Odd-even staggering of binding energy for nuclei in thesdshell

Abstract

In this paper we study odd-even staggering phenomena of binding energy in the framework of the nuclear shell model for nuclei in the $sd$ shell. We decompose the USDB effective interaction into the monopole interaction and multipole (residual) interactions. We extract the empirical proton-neutron interaction, the Wigner energy, and the one-neutron separation energy using calculated binding energies. The monopole interaction, which represents the spherical mean field, provides contributions to the empirical proton-neutron interaction, the symmetry energy, and the Wigner energy. It does not induce odd-even staggering of the empirical proton-neutron interaction or the one-neutron separation energy. Isovector monopole and quadrupole pairing interactions and isoscalar spin-1 pairing interactions play a key role in reproducing an additional binding energy in both even-even and odd-odd nuclei. The Wigner energy coefficients are sensitive to residual two-body interactions. The nuclear shell structure has a strong influence on the evolution of the one-neutron separation energy, but not on empirical proton-neutron interactions. The so-called three-point formula is a good probe of the shell structure.