Barrett moments and rms charge radii

An empirical relation is established between Barrett equivalent radii Rk,α and rms charge radii 1/2 based on the results of model-independent and Fermi model analyses of 2p → 1s transitions in muonic atoms. This relation follows simple Z dependence, and can be usefully applied to derive rms radii 1/2 or differences δAA′ 1/2 in cases where only Rk,α data or isotope shifts δAA′ Rk,α are published. The atomic number dependence of the Barrett parameters k(Z) and α(Z) is also given by empirical formulae. It is shown that the Barrett moment can be expanded in a sum of integer moments (m ≥ 2) using an effective exponential parameter αeff(Z). The moments and isotopic differences δ of the two-parameter Fermi distribution expressed in terms of the parameters c and a are given in the Appendix for m = 1 – 10.