Calculation of the Coulomb Energy Shift BetweenSc41andCa41

A straightforward, purely single-particle analysis of the Coulomb energy shift in ${\mathrm{Sc}}^{41}$, ${\mathrm{Ca}}^{41}$ leads to an abnormally small radius for the $f_{\frac{7}{2}}$ valence neutron. Presented in this note is a correlational correction that may help to increase this radius. The calculation of this correction is stated in as general a fashion as is possible, and an estimate is made which leans heavily on a parametrization of the proton and neutron densities.