Correlation trends in the hyperfine structures ofFr210,212

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.

An optimized ion trap geometry to measure quadrupole shifts of 171 Yb + clocks

“…We account contributions from these non-truncative series by adopting iterative procedures as described in our previous works [38,39]. We also give results considering only the linear terms of Eq.…”

Determination of magic wavelengths for the7s S1/22−7p PSingh1, Sahoo2, Arora3 2016Phys. Rev. ASelf Cite12090View full textAdd to dashboardCite

“…We have also included important triply excited configurations involving valence electron to elevate amplitudes of the RCC operators in the CCSD method wave operators (known as CCSD(T) method) in a perturbative approach as discussed in Ref. [8].…”

“…In the above equations, sum is restricted by involving states denoted by k after N c and up to I, where N c represents for the core orbitals and I represents for the bound states up to which we can determine the γ n J n ||D||γ k J k matrix elements explicitly in our calculation. In the RCC ansatz, these states can be commonly expressed for |Ψ n as [3,5,[7][8][9][10] |Ψ n = e T {1 + S n }|Φ n , where the operators T and S n are responsible for accounting core and valence correlations by exciting electrons from the core orbitals and valence orbital along with from the core orbitals, respectively. It can be noted that the core-valence correlations are accounted together by the simultaneous operations of a † n and T as well as S n and T operators.…”

“…Recent theoretical studies on hyperfine structures in 210 Fr and 212 Fr demonstrate inconsistencies between the theoretically evaluated and measured hyperfine structure constants of few excited states [8]. The hyperfine structure constants and lifetimes of the 6d 2 D 3,5/2 states of Fr, which are important for PNC studies [8,9], have not been measured yet. Also, suggestion to measure hyperfine splitting in the suitable transitions to observe nuclear octupole moment of its 211 Fr isotope have been made [10].…”

Calculation of Francium Hyperfine Anomaly

“…We study francium atom, because for its isotopic chain there are comprehensive experimental data [13][14][15][16][17][18] and many theoretical calculations [19][20][21][22]. In particular, changes of the nuclear charge radii in the Fr isotopic series were calculated from the isotope shift measurements [23,24].…”