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

Ultracold inelastic atomic collisions: Threshold relaxation of O(^{3}P_{0}) by He

Roman V. Krems, Alexei A. Buchachenko

Published Jul 1, 2001• 9 citations
Publisher

Abstract

Relaxation of $\mathrm{O}{(}^{3}{P}_{j=0})$ by collisions with He at ultracold temperatures is investigated, and it is illustrated that cross sections and rate constants for the $j=\stackrel{\ensuremath{\rightarrow}}{0}j=2$ and $j=\stackrel{\ensuremath{\rightarrow}}{0}j=1$ transitions exhibit qualitatively different threshold behaviors stemming from the different mechanisms of these nonadiabatic transitions. The results allow us to make the conclusion that, in general, rate constants for the nonadiabatic transitions governed by electrostatic couplings should obey Wigner's threshold law for s-wave scattering approaching a finite value at $\stackrel{\ensuremath{\rightarrow}}{T}0\mathrm{K},$ while cross sections and rate constants for the transitions determined by Coriolis couplings should vanish in the zero-temperature limit.

DOI
10.1103/physreva.64.024704

Related papers

Rotational relaxation in ultracold He+BH collisions

Ming-Yan Gong, Xiaotao Xu, Eryin Feng

Collisions of cold and ultracold BH in the ν = 0 level with the He atom are investigated using the quantum mechanical scattering formulation. The elastic and the inelastic cross sections are calculated using the two-dimensional ab initio potential energy surface. It is shown that the elastic cross section is larger than the inelastic one. When the collision energy is very low, the elastic cross section follows the Wigner threshold law and is one order of magnitude larger than that of He-O 2 , while it is much smaller than that of He-H 2 . The efficiency of the rotationally quenching state is given. The Δ j = −1 transition is most efficient. The resonances are also found to occur at about the same translational energy (0.1–1 cm −1 ), which gives rise to steps in the rate coefficient at temperatures around 0.1–1 K.

Chinese Physics B•Nov 1, 2011•1 citation

Quenching of H2 Vibrations in Ultracold 3He and 4He Collisions

N. Balakrishnan, Robert C. Forrey, A. Dalgarno

We present results of quantum mechanical scattering calculations including full rovibrational coupling on the relaxation of vibrationally excited ${\mathrm{H}}_{2}$ molecules in collision with ultracold ${}^{3}\mathrm{He}$ and ${}^{4}\mathrm{He}$ atoms. The exothermic vibrational deactivation cross sections exhibit minima at translational temperatures near 10 K and show an inverse velocity dependence in accordance with Wigner's threshold law in the limit of zero kinetic energy. The corresponding rate coefficients exhibit minima before attaining constant values below ${10}^{\ensuremath{-}3}$ K. The rate coefficients increase by 3 orders of magnitude when the initial vibrational level of the molecule is raised from $v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ to $v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$. The results suggest that quasibound resonance states of ${}^{3}{\mathrm{HeH}}_{2}$ and ${}^{4}{\mathrm{HeH}}_{2}$ exist, associated with each excited vibrational state of ${\mathrm{H}}_{2}$, and that both the triatomic species ${}^{3}{\mathrm{HeH}}_{2}$ and ${}^{4}{\mathrm{HeH}}_{2}$ have one bound vibrational state.

Physical Review Letters•Apr 13, 1998•166 citations

Disalignment transitions in cold collisions of 3P atoms with structureless targets in a magnetic field

Roman V. Krems, A. Dalgarno

A method for quantum-mechanical calculations of cross sections for the Zeeman transitions in collisions of ${}^{3}P$ atoms with structureless targets in a magnetic field is presented and applied to the study of magnetic and electronic relaxation in oxygen-helium and carbon-helium collisions at cold and ultracold temperatures. The rate constants for collisionally induced transitions between Zeeman levels in ground-state oxygen have large magnitudes in a 1 T field. It is shown that magnetic fields induce the forbidden ${}^{3}{P}_{1}$ $\ensuremath{\rightarrow}$ ${}^{3}{P}_{0}$ transition in ultracold collisions of carbon with helium. The cross section vanishes at zero energy for field-free collisions, but becomes infinitely large in a finite magnetic field, varying with velocity $v$ and magnetic field B as ${B}^{2}/v.$

Physical Review A•Jul 11, 2003•36 citations

Cold and ultracold ion-neutral inelastic collisions: Spin–orbit relaxation in He+Ne+

