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Physical Review A

Many-body calculations of the static atom-wall interaction potential for alkali-metal atoms

Andrei Derevianko, W. R. Johnson, S. Fritzsche

Published Apr 1, 1998• 16 citations
Publisher

Abstract

We present third-order many-body perturbation theory calculations of the Lennard-Jones ${C}_{3}$ coefficient for the alkali-metal atoms lithium, sodium, potassium, rubidium, cesium, and francium. All-order singles-doubles calculations of ${C}_{3}$ are also presented for lithium, sodium, and potassium. For lithium and sodium the present values of ${C}_{3}$ are compared with other theoretical and semiempirical values.

DOI
10.1103/physreva.57.2629

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We present third-order many-body perturbation theory calculations of the Lennard-Jones C3{C}_{3}C3​ coefficient for the alkali-metal atoms lithium, sodium, potassium, rubidium, cesium, and francium. All-order singles-doubles calculations of C3{C}_{3}C3​ are also presented for lithium, sodium, and potassium. For lithium and sodium the present values of C3{C}_{3}C3​ are compared with other theoretical and semiempirical values.
A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C3{C}_{3}C3​ for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory.
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 study the nonadditive part of the long-range interaction among three alkali-metal atoms in their ground states. Using nondegenerate perturbation theory, up to the third order, we have computed the dispersion coefficients C for three alkali-metal atoms interacting via their electric dipole moments. Both heteronuclear and homonuclear cases are considered. The numerical values for the C coefficients suggest that such three-body dipole interaction effects may not be neglected in the description of the long-range surface potential interaction for alkali-metal atoms. Furthermore, we show that approximate formulas for C of Midzuno and Kihara [J. Phys. Soc. Jpn. 11, 1045 (1956)] give results in excellent agreement with results of our calculations. Comparisons are given of our results with results of others and with results of other approximate formulas. The effect on our results for the C coefficient of uncertainties in the experimental values of the static dipole polarizabilities, on which our results depend, is also analyzed.
The third-order expression for the dispersion interaction between two atoms is written as a sum over lists of transition matrix elements. Particular attention is given to the C9/R9{C}_{9}/{R}^{9}C9​/R9 interaction which occurs in the homonuclear case when one atom is in an SSS state and the other is in a PPP state. Numerical values of the C9{C}_{9}C9​ coefficient are given for the homonuclear alkali-metal dimers. The size of the C9{C}_{9}C9​:C3{C}_{3}C3​ dispersion coefficient ratio increases for the heavier alkali-metal atoms. The C11{C}_{11}C11​ and C13{C}_{13}C13​ coefficients between two helium atoms and lithium atoms in their ground states are also given.
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.
We present ab initio potentials for ground state lithium, sodium, potassium and rubidium atoms interacting with ground state chromium atoms via the 6 Σ + and 8 Σ + states of the corresponding dimers. Each potential is matched to the leading van der Waals dispersion energy − C 6 / R 6 − C 8 / R 8 and an exchange energy; we list the values of C 6 , C 8 and the exchange fitting parameters. We present calculated values from quantal and semi-classical approximations for the s-wave scattering length and effective range and the p-wave scattering volume for collisions of each of the alkali-metal atoms lithium, sodium, potassium and rubidium with 52 chromium atoms and comment on s-wave scattering by 53 chromium atoms.