Coulomb Energy and Nuclear Radius

This is the authors' abstract. We don't add key points for this paper.

The apparent discrepancy between the values (1.45×10^-13A1/3 cm) for the nuclear radii derived from mirror nuclei and those (1.2×10^-13A1/3 cm) derived from μ-mesonic atoms was investigated. The conventional calculation of the Coulomb energy difference ΔEc between mirror nuclei is improved in two respects: the usual uniform model is replaced by the more elaborate shell model with a finite square well potential, and the exchange terms are taken into account. An equivalent Coulomb radius Rc is defined by Rc=(6/5) (Ze²ΔEc); an equivalent meson radius is defined by RM=(5/3)1/2〈r²〉Av1/2, where 〈r²〉Av1/2 is the mean square radius of the electrical charge distribution. The two extreme cases of the pairs (F¹⁷, O¹⁷) and (O¹⁵, N¹⁵) are investigated. The computation gives RcRM=1.18 in O¹⁷, RcRM=1.07 in N¹⁵. These results are smaller by about 8 percent than the experimental ratios. However, the experimental discontinuity in Rc at the closure of the p shell is reproduced.