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Physical Review A

Relativistic multireference coupled-cluster theory based on a B -spline basis: Application to atomic francium

Yong-Bo Tang, Bing-Qiong Lou, Ting-Yun Shi

Published Aug 18, 2017• 23 citations
Publisher

Abstract

In this paper, we report the relativistic Fock space multireference coupled-cluster method for atomic structure calculations. We use the no-pair Dirac-Coulomb-Breit Hamiltonian, together with a finite $B$-spline basis set to expand the large and small components of the Dirac wave function. Our method is applied to calculate ionization energies, reduced matrix elements, lifetimes, and polarizabilities for many states of atomic francium. To evaluate uncertainties of our results and investigate the role of electron correlation effects, we carry out calculations using approximated models at different levels. The quality of our calculations is assessed by comparing with available experimental results, showing a good agreement. In addition, the tune-out wavelengths of the ground state in the range of 340--800 nm, the magic wavelengths for the transition $7s\ensuremath{-}8s$ in the range of 800--1500 nm and the transition $7s\ensuremath{-}7p$ in the range of 600--1500 nm are determined by evaluating the dynamic polarizabilities of the $7s, 8s$, and $7p$ states for a linearly polarized light. These tune-out and magic wavelengths may be useful for laser cooling and trapping of the Fr atom, and for related high-precision trapping measurements.

DOI
10.1103/physreva.96.022513

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In this paper, we report the relativistic Fock space multireference coupled-cluster method for atomic structure calculations. We use the no-pair Dirac-Coulomb-Breit Hamiltonian, together with a finite BBB-spline basis set to expand the large and small components of the Dirac wave function. Our method is applied to calculate ionization energies, reduced matrix elements, lifetimes, and polarizabilities for many states of atomic francium. To evaluate uncertainties of our results and investigate the role of electron correlation effects, we carry out calculations using approximated models at different levels. The quality of our calculations is assessed by comparing with available experimental results, showing a good agreement. In addition, the tune-out wavelengths of the ground state in the range of 340--800 nm, the magic wavelengths for the transition 7s\ensuremath−8s7s\ensuremath{-}8s7s\ensuremath−8s in the range of 800--1500 nm and the transition 7s\ensuremath−7p7s\ensuremath{-}7p7s\ensuremath−7p in the range of 600--1500 nm are determined by evaluating the dynamic polarizabilities of the 7s,8s7s, 8s7s,8s, and 7p7p7p states for a linearly polarized light. These tune-out and magic wavelengths may be useful for laser cooling and trapping of the Fr atom, and for related high-precision trapping measurements.
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The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the 7s7s7s 2S1/2^{2}{S}_{1/2}2S1/2​, 7p7p7p 2P1/2,3/2^{2}{P}_{1/2,3/2}2P1/2,3/2​, and 8s8s8s 2S1/2^{2}{S}_{1/2}2S1/2​ levels of the 7s7s7s $^{2}{S}_{1/2}\ensuremath{-}7p$ 2P1/2,3/2^{2}{P}_{1/2,3/2}2P1/2,3/2​ and 7s7s7s $^{2}{S}_{1/2}\ensuremath{-}8s$ 2S1/2^{2}{S}_{1/2}2S1/2​ transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground 7s7s7s 2S1/2^{2}{S}_{1/2}2S1/2​ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.
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