Fission barriers with Weizs\"acker-Skyrme mass model

Abstract

Based on Weizs\"acker-Skyrme (WS4) mass model, the fission barriers of nuclei are systematically studied. Considering the shell corrections, the macroscopic deformation energy and a phenomenological residual correction, the fission barrier heights for nuclei with $Z\geqslant 82$ can be well described, with an rms deviation of 0.481 MeV with respect to 71 empirical barrier heights. In addition to the shell correction at the ground state, the shell correction at the saddle point and its relative value are also important for both deformed nuclei and spherical nuclei. The fission barriers for nuclei far from the $\beta$-stability line and super-heavy nuclei are also predicted with the proposed approach.