The theory of the Bohr-Weisskopf effect in the hyperfine structure

TL;DR

This paper proposes a model-independent method to estimate nuclear radii from hyperfine splitting data, linking it to internal conversion anomalies, and discusses its implications for QED tests and experimental measurements.

Contribution

It introduces a novel approach to determine nuclear moments and radii from hyperfine structure, independent of models, and connects these to internal conversion coefficient anomalies.

Findings

Nuclear radii R_2 and R_4 are obtained from hyperfine splitting data.

The method provides a basis for strict QED tests using hyperfine structure.

Predictions for hyperfine splitting in specific atomic states are discussed.

Abstract

For twenty years research into the anomalies in the HF spectra was going in a wrong direction by fighting the related Bohr-Weisskopf effect. As a way out, the model-independent way is proposed of estimating the nuclear radii from the hyper-fine splitting. The way is based on analogy of HFS to internal conversion coefficients, and the Bohr-Weisskopf effect - to the anomalies in the internal conversion coefficients. This makes transparent It is shown that the parameters which can be extracted from the data are the even nuclear moments of the magnetization distribution. The radii $R_2$ and (for the first time) $R_4$ are thus obtained by analysis of the experimental HFS for the H- and Li-like ions of $^{209}$Bi. The critical prediction of the HFS for the $2p_{1/2}$ state is discussed. The moments may be determined in this way only if the higher QED effects are properly taken into account. Therefore, this set of the parameters form a basis of a strict QED test. Experimental prospects are discussed, aimed at retrieving data on the HFS values for a set of a few-electron configurations of the atom.