Relation between Wigner energy and proton-neutron pairing

TL;DR

This paper models the Wigner energy in nuclei using isovector pairing and a  interaction, showing it arises from isospin symmetry restoration and is insensitive to moderate isoscalar pairing.

Contribution

It introduces a model combining isovector pairing and  interaction to explain the Wigner energy and its relation to isospin symmetry restoration.

Findings

Reproduces experimental binding energies for ND7Z nuclei.

Shows Wigner energy is insensitive to moderate isoscalar pairing.

Demonstrates Wigner energy as a consequence of isospin symmetry restoration.

Abstract

The linear term proportional to $|N-Z|$ in the nuclear symmetry energy (Wigner energy)is obtained in a model that uses isovector pairing on single particle levels from a deformed potential combined with a $\vec T^2$ interaction. The pairing correlations are calculated by numerical diagonalization of the pairing Hamiltonian acting on the six or seven levels nearest the $N=Z$ Fermi surface. The experimental binding energies of nuclei with $N\approx Z$ are well reproduced. The Wigner energy emerges as a consequence of restoring isospin symmetry. We have found the Wigner energy to be insensitive to the presence of moderate isoscalar pair correlations.