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Calculations of the magnetic hyperfine structure rely on the input of nuclearproperties -- nuclear magnetic moments and nuclear magnetization distributions-- as well as quantum electrodynamic (QED) radiative corrections forhigh-accuracy evaluation in heavy atoms. The uncertainties associated withassumed values of these properties limit the accuracy of hyperfinecalculations. For example, for the heavy alkali-metal atoms Cs and Fr, theseuncertainties may amount collectively to almost 1\% or 2\%, respectively. Inthis paper we propose a method for removing the dependence of hyperfinestructure calculations on assumed values of nuclear magnetic moments andnuclear magnetization distributions by determining these effects empiricallyfrom measurements of the hyperfine structure for high states. The method isvalid for $s$, $p_{1/2}$, and $p_{3/2}$ states of alkali-metal atoms andalkali-metal-like ions. We have shown that for $s$ states the dependence on QEDeffects may also be removed to high accuracy. The ability to probe theelectronic wave functions, through hyperfine comparisons, with significantlyincreased accuracy is important for the analysis of atomic parity violationmeasurements and may enable the accuracy of atomic parity violationcalculations to be improved. More broadly, it opens the way for furtherdevelopment of high-precision atomic many-body methods.

Testing atomic wave functions in the nuclear vicinity: the hyperfine structure with empirically-deduced nuclear and quantum electrodynamic effects