Nuclear shell model with delta excitations

Abstract

Working in an oscillator basis, we define the nuclear Hamiltonian in a no-core model space to consist of an effective nucleon-nucleon interaction obtained with Brueckner theory from the Reid Soft Core interaction, a Coulomb term, nucleondelza transition potentials, and delta-delta interaction terms. This Hamiltonian is suitable for direct diagonalization and will account for interaction effects usually attributed to three-body, four-body, etc., forces arising from the virtual excitation of deltas. A natural outcome of this approach is a nuclear shell-model involving single particle states which are primarily nucleon in character and others, at higher energies, which are primarily delta in character. By performing spherical Hartree Fock calculations with this “realistic baryon Hamiltonian” we have found that the ground states of 16O, 40Ca and 56Ni are nearly pure nucleonic states while 2 Sn has about 10% of one delta in the ground state. For an estimate of how the delta degree of freedom is excited as one goes away from the ground state, we have performed spherical Hartree-Fock calculations with a radial constraint to compress the nucleus. The delta degree of freedom is gradually populated as the nucleus is compressed. Our results suggest that inclusion of the delta in the nuclear dynamics could lead to a significant softening of the nuclear equation of state.