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Journal of Physics B Atomic and Molecular Physics

Calculated long-range coefficients Cn(n=6, 8, 10) for the interactions Na(3s)+K(4s) and Na(3s)+K(4p)

Béatrice Bussery‐Honvault, Monique Aubert-Frécon

Published Jun 28, 1985• 10 citations
Publisher

Abstract

The long-range coefficients C n (n=6, 8, 10) have been calculated for the molecular states corresponding to the interactions Na(3s)+K(4s) and Na(3s)+K(4p) using a perturbative model the authors recently proposed. For the ground state they obtained the following results (in au) C 6 =-2803, C 8 =-201516, C 10 =-17674349 in good agreement with the values deduced from an accurate RKR potential curve just determined.

DOI
10.1088/0022-3700/18/12/006

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The long-range coefficients C n (n=6, 8, 10) have been calculated for the molecular states corresponding to the interactions Na(3s)+K(4s) and Na(3s)+K(4p) using a perturbative model the authors recently proposed. For the ground state they obtained the following results (in au) C 6 =-2803, C 8 =-201516, C 10 =-17674349 in good agreement with the values deduced from an accurate RKR potential curve just determined.
We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C -coefficients are determined for all symmetries of molecular states that correlate to the n s– n s, n p– n p and n d– n d asymptotes. Fitted parameters are given for the scaling of the C -coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.
The dipole polarizabilities of the potassium atom in its ground (4 2S) and low-lying excited (4 2P, 5 2S) states have been calculated using the time-dependent gauge-invariant variational method [Mérawa, Rérat, and Pouchan, J. Chim. Phys. 91, 1387 (1994)]. The variation of these polarizabilities versus imaginary frequencies [Casimir and Polder, Phys. Rev. 73, 360 (1948)] have been computed, and the long-range dispersion coefficients for the molecular states of K2 dissociating to K(4S)+K(4S), K(4S)+K(4P), K(4P)+K(4P), K(4S)+K(5S), K(5S)+K(4P) and K(5S)+K(5S) have been evaluated. The results obtained for K(4S)+K(4P) interactions are in very good agreement with the recent experimental high-resolution photoassociative data of Wang et al. [J. Chem. Phys. 106, 7899 (1997)]. The long-range dispersion coefficients for the K(4P)+K(4P), K(4P)+K(5S) and K(5S)+K(5S) interactions are new.
We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}\ensuremath{-}{n}^{\ensuremath{'}}S,nS\ensuremath{-}{n}^{\ensuremath{'}}P,nS\ensuremath{-}{n}^{\ensuremath{'}}D,$ and $\mathrm{nP}\ensuremath{-}{n}^{\ensuremath{'}}P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{Rb}(6S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P){ }^{1,3}\ensuremath{\Sigma},\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P){ }^{1,3}\ensuremath{\Sigma},$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{N}\mathrm{a}(3D){ }^{1,3}\ensuremath{\Sigma}$ molecules to be the most attractive. The $\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P)$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P)$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{K}(4P)$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the 1/R6{1/R}^{6}1/R6 van der Waals coefficient for the interaction between Cs(6S)\mathrm{Cs}(6S)Cs(6S) and Li(2P)\mathrm{Li}(2P)Li(2P) atoms.
We report results of theoretical calculations for the dispersion coefficients associated with the long-range interaction of two 39{}^{39}39K atoms in the states 39{}^{39}39K(4s)(4s)(4s)-39{}^{39}39K(5d,6d,7s)(5d,6d,7s)(5d,6d,7s). These results have been found by Wang et al. [Phys. Rev. Lett. 78, 4173 (1997)] to be in a good agreement with their measurements.
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.