Complete Semirealistic Effective Interactions for the Nuclear Shell Model

Abstract

Since there exists considerable uncertainty in the short-range part of the real nucleon-nucleon interaction, any attempt at a rigorous derivation of the effective interaction is illusory. Rather, we have argued that requiring the effective interaction to conform to the real interaction in the long-range part is the furthest that one can meaningfully go in relating the two, and that the short-range part of the effective interaction should be chosen phenomenologically. Our earlier work is here extended to impose phenomenological constraints on the vector (spin-orbit) and tensor components of the effective interaction. The short-range phenomenological part of our effective interaction is to be chosen in such a way that the entire interaction satisfies the following conditions: (a) Nuclear matter is correctly saturated in first-order perturbation theory, with small second-order corrections. (b) The odd-state scattering parameters are fitted up to 300 MeV. (c) The low-energy singlet scattering parameters are fitted. (d) The low-energy triplet scattering parameters and the quadrupole moment of the deuteron are fitted. We find that it is never possible to satisfy more than three conditions simultaneously, and so arrive at four effective interactions, each of which is characterized by the violation of one of the above conditions. Two of these interactions are found to work well for both Hartree-Fock and spectroscopic calculations, and, hence, may be regarded as having some measure of universality.