Correlation trends in the hyperfine structure for Rb, Cs, Fr and high-accuracy predictions for hyperfine constants

Abstract

We have performed high-precision calculations of the hyperfine structure for n 2S_1/2 and n 2P_1/2 states of the alkali-metal atoms Rb, Cs, and Fr across principal quantum number n, and studied the trend in the size of the correlations. Our calculations were performed in the all-orders correlation potential method. We demonstrate that the relative correlation corrections fall off quickly with n and tend towards constant and non-zero values for highly-excited states. This trend is supported by experiment, and we utilize the smooth dependence on n to make high-accuracy predictions of the hyperfine constants, with uncertainties to within 0.1% for most states of Rb and Cs.

arXiv commentreferences updated

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• Empirical determination of the Bohr-Weisskopf effect in cesium and improved tests of precision atomic theory in searches for new physics
• Nuclear magnetic moments of francium 207-213 from precision hyperfine comparisons
• The Bohr-Weisskopf effect: from hydrogenlike-ion experiments to heavy-atom calculations of the hyperfine structure
• Measurement of the hyperfine coupling constants and absolute energies of the $12s{}^2{S}_{1/2}$, $13s{}^2{S}_{1/2}$, and $11d{}^2{D}_J$ levels in atomic cesium
• Measurement of the hyperfine coupling constants and absolute energies of the $8p{}^2{P}_{1/2}$ and $8p{}^2{P}_{3/2}$ levels in atomic cesium
• Measurement of hyperfine constants and the isotope shift of rubidium 5P${}_{1/2}$ excited-state using Saturated Absorption Spectroscopy
• Theoretical characterisation of the barium II and radium II ions
• Measurements of the hyperfine structure of $n{P}_J$ Rydberg states by microwave spectroscopy in Cs atoms
• The hyperfine anomaly in mercury and test of the Moskowitz-Lombardi rule
• Applicability of the Dirac-Fock method combined with Core Polarization in calculations of alkali atoms