Isospin nonconserving interaction in the $T=1$ analogue states of the mass-70 region

Mirror energy differences (MEDs) and triplet energy differences (TEDs) in the $T=1$ analogue states are important probes of isospin-symmetry breaking. Inspired by the recent spectroscopic data of ${}^{66}$Se, we investigate these quantities for $A=66–78$ nuclei with large-scale shell-model calculations. For the first time, we find clear evidence suggesting that the isospin nonconserving (INC) nuclear force has a significant effect for the upper $fp$ shell region. Detailed analysis shows that, in addition to the INC force, the electromagnetic spin-orbit interaction plays an important role for the large, negative MED in $A=66$ and 70 and the multipole Coulomb term contributes to the negative TED in all the $T=1$ triplet nuclei. The INC force and its strength needed to reproduce the experimental data are compared with those from the $G$-matrix calculation using the modern charge-dependent nucleon-nucleon forces.

Figure 1

Experimentally known MED and TED for masses of $A=22$ to 66. Data are taken from Refs. [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29].

Figure 2

Comparison of calculated MED and TED for $A=66$ with experimental data taken from Refs. [19, 20, 21, 22].

Figure 3

Calculated CED for mass numbers $A=66$, 70, 74, and 78. Data are taken from Refs. [19, 20, 21, 22].

Figure 4

Calculated MED for mass number $A=66$, 70, 74, and 78. Data are taken from Refs. [19, 20, 21, 22].

Figure 5

Calculated TED for mass number $A=66$, 70, 74, and 78. Data are taken from Refs. [19, 20, 21, 22].