Evolution of the N=20 and 28 shell gaps and two-particle-two-hole states in the FSU interaction

Abstract

The connection between fundamental nucleon-nucleon forces and the observed many-body structure of nuclei is a main question of modern nuclear physics. Evolution of the mean field, inversion of traditional shell structures, and structure of high spin states in nuclei with extreme proton-to-neutron ratios are at the center of numerous recent experimental investigations targeting the matrix elements of the effective nuclear Hamiltonian that is responsible for these phenomena. The FSU spsdfp cross-shell interaction for the shell model was successfully fitted to a wide range of mostly intruder negative parity states of the sd shell nuclei. In this paper, we explore the evolution of nuclear structure in and around the island of inversion (IoI), where low-lying states involve cross-shell particle-hole excitations. We apply the FSU interaction to systematically trace out the relative positions of the effective single-particle energies of the 0f_{7/2} and 1p_{3/2} orbitals forming the N=20 and 28 shell gaps. We find that above a proton number of about 13, the 0f_{7/2} neutron orbital lies below that of 1p_{3/2}, which is considered normal ordering but, systematically, for more exotic nuclei with lower Z=12 and 10 the order of orbitals reversed. The crossing of the neutron orbitals happens right near the neutron separation threshold. Our Hamiltonian reproduces remarkably well the absolute binding energies for a broad range of nuclei and the inversion in the configurations of nuclei inside the IoI. The effective interaction accounts well for the energies and variations with mass number A of aligned high-spin states that involve nucleon pairs prompted across the shell gap. This paper puts forward an empirically determined effective Hamiltonian where data from many recent experiments allowed us to significantly improve our knowledge about cross-shell nuclear interaction matrix elements. The quality with which this Hamiltonian describes the two-particle, two-hole cross-shell excitations, binding energies, and the physics of aligned states that were not a part of the fit, is remarkable, making the FSU interaction an important tool for the future exploration of exotic nuclei.