# The critical notes to the solutions of the "puzzle" of hyperfine structure in 82+ and 80+ $^{209}$Bi ions

## TL;DR

This paper analyzes the Bohr-Weisskopf effect in hyperfine splitting of 209Bi ions using surface and volume nuclear current models, successfully describing the effect without specific differences and highlighting model-dependent nuclear magnetization radii.

## Contribution

It extends internal conversion models to hyperfine splitting, eliminating the need for specific differences and revealing strong model dependence of nuclear magnetization radius.

## Key findings

- Successful description of hyperfine splitting without specific differences
- Models yield different nuclear magnetization radii, akin to the proton radius puzzle
- Comparison shows satisfactory agreement with experimental data

## Abstract

Some aspects of description of the Bohr-Weisskopf effect in hyperfine splitting of the H- and Li-like ions of 209Bi are considered by application of the surface and volume models of the nuclear currents. Extension of these models, used in internal conversion theory, to description of the HFS allows one to successfully describe the effect, without resorting to the specific differences. The latters are shown not to be needed at all. Moreover, they turn out to depend on the nuclear model even stronger than the HFS values themselves. Comparison of the calculated HFS values to experiment shows a satisfactory agreement. Both models provide equally good description of the effect. However, they result in different values of the retrieved rms radius of the nuclear magnetization. In this respect, situation resembles the proton radius puzzle. Prospects of future research are discussed.