the detection and identification of these nuclei in the future.