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 long-range asymptotic form of the interaction potential surface for three neutral alkali-metal atoms in their ground states may be expressed as an expansion in inverse powers of inter-nuclear distances. The first leading powers are proportional to the dispersion coefficients for pairwise atomic interactions. They are followed by a term responsible for a three body dipole interaction. The authors results consist in evaluation of the three body dipole interaction coefficient between three alkali-metal atoms. The generalization to long-range n atom interaction terms will be discussed qualitatively.
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,
C8, and
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,
C8, and
C10 for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.
The scalar and tensor dynamic polarizabilities of the first excited
2P1∕2,3∕2 states of the alkali-metal atoms
Na,
K, and
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%.
Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole
C6 and three-dipole
C9 dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The
C6 and
C9 coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated
C6 coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the
C6 coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the
C9 coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e.,
Be+,Mg+,Ca+,Sr+, and
Ba+, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.
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.
General formulas for calculating the several leading long-range interactions among three identical atoms where two atoms are in identical
S states and the other atom is in a
P state are obtained using perturbation theory for the energies up to second order. The first-order (dipolar) interactions depend on the geometrical configurations of the three atoms. In second order, additive and nonadditive dispersion interactions are obtained. The nonadditive interactions depend on the geometrical configurations in marked contrast to the case where all three atoms are in identical
S states, for which the nonadditive (also known as triple-dipole or as Axilrod-Muto-Teller) dispersion interactions appear at the third order. The formalism is demonstrated by the calculation of the coefficients for the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}P)$ system using variationally generated atomic lithium wave functions in Hylleraas coordinates. The present dipolar coefficients and additive and nonadditive dispersion coefficients may be useful in constructing precise potential energy surfaces for this three lithium atom system.