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.
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Angeli, I. Barrett moments and rms charge radii. Acta Physica Hungarica A 15, 87–102 (2002). https://doi.org/10.1556/APH.15.2002.1-2.4
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DOI: https://doi.org/10.1556/APH.15.2002.1-2.4