Barrett moments and rms charge radii

Abstract

An empirical relation is established between Barrett equivalent radii R _k,α and rms charge radii < r ² >^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 < r ² >^1/2 or differences δ ^AA′ < r ² >^1/2 in cases where only R _k,α data or isotope shifts δ ^AA′ R _k,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 < r ^m > (m ≥ 2) using an effective exponential parameter α _eff(Z). The moments < r ^m > and isotopic differences δ < r ^m > of the two-parameter Fermi distribution expressed in terms of the parameters c and a are given in the Appendix for m = 1 – 10.