Calculation of the equilibrium characteristics of nuclei using the modified Thomas--Fermi approximation

The self--consistent equations of the modified Thomas-Fermi approximation are solved numerically for the proton and neutron densities in the ground state of a spherical nucleus. In the equation of state of the nucleus, Skyrme forces are used and gradient corrections to the nucleon kinetic-energy density as well as Coulomb and spin-orbit interactions are taken into account. It is shown that this method reproduces the empirical smooth A-dependence of the nuclear binding energy as well as the average properties of the nucleon distribution (nucleon density at the center of the nucleus, size of the nucleus, and diffusion parameter). A self-consistent nuclear mean field is obtained in the modified Thomas-Fermi aproximation and it is shown that this field and the mean spin-orbit potential are (for Z< or =114) near the corresponding potentials in the phenomenological shell model