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Physical Review A

Retardation long-range potentials between two helium atoms

Ming-Keh Chen, Kwong T. Chung

Published Mar 1, 1996• 35 citations
Publisher

Abstract

The retardation long-range potentials between two 1${\mathrm{}}^{1}$S (or 2${\mathrm{}}^{3}$S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1${\mathrm{}}^{1}$S and 2${\mathrm{}}^{3}$S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1${\mathrm{}}^{1}$S--2${\mathrm{}}^{3}$S ${\mathrm{He}}_{2}$ state is estimated. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1439

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We theoretically investigate long-range interactions between an excited LLL-state He atom and two identical SSS-state He atoms for the cases of the three atoms all in spin-singlet states or all in spin-triplet states, denoted by He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{'}\ensuremath{\lambda}}L$), with n0{n}_{0}n0​ and ${n}_{0}^{\ensuremath{'}}$ principal quantum numbers, $\ensuremath{\lambda}=1$ or 3 the spin multiplicity, and LLL the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients C3{C}_{3}C3​ of the first-order dipolar interactions and the coefficients C6{C}_{6}C6​ and C8{C}_{8}C8​ of the second-order additive and nonadditive interactions. Both the dipolar and dispersion interaction coefficients, for these three-body degenerate systems, show dependences on the geometrical configurations of the three atoms. The nonadditive interactions start to appear in second-order. To demonstrate the results and for applications, the obtained coefficients Cn{C}_{n}Cn​ are evaluated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates for $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)$, $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, and $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}P)$. The calculations are given for three like nuclei for the cases of hypothetical infinite mass He nuclei, and of real finite mass 4He^{4}\mathrm{He}4He or 3He^{3}\mathrm{He}3He nuclei. The special cases of the three atoms in equilateral triangle configurations are explored in detail, and for the cases in which one of the atoms is in a PPP state, we also present results for the atoms in an isosceles right triangle configuration or in an equally spaced collinear configuration. The results can be applied to construct potential energy surfaces for three helium atom systems.
We calculate the energy shifts, in Rydberg states of helium, due to retardation corrections to the two-photon exchange potential. The correction to the level spacings is at the accuracy of existing measurements in the n=10n=10n=10 states of neutral He. It may soon be possible for the first time to detect the effect of these corrections in atomic systems. Estimates of the energy shifts for high-ZZZ He-like ions yield effects of several percent of the total spacing.
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