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

Physical Review A

Symmetric resonant charge transfer in H+ +H and He2+ +He collisions at extremely low energies

Masahiro Kimura, Neal F. Lane

Published Nov 1, 1986• 2 citations
Publisher

Abstract

Symmetric resonant charge transfer (RCT) in ${\mathrm{H}}^{+}$+H and ${\mathrm{He}}^{2+}$+He collisions has been investigated in the ultralow-collision-energy range ${10}^{\mathrm{\ensuremath{-}}3}$--${10}^{\mathrm{\ensuremath{-}}7}$ eV. The RCT cross section has been computed by partial-wave expansion in the molecular-orbital expansion method within the fully quantum-mechanical formalism. The calculated RCT cross sections become constant below E\ensuremath{\simeq}${10}^{\mathrm{\ensuremath{-}}6}$ eV, corresponding to a scattering length of \ensuremath{\sim}6${a}_{0}$ and \ensuremath{\sim}2${a}_{0}$ for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ and ${\mathrm{He}}_{2}$${\mathrm{}}^{2+}$, respectively.

DOI
10.1103/physreva.34.4421

Related papers

Resonances in Ca ++ Rb nonadiabatic collisions at ultralow energies

Andrey K. Belyaev, Svetlana A. Yakovleva, M. Tacconi +1 more

Nonadiabatic inelastic collision cross sections have been computed at low and ultralow energies, focusing in the present work on the Ca${}^{+}$$(4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)$ + Rb$(5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)$ $\ensuremath{\rightarrow}$ Ca$(4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}P)$ + Rb${}^{+}{(}^{1}\phantom{\rule{-0.16em}{0ex}}S)$ charge-exchange process at ultralow collision energies ($E$ $\ensuremath{\leqslant}$ 10${}^{\ensuremath{-}6}$ eV) induced by spin-orbit nonadiabatic coupling terms. The calculations reveal a wealth of sharp resonances which can substantially enhance charge-exchange probabilities over a specific energy window of around 10${}^{\ensuremath{-}6}$ to 10${}^{\ensuremath{-}8}$ eV. Such resonances are analyzed in detail, and the corresponding molecular mechanism is discussed for a specific example, where the nonadiabatic transition probabilities are seen to increase by nearly 2 orders of magnitude.

Physical Review A•Apr 23, 2012•18 citations

Elastic and charge-transfer collisions of He + –He at ultralow energies

Syham Lias, Fouzia Bouchelaghem, L. Aissaoui

Abstract Elastic, momentum-transfer (diffusion), and non-radiative charge-transfer cross sections are calculated for collisions between ground-state He + ( 2 S) ions and neutral He( 1 S) atoms over an energy range spanning fourteen orders of magnitude, from 10 −12 to 1 atomic unit. In this ultralow-energy regime, quantum mechanical effects dominate and the indistinguishability of helium nuclei necessitates a rigorous treatment of exchange symmetry. Phase shifts are computed using highly accurate ab initio potential energy curves for the X 2 Σ u and A 2 Σ g molecular states. The resulting elastic σ el , diffusion σ d , and charge-transfer σ ct cross sections reveal three distinct regimes: at energies below 10 −9 a.u., cross sections exceed 10 5 a 0 2 and are dominated by long-range polarization forces; in the intermediate range (10 −8 –10 −4 a.u.), pronounced quantum interference structures appear; at higher energies, results converge to semiclassical E −1/3 behavior. The data provide benchmark cross sections for ultracold ion–atom collision modeling relevant to cold-ion physics and hybrid atom–ion trapping experiments.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 15, 2026•1 citation

Scattering of Yb and Yb+

Peng Zhang, A. Dalgarno, Robin Côté

We calculate the cross sections for scattering of a neutral ytterbium atom with its positive ion at energies up to 30 eV. We identify peaks in the forward direction as arising from elastic collisions and those in the backward direction as from charge transfer. We show that the total cross section follows a semiclassical expression over a large range of energies and that the resonant charge transfer may be characterized by four energy regimes: an $s$-wave regime at ultralow energies, a modified Langevin regime at low energy, a Langevin regime at medium energy, and an ``exchange'' regime at high energy. We find large variations between the different isotopes for the two lowest-energy regimes and very little variation for the two highest-energy regimes. Our results are consistent with recent measurements.

