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

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.

References in corpus (19)

• Trapping of Neutral Mercury Atoms and Prospects for Optical Lattice Clocks
• Parity and Time-Reversal Violation in Atomic Systems
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Shape staggering of mid-shell mercury isotopes from in-source laser spectroscopy compared with Density Functional Theory and Monte Carlo Shell Model calculations
• Ground-state hyperfine structure of H-, Li-, and B-like ions in middle-Z region
• Nuclear magnetization distribution effect in molecules: Ra${}^{+}$ and RaF hyperfine structure
• Ground-state hyperfine splitting for Rb, Cs, Fr, Ba^+, and Ra^+
• Nuclear deformation as a source of the non-linearity of King plot in the Yb${}^{+}$ ion
• The hyperfine anomaly in heavy atoms and its role in precision atomic searches for new physics
• Empirical determination of the Bohr-Weisskopf effect in cesium and improved tests of precision atomic theory in searches for new physics
• The Bohr-Weisskopf effect: from hydrogenlike-ion experiments to heavy-atom calculations of the hyperfine structure
• Effect of nuclear magnetization distribution within the Woods-Saxon model: Hyperfine splitting in neutral Tl
• MCDHF-CI calculations for Hg and Cd with estimates for unknown clock transition frequencies
• Precision spectroscopy on ${}^9$Be overcomes limitations from nuclear structure
• Electric dipole transition amplitudes for atoms and ions with one valence electron
• Electromagnetic moments of the antimony isotopes ${}^{112-133}$Sb
• Atomic calculations of hyperfine structure anomaly in gold
• Refined nuclear magnetic dipole moment of rhenium: ${}^{185}$Re and ${}^{187}$Re
• Smallness of the nuclear polarization effect in the hyperfine structure of heavy muonic atoms as a stimulus for next-generation experiments