Exploring isospin-nonconserving effects in the upper $fp$ shell with new mass measurements

Nuclear mass measurements have recently been extended conspicuously to proton-rich region in the upper $fp$ shell. The new data are utilized to study isospin symmetry breaking phenomena}using Coulomb displacement energy (CDE) and triplet displacement energy (TDE) as probes. The new mass data, either measured for the first time or with greatly improved accuracy, removed several previously found ``anomalies" in the systematical behavior in the $fp$ shell. Remarkably, more regular odd-even staggering patterns can be established in both CDE and TDE, calling for a uniform explanation in terms of isospin-nonconserving (INC) forces across the $sd$, $f_{7/2}$, and upper $fp$ shells. By extending the large-scale shell-model calculation [Phys. Rev. Lett. \textbf{110}, 172505 (2013)] to the upper $fp$-shell region, we found that, in order to describe the new data, the same INC force is required as previously used for the $f_{7/2}$ shell. Especially, we propose the $T=1$ TDE for those triplet nuclei, that have $pp$, $nn$, and $pn$ pairs on top of a common even-even $N=Z$ core, to be a good indicator for the isotensor component of isospin violating interactions, which is estimated here to be 150 keV.