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

## TL;DR

This paper presents high-precision calculations of hyperfine structures in alkali-metal atoms Rb, Cs, and Fr, revealing correlation trends and enabling accurate predictions of hyperfine constants with minimal uncertainties.

## Contribution

It introduces a comprehensive analysis of correlation trends across principal quantum numbers and provides high-accuracy hyperfine constant predictions for Rb, Cs, and Fr.

## Key findings

- Correlation corrections decrease rapidly with n
- Corrections tend to constant non-zero values for high n
- Predictions achieve uncertainties within 0.1% for most states

## 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.