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Physical Review A

Radiative transitions and van der Waals coefficients for francium

M. Marinescu, D. Vrinceanu, H. R. Sadeghpour

Published Dec 1, 1998• 21 citations
Publisher

Abstract

Francium has been the least-studied alkali-metal atom until recently. We present accurate calculations for the discrete and continuum optical transitions, and dispersion coefficients for two colliding francium atoms. Spin-orbit coupling is explicitly included and the influence of core polarization on the energies and the electric dipole operator is considered. Predictions for a range of transition amplitudes that are needed for parity violation experiments are made. The van der Waals coefficients for the long-range collision of two-ground-state Fr atoms in different fine-structure levels show a departure from an established trend in other alkali-metal atoms. We comment on the differences.

DOI
10.1103/physreva.58.r4259

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Francium has been the least-studied alkali-metal atom until recently. We present accurate calculations for the discrete and continuum optical transitions, and dispersion coefficients for two colliding francium atoms. Spin-orbit coupling is explicitly included and the influence of core polarization on the energies and the electric dipole operator is considered. Predictions for a range of transition amplitudes that are needed for parity violation experiments are made. The van der Waals coefficients for the long-range collision of two-ground-state Fr atoms in different fine-structure levels show a departure from an established trend in other alkali-metal atoms. We comment on the differences.
The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric-dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies.
The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic C6{C}_{6}C6​ coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic C6{C}_{6}C6​ coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.
A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom+molecule and molecule+molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing high-level quantum chemistry calculations. The dispersion, induction, and rotational parts of the isotropic van der Waals coefficient are evaluated. The known van der Waals coefficients are then used to derive characteristics essential for simple models of the collisions involving the corresponding ultracold polar molecules.
The van der Waals coefficients, C6,C8,{C}_{6},{C}_{8},C6​,C8​, and C10{C}_{10}C10​ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, D8{D}_{8}D8​ and the three-body coefficient, C9{C}_{9}C9​ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.
We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C6 dispersion coefficients [Phys. Rev. Lett. 82, 3589 (1999)] to higher-multipole coefficients C8 and C10. Special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and heteronuclear dimers and estimate theoretical uncertainties. The estimated uncertainties for C8 coefficients range from 0.5% for Li2 to 4% for Cs2.
In this paper, we have calculated the values of the C6{\mathrm{C}}_{6}C6​ coefficients and the anisotropy parameters $\ensuremath{\gamma}$ of the leading term of the van der Waals interactions between molecular hydrogen and alkali-metal atoms from Li to Fr. The uncertainties in our results are less than 22%.2