Correlation trends in the hyperfine structures of 210, 212Fr

Abstract

We demonstrate the importance of electron correlation effects in the hyperfine structure constants of many low-lying states in 210Fr and 212Fr. 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 7D5/2 state obtained from the experimental and theoretical studies, whereas good agreement is found for the other D5/2 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.