Peter E. Siska

Electronic close-coupling scattering calculations are reported on the relaxation process Ne+(2p5 2Pj1=1/2,m1)+He→Ne+(2p5 2Pj2=3/2,m2)+He using a new interaction potential derived by combining spectroscopy and ab initio theory. Collision energies range from E/kB=300 K to less than 1 μK. As E is reduced, the total inelastic cross section σj1→j2=σ1/2→3/2 passes through a resonance-dominated regime and apparently approaches the Wigner limit below 10 μK, where the cross section is found to diverge in accord with the predicted E−1/2 dependence. A complex scattering length a=−53.0−0.04145i Å is derived from the low-energy behavior. m-dependent alignment and orientation cross sections, σj1|m1|→j2|m2| and σj1m1→j2m2, undergo rapid changes near resonances, and approach limiting behavior below 10 μK as well, while their ratios become asymptotically constant below 100 μK. Analysis of the scattering amplitude in the s-wave limit shows that the latter behavior is expected in general, with the ratios depending only on the geometry of angular momentum coupling. This geometrical effect disentangles s-wave dominance from the Wigner regime, and provides a new criterion for assessing the approach to the ultracold limit. Boltzmann averaging to simulate ultracold trapping conditions shows that a remnant of the resonance region and the characteristic limiting behavior remain observable.

The Journal of Chemical Physics•Sep 8, 2001•12 citations

Near-threshold scaling of resonant inelastic collisions at ultralow temperatures

Rebekah Hermsmeier, Adrien Devolder, Paul W. Brumer +1 more

We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, F\"orster resonance, or angular momentum exchange) exhibit a near-threshold scaling ${E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}}$, where $E$ is the collision energy, $\mathrm{\ensuremath{\Delta}}{m}_{12}={m}_{1}^{\ensuremath{'}}+{m}_{2}^{\ensuremath{'}}\ensuremath{-}{m}_{1}\ensuremath{-}{m}_{2}$, and ${m}_{i}$ and ${m}_{i}^{\ensuremath{'}}$ are the initial and final angular momentum projections of the colliding species ($i=1,2$). In particular, the inelastic cross sections for $\mathrm{\ensuremath{\Delta}}{m}_{12}=0$ transitions display an unconventional ${E}^{0}$ scaling similar to that of elastic cross sections, and their rates vanish as ${T}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\ensuremath{\sigma}}_{\text{inel}}\ensuremath{\propto}{E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1}$ if $\mathrm{\ensuremath{\Delta}}{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold $\text{Rb}+\text{Rb}$ and ${\mathrm{O}}_{2}+{\mathrm{O}}_{2}$ collisions. Our results illustrate that the well-known ${k}^{\ensuremath{-}1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.

arXiv:2105.11995•Physical Review A•Jan 14, 2022•3 citations

Ultracold homonuclear and heteronuclear collisions in metastable helium

Daniel Cocks, Ian B. Whittingham, G. Peach

Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic $^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ and fermionic $^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}$ systems, and heteronuclear collisions of the mixed $^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}$ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.

