Wigner energy and nuclear mass relations

Abstract

In this paper we construct an approach to extract the Wigner energy $[{B}_{\mathrm{w}}(N,Z)=\ensuremath{-}W(A)|N\ensuremath{-}Z|\ensuremath{-}d(A){\ensuremath{\delta}}_{N,Z}{\ensuremath{\pi}}_{np}]$ by using local mass relations, in the first-order approximation. We obtain $W(A)=(42.7\ifmmode\pm\else\textpm\fi{}1.2)/A$ MeV, $d(A)=(28.7\ifmmode\pm\else\textpm\fi{}1.5)/A$ MeV. By using the Wigner energies such obtained as well as empirical pairing and symmetry energies, the resultant binding-energy difference between the lowest $T=0$ and $T=1$ states of odd-odd $N=Z$ nuclei is in good agreement with experimental data.