Mirror energy differences in T=1/2f7/2 -shell nuclei within isospin-dependent density functional theory

Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks leads to the isospin symmetry breaking. The isospin non-conservation affects broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent DFT that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of Mirror and Triplet Displacement energies in a very broad range of masses. The aim of this work is to further test the charge-dependent functional by studying Mirror Energy Differences (MEDs) in function of angular momentum $I$. Methods: To compute MEDs we use DFT-rooted no core configuration interaction model. This post mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants. Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$, $45$, $47$, and $49$ focusing on MEDs in low-spin part (below band crossing) what allowed us to limit the model space to seniority one and three (one broken pair) configurations. Conclusions: We demonstrate that, for spins $I\leq 15/2$ being subject of the present study, our model reproduces well experimental MEDs which vary strongly in function of $I$ and $A$. The quality of model's predictions is comparable to the nuclear shell-model results by Bentley et al. Phys. Rev. C 92, 024310 (2015).