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. This should be generalized for a general situation. In addition, the Nolen-Schiffer anomaly is a longstanding historical problem, which is an anomaly because when all the corrections were taken into account, there remained a consistent underestimate of theCoulomb displacement energy by about a few to ten percent. The Coulomb displacement energy—the difference in binding energy between two members of a multiplet—is directly related to the IMME coefficients.  

The chargesymmetry 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 by the researchers in the Institute of Modern Physics (IMP), Chinese Academy of Sciences, as shown in Fig. 1. 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, a generalized IMME (GIMME) that modifies the coefficients of the original IMME was derived. As the first application of GIMME, we study the long-standing question of 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. 

The work is supported by the National Natural Science Foundation of China, the 973 Program of China, and has been published in Phys. Rev. C 97, 021301(R) (2018). 

Weblink: https://journals.aps.org/prc/abstract/10.1103/PhysRevC.97.021301 

Fig. 1.  The contributions of charge-symmetry breaking and charge-independent breaking components of the nucleon-nucleon force in nuclear medium.