Uniform-sphere Coulomb displacement energy ($\Delta E_C=3\alpha \hslash c\Delta (Z^2)/(5R)$)

The electrostatic self-energy of a uniformly charged sphere of sharp radius $R$ is $3Z^2\alpha \hslash c/(5R)$. For mirror nuclei, subtract the changed neutron/proton rest-mass contribution from their nuclear mass difference before identifying the residual with a nuclear Coulomb energy difference. The inferred $R$ is a sharp-sphere radius; the corresponding nuclear charge radius defined as an rms radius is $\sqrt{3/5}R$. Replacing $Z^2$ by $Z(Z-1)$ removes a proton self-interaction approximation and shifts the estimate.