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Physical Review A

Dynamic polarizabilities of rare-earth-metal atoms and dispersion coefficients for their interaction with helium atoms

Xi Chu, A. Dalgarno, Gerrit C. Groenenboom

Published Mar 29, 2007• 50 citations
Publisher

Abstract

The dynamic scalar and tensor polarizabilities of the rare-earth-metal atoms are calculated with time-dependent density functional theory. The frequency-dependent polarizabilities at imaginary frequencies are used to determine the isotropic and orientation-dependent van der Waals coefficients for the interactions of the rare-earth-metal atoms with helium atoms. The static polarizabilities are compared with other theoretical values and with experimental results. The agreement is satisfactory in most cases but there are some exceptions where the discrepancy between theory and experiment is significant. The derived isotropic van der Waals coefficients range between 37 and 50 ${E}_{H}{a}_{0}^{6}$ and the orientation-dependent coefficients between 2 and $\ensuremath{-}1$ ${E}_{H}{a}_{0}^{6}$. Thus the ratio of elastic to inelastic scattering cross sections is expected to be substantial and any one of the rare-earth-metal atoms is an excellent candidate for trapping and cooling in a He gas.

DOI
10.1103/physreva.75.032723

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The dynamic scalar and tensor polarizabilities of the rare-earth-metal atoms are calculated with time-dependent density functional theory. The frequency-dependent polarizabilities at imaginary frequencies are used to determine the isotropic and orientation-dependent van der Waals coefficients for the interactions of the rare-earth-metal atoms with helium atoms. The static polarizabilities are compared with other theoretical values and with experimental results. The agreement is satisfactory in most cases but there are some exceptions where the discrepancy between theory and experiment is significant. The derived isotropic van der Waals coefficients range between 37 and 50 EHa06{E}_{H}{a}_{0}^{6}EH​a06​ and the orientation-dependent coefficients between 2 and \ensuremath−1\ensuremath{-}1\ensuremath−1 EHa06{E}_{H}{a}_{0}^{6}EH​a06​. Thus the ratio of elastic to inelastic scattering cross sections is expected to be substantial and any one of the rare-earth-metal atoms is an excellent candidate for trapping and cooling in a He gas.
The scalar and tensor dynamic polarizabilities of the first excited 2P1∕2,3∕2^{2}P_{1∕2,3∕2}2P1∕2,3∕2​ states of the alkali-metal atoms Na\mathrm{Na}Na, K\mathrm{K}K, and Rb\mathrm{Rb}Rb are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.
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 dynamic scalar and tensor polarizabilities of Sc and Ti are computed with time-dependent density functional theory. These polarizabilities are used to compute the isotropic and anisotropic dispersion interactions in ScHe and TiHe. We find C6,0(ScHe)=30.00{C}_{6,0}(\mathrm{ScHe})=30.00C6,0​(ScHe)=30.00, ${C}_{6,2}(\mathrm{ScHe})=\ensuremath{-}1.63$, C6,0(TiHe)=28.40{C}_{6,0}(\mathrm{TiHe})=28.40C6,0​(TiHe)=28.40, and ${C}_{6,2}(\mathrm{TiHe})=\ensuremath{-}0.90$ (Eha06)({E}_{h}{a}_{0}^{6})(Eh​a06​). We show that an estimate of the dispersion anisotropy based on static polarizabilities results in an overestimation by a factor of 2.
The random-phase approximation with exchange (RPAE) is used with a BBB-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals C6{C}_{6}C6​ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of C6{C}_{6}C6​ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the C6{C}_{6}C6​ coefficients for the alkali-metal atoms. Implications of increased C6{C}_{6}C6​ values for Ps scattering from more polarizable atoms are discussed.