Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0603232 · Physical Review A

Long-range interactions for He(nS)–He(n′S) and He(nS)–He(n′P)

Junlang Zhang, Z.-C. Yan, D. Vrinceanu, J. F. Babb, H. R. Sadeghpour

Published Jul 26, 2006• 33 citations
arXivHTMLPDF

Abstract

For helium, long-range interaction coefficients ${C}_{3}$, ${C}_{6}$, ${C}_{8}$, ${C}_{9}$, and ${C}_{10}$ for all $S\text{\ensuremath{-}}S$ and $S\text{\ensuremath{-}}P$ pairs of the energetically lowest five states $(1\phantom{\rule{0.2em}{0ex}}^{1}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{3}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{1}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{3}P,$ and $2\phantom{\rule{0.2em}{0ex}}^{1}P)$ are calculated precisely using correlated wave functions in Hylleraas coordinates. Finite nuclear isotope mass effects are included.

DOI
10.1103/physreva.74.014704

Related papers

Long-range interactions between excited helium and alkali-metal atoms

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi +2 more

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5$%$. For interactions with other alkali-metal atoms the uncertainty is 1--3$%$ in the coefficient ${C}_{5}$, 1--5$%$ in the coefficient ${C}_{6}$, and 1--10$%$ in the coefficients ${C}_{8}$ and ${C}_{10}$. The dispersion coefficients ${C}_{n}$ for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$) with the ground-state alkali-metal atoms and for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) with the alkali-metal atoms in their first ${}^{2}$$P$ states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.

Physical Review A•Dec 3, 2012•10 citations

Calculations of long-range three-body interactions for He( n0λS )-He( n0λS )-He( n0′λL )

Pei-Gen Yan, Li-Yan Tang, Zong-Chao Yan +1 more

We theoretically investigate long-range interactions between an excited $L$-state He atom and two identical $S$-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 ${n}_{0}$ and ${n}_{0}^{\ensuremath{'}}$ principal quantum numbers, $\ensuremath{\lambda}=1$ or 3 the spin multiplicity, and $L$ the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients ${C}_{3}$ of the first-order dipolar interactions and the coefficients ${C}_{6}$ and ${C}_{8}$ 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 ${C}_{n}$ 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 $^{4}\mathrm{He}$ or $^{3}\mathrm{He}$ 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 $P$ 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.

arXiv:1712.07584•Physical Review A•Apr 23, 2018•3 citations

Long-range interactions between a He(2S3) atom and a He(2P3) atom for like isotopes

Junlang Zhang, Z.-C. Yan, D. Vrinceanu +2 more

For the interactions between a $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)$ atom and a $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ atom for like isotopes, we report perturbation theoretic calculations using accurate variational wave functions in Hylleraas coordinates of the coefficients determining the potential energies at large internuclear separations. We evaluate the coefficient ${C}_{3}$ of the first order resonant dipole-dipole energy and the van der Waals coefficients ${C}_{6}$, ${C}_{8}$, and ${C}_{10}$ for the second order energies arising from the mutual perturbations of instantaneous electric dipole, quadrupole, and octupole interactions. We also evaluate the leading contribution to the third-order energy. We establish definitive values including treatment of the finite nuclear mass for the $^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ and $^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ interactions.

arXiv:physics/0510232•Physical Review A•Feb 9, 2006•23 citations

Long-range interactions of metastable helium atoms

Zong-Chao Yan, J. F. Babb

The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic $n=2$ singlet and triplet states, respectively, $\mathrm{He}(2{}^{1}S)$ and $\mathrm{He}(2{}^{3}S)$. The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two $\mathrm{He}(2{}^{1}S)$ or two $\mathrm{He}(2{}^{3}S)$ atoms and for the atom-surface interaction potentials of a $\mathrm{He}(2{}^{1}S)$ or a $\mathrm{He}(2{}^{3}S)$ atom with a perfectly conducting or a dielectric wall.

arXiv:physics/9802054•Physical Review A•Aug 1, 1998•92 citations

Long range interaction of antiprotonic helium with helium

Quan-Long Tian, Zhen-Xiang Zhong, V. I. Korobov

We intent to report our study of dispersion coefficients as well as long range interaction between helium ground state and antiprotonic helium 3 He + and 4 He + states, ( n , ℓ = n –l). Sstatic polarizabilities of antiprotonic helium metal states are present as well.

Journal of Physics Conference Series•Apr 10, 2014•0 citations

Long-range interaction of Li(2S2)−Li(2S2)−Li+(1S1)

Pei-Gen Yan, Li-Yan Tang, Zong-Chao Yan +1 more

The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the ${\mathrm{Li}}^{+}$ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients ${C}_{n}$ in the potential energy for the three well-separated constituents, where $n$ refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients ${C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}$ and the nonadditive interaction coefficients ${C}_{7}, {C}_{9}$. The obtained coefficients ${C}_{n}$ are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$.

Physical Review A•Mar 16, 2020•3 citations
For helium, long-range interaction coefficients C3{C}_{3}C3​, C6{C}_{6}C6​, C8{C}_{8}C8​, C9{C}_{9}C9​, and C10{C}_{10}C10​ for all S\ensuremath-SS\text{\ensuremath{-}}SS\ensuremath-S and S\ensuremath-PS\text{\ensuremath{-}}PS\ensuremath-P pairs of the energetically lowest five states (11S,23S,21S,23P,(1\phantom{\rule{0.2em}{0ex}}^{1}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{3}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{1}S,\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}^{3}P,(11S,23S,21S,23P, and 21P)2\phantom{\rule{0.2em}{0ex}}^{1}P)21P) are calculated precisely using correlated wave functions in Hylleraas coordinates. Finite nuclear isotope mass effects are included.
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.
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.
For the interactions between a He(23S)\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)He(23S) atom and a He(23P)\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)He(23P) atom for like isotopes, we report perturbation theoretic calculations using accurate variational wave functions in Hylleraas coordinates of the coefficients determining the potential energies at large internuclear separations. We evaluate the coefficient C3{C}_{3}C3​ of the first order resonant dipole-dipole energy and the van der Waals coefficients C6{C}_{6}C6​, C8{C}_{8}C8​, and C10{C}_{10}C10​ for the second order energies arising from the mutual perturbations of instantaneous electric dipole, quadrupole, and octupole interactions. We also evaluate the leading contribution to the third-order energy. We establish definitive values including treatment of the finite nuclear mass for the $^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ and $^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ interactions.
The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic n=2n=2n=2 singlet and triplet states, respectively, He(21S)\mathrm{He}(2{}^{1}S)He(21S) and He(23S)\mathrm{He}(2{}^{3}S)He(23S). The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two He(21S)\mathrm{He}(2{}^{1}S)He(21S) or two He(23S)\mathrm{He}(2{}^{3}S)He(23S) atoms and for the atom-surface interaction potentials of a He(21S)\mathrm{He}(2{}^{1}S)He(21S) or a He(23S)\mathrm{He}(2{}^{3}S)He(23S) atom with a perfectly conducting or a dielectric wall.
The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the Li+{\mathrm{Li}}^{+}Li+ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients Cn{C}_{n}Cn​ in the potential energy for the three well-separated constituents, where nnn refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients C4,C6,C7,C8,C9{C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}C4​,C6​,C7​,C8​,C9​ and the nonadditive interaction coefficients C7,C9{C}_{7}, {C}_{9}C7​,C9​. The obtained coefficients Cn{C}_{n}Cn​ are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of 6Li^{6}\mathrm{Li}6Li and 7Li^{7}\mathrm{Li}7Li.