Isospin symmetry breaking and large-scale shell-model calculations with the Sakurai-Sugiura method

Recently isospin symmetry breaking for mass 60-70 region has been investigated based on large-scale shell-model calculations in terms of mirror energy differences (MED), Coulomb energy differences (CED) and triplet energy differences (TED). Behind these investigations, we have encountered a subtle problem in numerical calculations for odd-odd N = Z nuclei with large-scale shell-model calculations. Here we focus on how to solve this subtle problem by the Sakurai-Sugiura (SS) method, which has been recently proposed as a new diagonalization method and has been successfully applied to nuclear shell-model calculations. The isospin symmetry breaking is one of the current topics in nuclear structure physics. An asymmetry be- tween spectra of isospin analogue states with mirror pair nuclei has been extensively investigated in the upper sd− and the lower fp −shell regions (1), and in mass 60-70 region (2-6). This asymmetry, that is, isospin symmetry breaking arises partly due to the Coulomb force and partly due to the strong nucleon-nucleon interaction. To analyze this isospin symmetry breaking, mirror en- ergy differences (MED) (7), Coulomb energy differences (CED)(8) and triplet energy differences(TED) (7) have been discussed. The MED is a measure of charge sym- metry breaking in an effective interaction and is defined as