Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei

TLDR

Hartree‑Fock calculations for spherical nuclei using Skyrme’s density‑dependent effective nucleon‑nucleon interaction are systematically examined. The study analyzes how Skyrme force parameters relate to general properties of nuclear matter and finite nuclei. The authors derive the mean energy and Hartree‑Fock equations for spherical nuclei using Skyrme’s interaction, then perform calculations for closed‑shell nuclei with two distinct parameter sets that reproduce binding energies and radii. Both parameter sets yield accurate binding energies, charge radii, and electron‑scattering angular distributions, correctly reproduce the order and density of single‑particle levels near the Fermi surface, though they differ most in the predicted energies of 1s states.

Abstract

Hartree-Fock calculations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically. Skyrme's interaction is described and the general formula for the mean energy of a spherical nucleus derived. Hartree-Fock equations are obtained by varying the mean energy with respect to the single-particle wave functions of occupied states. Relations between the parameters of the Skyrme force and various general properties of nuclear matter and finite nuclei are analyzed. Calculations have been made for closed-shell nuclei using two rather different sets of parameters, both of which give good binding energies and radii for $^{16}\mathrm{O}$ and $^{208}\mathrm{Pb}$. Both interactions give good binding energies and charge radii for all closed-shell nuclei. Calculated electron scattering angular distributions agree qualitatively with experiment, and for one interaction there is good quantitative agreement. The single-particle energies calculated with the two interactions are somewhat different owing to a different nonlocality of the Hartree-Fock potentials, but both interactions give the correct order and density of single-particle levels near the Fermi level. They differ most strongly in their predictions for the energies of $1s$ single-particle states.