Nuclear Coulomb energy ($E_C\simeq a_C{Z}^2/A^{1/3}$)

Nuclear Coulomb energy is the positive electrostatic mass-energy contribution from proton repulsion in a nucleus. A uniform-charge model gives scaling $Z^2/R$, and approximately constant nuclear density gives $R\propto A^{1/3}$. It reduces conventional positive nuclear binding energy.

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.