Coulomb displacement energies of the $A=4n+3\mathrm{}$, $T=\frac{1}{2}$ mirror nuclei in the $1f_{\frac{7}{2}}$ shell

The $Q$ values of the (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$) reaction on ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ have been measured, and the excitation energy of levels up to 7 MeV has been determined. Angular distributions from the more strongly populated states have been taken from 4.5 to 27.0° in the laboratory. These angular distributions together with comparison to their $T_z=+\frac{1}{2}$ mirrors have been used as empirical guides to determine the spin and parity of several of the states. The Coulomb displacement energies of particle-hole states in the $T=\frac{1}{2}$ mirrors have been compared to a simple model.