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Physical Review A

Long-range dispersion interactions. II. Alkali-metal and rare-gas atoms

J. Mitroy, J.-Y. Zhang

Published Sep 11, 2007• 63 citations
Publisher

Abstract

The dispersion coefficients for the van der Waals interactions between the rare gases Ne, Ar, Kr, and Xe and the low-lying states of Li, Na, K, and Rb are estimated using a combination of ab initio and semiempirical methods. The rare-gas oscillator strength distributions for the quadrupole and octupole transitions were derived by using high-quality calculations of rare-gas polarizabilities and dispersion coefficients to tune Hartree-Fock single-particle energies and expectation values.

DOI
10.1103/physreva.76.032706

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The dispersion coefficients for the van der Waals interactions between the rare gases Ne, Ar, Kr, and Xe and the low-lying states of Li, Na, K, and Rb are estimated using a combination of ab initio and semiempirical methods. The rare-gas oscillator strength distributions for the quadrupole and octupole transitions were derived by using high-quality calculations of rare-gas polarizabilities and dispersion coefficients to tune Hartree-Fock single-particle energies and expectation values.
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 present semiempirical calculations of long-range van der Waals interactions for two interacting metastable rare-gas atoms Ne through Xe. Dispersion coefficients C6{C}_{6}C6​ are obtained for homonuclear molecular potentials asymptotically connecting to the ns(3/2)2+ns(3/2)2{\mathrm{ns}(3/2)}_{2}{+ns(3/2)}_{2}ns(3/2)2​+ns(3/2)2​ atomic states. The estimated uncertainty of the calculated C6{C}_{6}C6​ dispersion coefficients is 4%.
The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) and He(2 1,3{}^{1,3}1,3PPP), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5%. For interactions with other alkali-metal atoms the uncertainty is 1--3% in the coefficient C5{C}_{5}C5​, 1--5% in the coefficient C6{C}_{6}C6​, and 1--10% in the coefficients C8{C}_{8}C8​ and C10{C}_{10}C10​. The dispersion coefficients Cn{C}_{n}Cn​ for the interaction of He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) and He(2 1,3{}^{1,3}1,3PPP) with the ground-state alkali-metal atoms and for the interaction of He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) with the alkali-metal atoms in their first 2{}^{2}2PPP states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.
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.
Accurate knowledge of interaction potentials among the alkali-metal atoms and alkaline-earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali-metal atoms with the Ca+{\mathrm{Ca}}^{+}Ca+, Ba+{\mathrm{Ba}}^{+}Ba+, Sr+{\mathrm{Sr}}^{+}Sr+, and Ra+{\mathrm{Ra}}^{+}Ra+ alkaline-earth ions systematically, which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus RRR are given among all the alkaline ions with Rb.
The van der Waals coefficients, from C11{C}_{11}C11​ through to C16{C}_{16}C16​ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the Cn∕rn{C}_{n}∕{r}^{n}Cn​∕rn potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to C10∕r10{C}_{10}∕{r}^{10}C10​∕r10 results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than 20a020{a}_{0}20a0​. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive (C11,C13,C15)({C}_{11},{C}_{13},{C}_{15})(C11​,C13​,C15​) and attractive (C12,C14,C16)({C}_{12},{C}_{14},{C}_{16})(C12​,C14​,C16​) dispersion forces.