Physical Review A•Sep 28, 2009•56 citations

Charge transfer and association of Na + with 87 Rb atoms from extremely low to intermediate energies

Lisong Yan, L. Liu, Yong Wu +3 more

The nonradiative charge-transfer processes in Na${}^{+}$+${}^{87}$Rb(5$s$) collisions have been investigated by using the quantum-mechanical molecular-orbital close-coupling method and the two-center atomic-orbital close-coupling method for the energy range of 10${}^{\ensuremath{-}4}$--5 and 0.3--100 keV/u, respectively. The radiative charge-transfer, radiative-decay, and radiative-association processes have been investigated by using the fully quantum, optical-potential, and semiclassical methods for the energy range of 10${}^{\ensuremath{-}18}$--0.2 eV/u. The nonradiative charge-transfer processes dominate the collisions for energies above 0.2 eV/u and radiative-decay processes dominate in the lower-energy region. At the very low collision energies of 10${}^{\ensuremath{-}18}$--10${}^{\ensuremath{-}3}$ eV/u, the radiative-association process is more important than the radiative charge-transfer process. Most importantly, it is found that the radiative cross sections exhibit Langevin behavior as ${E}^{\ensuremath{-}1/2}$ for energies less than 10${}^{\ensuremath{-}2}$ eV/u.

Physical Review A•Jul 18, 2013•11 citations

Ultracold atom-ion collisions

Robin Côté, A. Dalgarno

Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for $\mathrm{Na}+{\mathrm{Na}}^{+}$ have been carried out with the best available ${}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and ${}^{2}{\ensuremath{\Sigma}}_{u}^{+}$ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.

Physical Review A•Jun 14, 2000•218 citations

Ultra-cold ion–atom collisions: near resonant charge exchange

Enrico Bodo, P Zhang, A. Dalgarno

Accurate calculations of the near resonant charge exchange cross-sections in HD + , HT + and DT + at very low energies are presented. The charge exchange process between an ion and its parent atom is a near resonant process that becomes inelastic when two different isotopes are involved. We find that, at very low energies, the charge exchange cross-section follows Wigner's law for inelastic processes and becomes much larger than the cross-section for elastic collisions which tends to a finite limit. The efficiency of inelastic charge exchange increases as the mass difference between the two isotopes decreases.

