Calculation of francium hyperfine anomaly

TL;DR

This paper uses advanced quantum mechanical calculations to determine hyperfine anomalies in francium isotopes, providing insights that can improve nuclear g-factor measurements.

Contribution

It introduces a combined DHF+MBPT computational approach to accurately calculate hyperfine anomalies and Bohr–Weisskopf corrections in francium isotopes.

Findings

Good agreement with analytical expressions for hydrogen-like ions

Weak dependence of anomaly ratios on principal quantum number

Estimates of Bohr–Weisskopf corrections for isotopes

Abstract

The Dirac-Hartree-Fock plus many-body perturbation theory (DHF+MBPT) method has been used to calculate hyperfine structure constants for Fr. Calculated hyperfine structure anomaly for hydrogen-like ion has been shown to be in good agreement with analytical expressions. It has been shown that the ratio of the anomalies for $s$ and $p_{1/2}$ states is weakly dependent on the principal quantum number. Finally, we estimate Bohr--Weisskopf corrections for several Fr isotopes. Our results may be used to improve experimental accuracy for the nuclear $g$ factors of short-lived isotopes.