Wigner energy and shell gaps in two-nucleon separation energies

Abstract

Two-nucleon separation energies are differences of binding energies. They provide important information on the relative stability of nuclei and, in particular, on shell gaps. In this work, the behavior of the decrements (change of slope) of two-nucleon separation energies has been studied. It has been shown that the bulk of this decrement at a shell-gap consists mainly of twice the difference of two effective single particle energies, plus a pairing correction. The decrement of the two-nucleon separation energies has a maximum (spike) for $N=Z$ nuclei. A comparison with values calculated by using a seniority binding energy formula shows that the spike is due to the Wigner energy. The evolution with nuclear mass of the isospin dependence of the Wigner energy is discussed.