Fourier shape parameterization in covariant density functional theory for nuclear fission

We implement the Fourier shape parameterization within the point-coupling covariant density functional theory to construct the collective space, potential energy surface (PES), and mass tensor, which serve as inputs for the time-dependent generator coordinate method to simulate the fission dynamics. Taking ²²⁶Th as a benchmark, we demonstrate the superiority of Fourier shape parameterization over conventional spherical harmonic parameterization: it significantly enhances the convergence of higher-order collective shape parameters by efficiently characterizing extreme nuclear deformations. Consequently, the new framework generates more reasonable highly mass-asymmetric configurations and scission configurations, and significantly improves the description of charge distribution near the symmetric fission peak. Moreover, the Fourier shape parameterization provides a smooth and well-defined three-dimensional (3D) PES with minimal correlations between degrees of freedom, enabling high-precision 3D dynamical simulations of fission.