Mirror Nuclei Radii Utilizing Self-Energy Term and Nonuniform Charge Distributions

The nature of the self-energy term in the mirror nucleus energy-difference formula is investigated. Two approaches are used. In the first this self-energy term is assumed to be a constant equal to the Coulomb self-energy of a single proton, and in the second a more refined quantum mechanical approach based on the Swamy and Green Coulomb exchange energy calculations is used. Both approaches yield $r_0$ values which possess the correct general trend with increasing $A$, but which disagree with theoretical values for very low $A$. The effect of nonuniform charge distributions on the values of nuclear radii obtained from mirror nuclei is investigated, and expressions for the Coulomb energy for various charge distributions are given. A direct comparison between the mirror nucleus radii and those obtained from electron scattering is made in the few cases where this is possible. Finally, the possible validity of a suggested value of 0.58 Mev for the Coulomb self-energy of the proton is discussed briefly.