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

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.

arXiv comment10 pages, 8 tables

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Cited by in corpus (16)

• Survey of hyperfine structure measurements in alkali atoms
• Analytic Response Relativistic Coupled-Cluster Theory: The first application to indium isotope shifts
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• Radiative Transition Properties of Singly Charged Magnesium, Calcium, Strontium and Barium Ions
• Enhanced spin-dependent parity non-conservation effect in the $7s{}^2{S}_{1/2}\to 6d{}^2{D}_{5/2}$ transition in Fr: A possibility for unambiguous detection of nuclear anapole moment
• Laser spectroscopy of indium Rydberg atom bunches by electric field ionization
• Relativistic coupled-cluster theory analysis of energies, hyperfine structure constants, and dipole polarizabilities of Cd${}^{+}$
• Determination of magic wavelengths for the $7s{}^2{S}_{1/2}-7p{}^2{P}_{3/2,1/2}$ transitions in Fr atom
• Relativistic coupled-cluster calculation of hyperfine-structure constants of ${}^{229}$Th${}^{3+}$ and evaluation of the electromagnetic nuclear moments of ${}^{229}$Th
• Diverse Trends of Electron Correlation Effects for Properties with Different Radial and Angular Factors in an Atomic System: A case study in Ca${}^{+}$
• Calculation of francium hyperfine anomaly
• Calculation of hyperfine magnetic anomaly in many-electron atoms
• High-precision Electric Dipole Polarizabilities of the Clock States in ${}^{133}$Cs
• Accurate determination of energy levels, hyperfine structure constants, lifetimes and dipole polarizabilities of triply ionized tin isotopes
• Relativistic density functional theory with finite-light-speed correction for the Coulomb interaction: a non-relativistic-reduction based approach
• Investigating the $4D_{3/2}|3,\pm 2⟩$--$4D_{5/2}|3,\pm 2⟩$ transition in Nb${}^{4+}$ for a THz atomic clock