Nuclear-Matter Criterion for Semirealistic Hartree-Fock Interactions

This work is an extension of an earlier paper by the authors in which it was proposed that the effective interaction for nuclear Hartree-Fock calculations should conform in the long-range part to the real nucleon-nucleon interaction, while the short-range part should be purely phenomenological, being adjusted so that the entire interaction saturates nuclear matter correctly in the Hartree-Fock approximation, with small second-order terms. Here we investigate in some detail to what extent the finite-nucleus results depend on the precise form of the phenomenological part of such an effective interaction. Considering the specific cases of the doubly-closed-shell nuclei ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$, calculated in the well-tested oscillator approximation, we find that their binding energies are quite insensitive to the phenomenological part of the interaction and are in good agreement with experiment, provided the range of this part of the interaction does not exceed a certain value, and the same nuclear-matter binding energy and density are always fitted. However, these conditions are not sufficient to obtain a unique nuclear radius: We find that the radius is also sensitive to the nuclear-matter compressibility. Experimental information on this latter quantity is lacking, but an estimate based on a very crude examination of breathing modes leads to reasonable values of nuclear radii.