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Physical Review A

van der Waals interaction in excited alkali-metal dimers

Mladen Movre, Robert Beuc

Published May 1, 1985• 30 citations
Publisher

Abstract

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 (${n}_{A}$P) and the other is in the ground state (${n}_{B}$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 ${C}_{6}$ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the ${C}_{6}$ 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 ${C}_{6}$ 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.

DOI
10.1103/physreva.31.2957

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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.
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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 C6{C}_{6}C6​ and C8{C}_{8}C8​ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the C8{C}_{8}C8​ coefficient of heteronuclear A+BA+BA+B dimers in terms of the C6{C}_{6}C6​ and C8{C}_{8}C8​ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states AAA and BBB. We report results of calculation of the C6{C}_{6}C6​ coefficients for the Yb-Rb 3P1o+5s2S1/2{}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}3P1o​+5s2S1/2​ and 1S0+5p2P1/2o{}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}1S0​+5p2P1/2o​ dimers, and the C8{C}_{8}C8​ coefficients for the Yb-Li 1S0+2s2S1/2{}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}1S0​+2s2S1/2​ and Yb-Rb 1S0+5s2S1/2{}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}1S0​+5s2S1/2​ dimers. Uncertainties are estimated for all predicted properties.
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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.
Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge distributions of two ground-state alkali-metal atoms can be expanded in inverse powers of R, the internuclear distance. The coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.
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.