Skyrme-Landau parameterization of effective interactions (I). Hartree-Fock ground states

An extended Skyrme-Landau interaction - SL1, which includes velocity-dependent three-body forces and a tensor force is developed. Unlike the effective interactions with density-dependent two-body forces, this form of the interaction yields, in finite nuclei, an anti-symmetric particle-particle interaction from the particle-hole interaction with the phonon-induced interaction included. The interaction parameters are determined by the better known Landau-Migdal parameters in nuclear matter and other physical quantities like the surface energy and the dipole sum rule. Due to the fact that sufficient degrees of freedom are introduced, previous problems with the high compression modulus K_∞ and spin instability, which plagued the earlier Skyrme interactions are thus removed. We present results on the Hartree-Fock ground states of spherical nuclei : ¹⁶O, ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr and ²⁰⁸Pb. The fitted binding energies, the radii and the single-particle energies are all comparable to those of the earlier Skyrme interactions. Comparison with experiments is also made. The self-consistent RPA calculation of the electric and magnetic resonances, Fermi and Gamow-Teller transitions will be presented in the sequel of the present paper.