Calculation of thallium hyperfine anomaly

TL;DR

This paper introduces a new method for calculating the hyperfine anomaly in many-electron atoms and ions, validated on thallium systems, with implications for precision nuclear g-factor measurements.

Contribution

The paper presents a novel computational approach for hyperfine anomaly calculation applicable to complex atoms and ions, validated against analytical models and tested on thallium.

Findings

Good agreement with analytical expressions for hydrogen-like thallium ion

The ratio of anomalies for s and p1/2 states is consistent across systems

Recommendations for optimal atomic states for precise nuclear g-factor measurements

Abstract

We suggest a method to calculate hyperfine anomaly for many-electron atoms and ions. At first, we tested this method by calculating hyperfine anomaly for hydrogen-like thallium ion and obtained fairly good agreement with analytical expressions. Then we did calculations for the neutral thallium and tested an assumption, that the the ratio between the anomalies for $s$ and $p_{1/2}$ states is the same for these two systems. Finally, we come up with recommendations about preferable atomic states for the precision measurements of the nuclear $g$ factors.