Microscopic-macroscopic approach for ground-state energies based on the Gogny force with the Wigner-Kirkwood averaging scheme

In the previous paper [Bhagwat, Centelles, Viñas, and Schuck, Phys. Rev. C 103, 024320 (2021)] we have shown that self-consistent extended Thomas-Fermi (ETF) potentials and densities associated with a given finite-range interaction can be parametrized by generalized Fermi distributions. As a next step, a comprehensive calculation of ground-state properties of a large number of spherical and deformed even-even nuclei is carried out in the present paper using the Gogny D1S force within the ETF scheme. The parametrized ETF potentials and densities of the previous paper are used to calculate the smooth part of the energy and the shell corrections within the Wigner-Kirkwood semiclassical averaging scheme. It is shown that the shell corrections thus obtained, along with a simple liquid drop prescription, yield a good description of ground-state masses and potential-energy surfaces for nuclei spanning the entire periodic table.