arXiv:1904.01281•Physical Review A•Jun 28, 2019•4 citations
Relaxation of O(3Pj=0)\mathrm{O}{(}^{3}{P}_{j=0})O(3Pj=0​) by collisions with He at ultracold temperatures is investigated, and it is illustrated that cross sections and rate constants for the j=0\ensuremath→j=2j=\stackrel{\ensuremath{\rightarrow}}{0}j=2j=0\ensuremath→​j=2 and j=0\ensuremath→j=1j=\stackrel{\ensuremath{\rightarrow}}{0}j=1j=0\ensuremath→​j=1 transitions exhibit qualitatively different threshold behaviors stemming from the different mechanisms of these nonadiabatic transitions. The results allow us to make the conclusion that, in general, rate constants for the nonadiabatic transitions governed by electrostatic couplings should obey Wigner's threshold law for s-wave scattering approaching a finite value at T\ensuremath→0K,\stackrel{\ensuremath{\rightarrow}}{T}0\mathrm{K},T\ensuremath→​0K, while cross sections and rate constants for the transitions determined by Coriolis couplings should vanish in the zero-temperature limit.
Collisions of cold and ultracold BH in the ν = 0 level with the He atom are investigated using the quantum mechanical scattering formulation. The elastic and the inelastic cross sections are calculated using the two-dimensional ab initio potential energy surface. It is shown that the elastic cross section is larger than the inelastic one. When the collision energy is very low, the elastic cross section follows the Wigner threshold law and is one order of magnitude larger than that of He-O 2 , while it is much smaller than that of He-H 2 . The efficiency of the rotationally quenching state is given. The Δ j = −1 transition is most efficient. The resonances are also found to occur at about the same translational energy (0.1–1 cm −1 ), which gives rise to steps in the rate coefficient at temperatures around 0.1–1 K.
We present results of quantum mechanical scattering calculations including full rovibrational coupling on the relaxation of vibrationally excited H2{\mathrm{H}}_{2}H2​ molecules in collision with ultracold 3He{}^{3}\mathrm{He}3He and 4He{}^{4}\mathrm{He}4He atoms. The exothermic vibrational deactivation cross sections exhibit minima at translational temperatures near 10 K and show an inverse velocity dependence in accordance with Wigner's threshold law in the limit of zero kinetic energy. The corresponding rate coefficients exhibit minima before attaining constant values below ${10}^{\ensuremath{-}3}$ K. The rate coefficients increase by 3 orders of magnitude when the initial vibrational level of the molecule is raised from v=1v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1v=1 to v=10v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10v=10. The results suggest that quasibound resonance states of 3HeH2{}^{3}{\mathrm{HeH}}_{2}3HeH2​ and 4HeH2{}^{4}{\mathrm{HeH}}_{2}4HeH2​ exist, associated with each excited vibrational state of H2{\mathrm{H}}_{2}H2​, and that both the triatomic species 3HeH2{}^{3}{\mathrm{HeH}}_{2}3HeH2​ and 4HeH2{}^{4}{\mathrm{HeH}}_{2}4HeH2​ have one bound vibrational state.
A method for quantum-mechanical calculations of cross sections for the Zeeman transitions in collisions of 3P{}^{3}P3P atoms with structureless targets in a magnetic field is presented and applied to the study of magnetic and electronic relaxation in oxygen-helium and carbon-helium collisions at cold and ultracold temperatures. The rate constants for collisionally induced transitions between Zeeman levels in ground-state oxygen have large magnitudes in a 1 T field. It is shown that magnetic fields induce the forbidden 3P1{}^{3}{P}_{1}3P1​ $\ensuremath{\rightarrow}$ 3P0{}^{3}{P}_{0}3P0​ transition in ultracold collisions of carbon with helium. The cross section vanishes at zero energy for field-free collisions, but becomes infinitely large in a finite magnetic field, varying with velocity vvv and magnetic field B as B2/v.{B}^{2}/v.B2/v.
Electronic close-coupling scattering calculations are reported on the relaxation process Ne+(2p5 2Pj1=1/2,m1)+He→Ne+(2p5 2Pj2=3/2,m2)+He using a new interaction potential derived by combining spectroscopy and ab initio theory. Collision energies range from E/kB=300 K to less than 1 μK. As E is reduced, the total inelastic cross section σj1→j2=σ1/2→3/2 passes through a resonance-dominated regime and apparently approaches the Wigner limit below 10 μK, where the cross section is found to diverge in accord with the predicted E−1/2 dependence. A complex scattering length a=−53.0−0.04145i Å is derived from the low-energy behavior. m-dependent alignment and orientation cross sections, σj1|m1|→j2|m2| and σj1m1→j2m2, undergo rapid changes near resonances, and approach limiting behavior below 10 μK as well, while their ratios become asymptotically constant below 100 μK. Analysis of the scattering amplitude in the s-wave limit shows that the latter behavior is expected in general, with the ratios depending only on the geometry of angular momentum coupling. This geometrical effect disentangles s-wave dominance from the Wigner regime, and provides a new criterion for assessing the approach to the ultracold limit. Boltzmann averaging to simulate ultracold trapping conditions shows that a remnant of the resonance region and the characteristic limiting behavior remain observable.
We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, F\"orster resonance, or angular momentum exchange) exhibit a near-threshold scaling ${E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}}$, where EEE is the collision energy, $\mathrm{\ensuremath{\Delta}}{m}_{12}={m}_{1}^{\ensuremath{'}}+{m}_{2}^{\ensuremath{'}}\ensuremath{-}{m}_{1}\ensuremath{-}{m}_{2}$, and mi{m}_{i}mi​ and ${m}_{i}^{\ensuremath{'}}$ are the initial and final angular momentum projections of the colliding species (i=1,2i=1,2i=1,2). In particular, the inelastic cross sections for $\mathrm{\ensuremath{\Delta}}{m}_{12}=0$ transitions display an unconventional E0{E}^{0}E0 scaling similar to that of elastic cross sections, and their rates vanish as ${T}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\ensuremath{\sigma}}_{\text{inel}}\ensuremath{\propto}{E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1}$ if $\mathrm{\ensuremath{\Delta}}{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold Rb+Rb\text{Rb}+\text{Rb}Rb+Rb and O2+O2{\mathrm{O}}_{2}+{\mathrm{O}}_{2}O2​+O2​ collisions. Our results illustrate that the well-known ${k}^{\ensuremath{-}1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.
Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic 4He∗+4He∗^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}4He∗+4He∗ and fermionic 3He∗+3He∗^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}3He∗+3He∗ systems, and heteronuclear collisions of the mixed 3He∗+4He∗^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}3He∗+4He∗ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.