Generalized seniority and structure of semi-magic nuclei

Abstract

Abstract Nuclei with either protons or neutrons in closed shells are considered. States in which a pair of nucleons with J = 0 is distributed with unequal amplitudes over several j-orbits are considered. Conditions are given under which states with definite numbers of such pairs are eigenstates of the shell-model Hamiltonian. It is shown that these conditions imply binding energies of even nuclei which have linear and quadratic terms in the nucleon number. It is shown that these conditions are satisfied by effective Hamiltonians constructed for the Ni isotopes. Also pseudonium nuclei seem to fall into this category. The problem is investigated whether a linear and quadratic dependence of ground state energies implies zero generalized seniority for these states. Finally, states with generalized seniority ν = 1 and ν = 2 are considered. It is shown that if the latter states are eigenstates, a constant separation between the ground state and ν = 2 states, independent of the number of pairs, follows.