Charge independence and charge symmetry breaking interactions and the Coulomb energy anomaly in isobaric analog states

Effects of CIB (charge independence breaking) and CSB (charge symmetry breaking) interactions on the Coulomb displacement energies of isobaric analog states are investigated for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The mass number dependence of the Coulomb energy anomalies is well explained when we employ CIB and CSB interactions which reproduce the differences of the scattering lengths as well as those of the effective ranges of low energy nucleon-nucleon scattering.