  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.
