The hyperfine anomaly in mercury and test of the Moskowitz-Lombardi rule

TL;DR

This paper investigates the hyperfine anomaly in mercury isotopes, testing the Moskowitz-Lombardi rule by combining experimental data and atomic calculations to determine the Bohr-Weisskopf effect and refine the rule's additive constant.

Contribution

It provides the first empirical determination of the additive constant in the Moskowitz-Lombardi rule for mercury, using experimental and theoretical approaches.

Findings

The empirical additive constant differs significantly from previous values.

The Bohr-Weisskopf effect was successfully extracted from experimental data.

Atomic many-body calculations validated the experimental results.

Abstract

The Moskowitz-Lombardi rule gives a simple relation between the magnetic moment of an atomic nucleus and the effect of its radial distribution on the hyperfine structure - the magnetic hyperfine anomaly or "Bohr-Weisskopf" effect. It was originally formulated for mercury, for which experimental data for nuclear magnetic moments and hyperfine constants were available for a number of isotopes. While the relation for the differential effect between isotopes may be completely determined experimentally, the value for the additive constant that is needed to give the Bohr-Weisskopf (BW) effect for a single isotope has remained untested. In this work, we determine the BW effect in singly-ionized and neutral mercury from experimental muonic Hg-199 data together with our atomic calculations. We check this result by directly extracting the BW effect from the hyperfine constant for singly-ionized Hg-199 using state-of-the-art atomic many-body calculations. From this we deduce an empirical value for the additive constant in the Moskowitz-Lombardi rule, which differs significantly from the values advocated previously.