New Journal of Physics•Mar 17, 2008•45 citations
Symmetric resonant charge transfer (RCT) in H+{\mathrm{H}}^{+}H++H and He2+{\mathrm{He}}^{2+}He2++He collisions has been investigated in the ultralow-collision-energy range 10\ensuremath−3{10}^{\mathrm{\ensuremath{-}}3}10\ensuremath−3--10\ensuremath−7{10}^{\mathrm{\ensuremath{-}}7}10\ensuremath−7 eV. The RCT cross section has been computed by partial-wave expansion in the molecular-orbital expansion method within the fully quantum-mechanical formalism. The calculated RCT cross sections become constant below E\ensuremath{\simeq}10\ensuremath−6{10}^{\mathrm{\ensuremath{-}}6}10\ensuremath−6 eV, corresponding to a scattering length of \ensuremath{\sim}6a0{a}_{0}a0​ and \ensuremath{\sim}2a0{a}_{0}a0​ for {\mathrm{H}}_{2}$${\mathrm{}}^{+} and {\mathrm{He}}_{2}$${\mathrm{}}^{2+}, respectively.
Nonadiabatic inelastic collision cross sections have been computed at low and ultralow energies, focusing in the present work on the Ca+{}^{+}+(4s2S)(4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)(4s2S) + Rb(5s2S)(5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)(5s2S) $\ensuremath{\rightarrow}$ Ca(4s4p3P)(4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}P)(4s4p3P) + Rb+(1S){}^{+}{(}^{1}\phantom{\rule{-0.16em}{0ex}}S)+(1S) charge-exchange process at ultralow collision energies (EEE $\ensuremath{\leqslant}$ 10${}^{\ensuremath{-}6}$ eV) induced by spin-orbit nonadiabatic coupling terms. The calculations reveal a wealth of sharp resonances which can substantially enhance charge-exchange probabilities over a specific energy window of around 10${}^{\ensuremath{-}6}$ to 10${}^{\ensuremath{-}8}$ eV. Such resonances are analyzed in detail, and the corresponding molecular mechanism is discussed for a specific example, where the nonadiabatic transition probabilities are seen to increase by nearly 2 orders of magnitude.
Abstract Elastic, momentum-transfer (diffusion), and non-radiative charge-transfer cross sections are calculated for collisions between ground-state He + ( 2 S) ions and neutral He( 1 S) atoms over an energy range spanning fourteen orders of magnitude, from 10 −12 to 1 atomic unit. In this ultralow-energy regime, quantum mechanical effects dominate and the indistinguishability of helium nuclei necessitates a rigorous treatment of exchange symmetry. Phase shifts are computed using highly accurate ab initio potential energy curves for the X 2 Σ u and A 2 Σ g molecular states. The resulting elastic σ el , diffusion σ d , and charge-transfer σ ct cross sections reveal three distinct regimes: at energies below 10 −9 a.u., cross sections exceed 10 5 a 0 2 and are dominated by long-range polarization forces; in the intermediate range (10 −8 –10 −4 a.u.), pronounced quantum interference structures appear; at higher energies, results converge to semiclassical E −1/3 behavior. The data provide benchmark cross sections for ultracold ion–atom collision modeling relevant to cold-ion physics and hybrid atom–ion trapping experiments.
We calculate the cross sections for scattering of a neutral ytterbium atom with its positive ion at energies up to 30 eV. We identify peaks in the forward direction as arising from elastic collisions and those in the backward direction as from charge transfer. We show that the total cross section follows a semiclassical expression over a large range of energies and that the resonant charge transfer may be characterized by four energy regimes: an sss-wave regime at ultralow energies, a modified Langevin regime at low energy, a Langevin regime at medium energy, and an ``exchange'' regime at high energy. We find large variations between the different isotopes for the two lowest-energy regimes and very little variation for the two highest-energy regimes. Our results are consistent with recent measurements.
The nonradiative charge-transfer processes in Na+{}^{+}++87{}^{87}87Rb(5sss) collisions have been investigated by using the quantum-mechanical molecular-orbital close-coupling method and the two-center atomic-orbital close-coupling method for the energy range of 10${}^{\ensuremath{-}4}$--5 and 0.3--100 keV/u, respectively. The radiative charge-transfer, radiative-decay, and radiative-association processes have been investigated by using the fully quantum, optical-potential, and semiclassical methods for the energy range of 10${}^{\ensuremath{-}18}$--0.2 eV/u. The nonradiative charge-transfer processes dominate the collisions for energies above 0.2 eV/u and radiative-decay processes dominate in the lower-energy region. At the very low collision energies of 10${}^{\ensuremath{-}18}$--10${}^{\ensuremath{-}3}$ eV/u, the radiative-association process is more important than the radiative charge-transfer process. Most importantly, it is found that the radiative cross sections exhibit Langevin behavior as ${E}^{\ensuremath{-}1/2}$ for energies less than 10${}^{\ensuremath{-}2}$ eV/u.
Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for Na+Na+\mathrm{Na}+{\mathrm{Na}}^{+}Na+Na+ have been carried out with the best available ${}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and ${}^{2}{\ensuremath{\Sigma}}_{u}^{+}$ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.
Accurate calculations of the near resonant charge exchange cross-sections in HD + , HT + and DT + at very low energies are presented. The charge exchange process between an ion and its parent atom is a near resonant process that becomes inelastic when two different isotopes are involved. We find that, at very low energies, the charge exchange cross-section follows Wigner's law for inelastic processes and becomes much larger than the cross-section for elastic collisions which tends to a finite limit. The efficiency of inelastic charge exchange increases as the mass difference between the two isotopes decreases.