Microscopic origin of the Wigner term in nuclear mass formulas

Determine the microscopic origin of the Wigner term—the linear |N−Z| contribution added phenomenologically to empirical nuclear mass formulas—by identifying the specific many-body correlations or interactions in nuclei that generate this term.

Background

The Wigner term is a linear contribution proportional to |N−Z| in empirical nuclear mass formulas and is distinct from the conventional quadratic symmetry energy term. Although mean-field approaches reproduce nuclear binding energies well, the Wigner term still needs to be included phenomenologically and its microscopic origin remains unresolved. Many studies have explored possible explanations, including proton–neutron pairing, yet a definitive microscopic mechanism is lacking.

In this work, the authors analyze quartet (alpha-like) correlations near nuclear surfaces and estimate their potential contribution to the Wigner term via nucleon–quartet scattering, finding a non-negligible but subleading magnitude relative to empirical values. This suggests multi-nucleon clusters may play a role, but the full microscopic origin of the Wigner term continues to be an open question.