Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly

TL;DR

This paper develops a generalized isobaric multiplet mass equation (GIMME) incorporating charge-symmetry and charge-independent breaking effects, providing a new explanation for the Nolen-Schiffer anomaly in nuclear physics.

Contribution

It introduces a new GIMME that accounts for density-dependent charge-violating interactions, extending the traditional IMME beyond tensor-based assumptions.

Findings

GIMME explains the Nolen-Schiffer anomaly effectively.

Charge-symmetry breaking term is key to understanding Coulomb displacement energies.

The approach uses Brueckner theory with AV18 and AV14 interactions.

Abstract

The Wigner Isobaric Multiplet Mass Equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question for the origin of the Nolen-Schiffer anomaly found in the Coulomb displacement energy of mirror nuclei. We find that the naturally-emerged CSB term in GIMME is largely responsible for explaining the Nolen-Schiffer anomaly.