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arXiv:1401.6585 · Physical Review A

Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko, Charles W. Clark

Published Feb 6, 2014• 15 citations
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Abstract

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.

DOI
10.1103/physreva.89.022703

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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.
We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the 6s21S06{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}6s21S0​, 6s6p3P0o6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}6s6p3P0o​, and 6s6p3P1o6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}6s6p3P1o​ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the C6{C}_{6}C6​ coefficients for the Yb-Yb 1S0+3P0,1o{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}1S0​+3P0,1o​ and 3P0o+3P0o{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}3P0o​+3P0o​ dimers and C8{C}_{8}C8​ coefficients for the 1S0+1S0{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}1S0​+1S0​ and 1S0+3P1o{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}1S0​+3P1o​ dimers.
Relativistic many-body calculations of van der Waals coefficients C6{C}_{6}C6​ for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined: C6=214(3){C}_{6}=214(3)C6​=214(3) for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.
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 have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state (nA{n}_{A}nA​P) and the other is in the ground state (nB{n}_{B}nB​S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding C6{C}_{6}C6​ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the C6{C}_{6}C6​ constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in C6{C}_{6}C6​ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.