Correlation Trends in the Hyperfine Structures of $^{210,212}$Fr

TL;DR

This paper emphasizes the significance of electron correlation effects in hyperfine structure constants of francium isotopes, using advanced relativistic calculations to refine nuclear moments and benchmark data.

Contribution

It introduces a comprehensive relativistic computational approach to accurately determine hyperfine constants and nuclear moments in francium isotopes, highlighting correlation effects.

Findings

Large discrepancies for the $7D_{5/2}$ state between theory and experiment.

Good agreement for other $D_{5/2}$ states.

New benchmark hyperfine constants for several states.

Abstract

We demonstrate the importance of electron correlation effects in the hyperfine structure constants of many low-lying states in $^{210}$Fr and $^{212}$Fr. This is achieved by calculating the magnetic dipole and electric quadrupole hyperfine structure constants using the Dirac-Fock approximation, second order many-body perturbation theory and the coupled-cluster method in the singles and doubles approximation in the relativistic framework. By combining our recommended theoretical results with the corresponding experimental values, improved nuclear magnetic dipole and electric quadrupole moments of the above isotopes are determined. In the present work, it is observed that there are large discrepancies between the hyperfine structure constants of the $7D_{5/2}$ state obtained from the experimental and theoretical studies whereas good agreements are found for the other $D_{5/2}$ states. Our estimated hyperfine constants for the $8P$, $6D$, $10S$ and $11S$ states could be very useful as benchmarks for the measurement of these quantities.