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The Journal of Chemical Physics

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

Peter E. Siska

Published Sep 8, 2001• 12 citations
Publisher

Abstract

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.

DOI
10.1063/1.1394938

Related papers

When experiment challenges theory: Scattering of vibrationally excited molecules in the cold collision energy regime

F. Javier Aoiz

The last decade has seen substantial advances in the exploration of inelastic and reactive collisions at collision energies in the cold ( < $<$ 1 K) and ultracold ( < 1 $<1$ mK) regime.1-13 These advances ushered in an understanding of cold and ultracold collisions that is impacting research areas ranging from molecular spectroscopy to quantum simulation and computation to quantum control of chemical reaction dynamics. Cold collisions are dominated by resonances, as amply manifest in most of the systems studied.1, 14 Resonances are also present in the thermal ( > $>$ 100 K) and hyperthermal ( > $>$ 1000 K) collision energy regimes,15 but obscured by background (non-resonant) scattering and the presence of many partial waves pertaining to higher angular momenta that blur the partial waves' individual contributions. Moreover, the outcome of thermal and hyperthermal collisions is somewhat insensitive to the details of the interaction potential – the potential energy surface (PES) – especially to its attractive long-range region. Only in a handful of cases, such as the F+HD exchange reaction, resonances in the thermal regime have been experimentally detected and theoretically accounted for by quantum mechanical scattering calculations.16, 17 In contrast, in the cold regime, collisions are dominated by only a few partial waves whose effects on the integral and differential scattering cross-sections can be singled out and linked to particular resonances. The cold collision energy regime has been attained by making use of crossed molecular beams that were either Stark- or Zeeman-decelerated or whose intersection angle could be reduced all the way down to the merging-beams limit. A beam emerging from a Stark or Zeeman decelerator has a variable, well-defined laboratory velocity. When crossed with a secondary beam at small angles (5 ∘ $^{\circ }$ –10 ∘ $^{\circ }$ ), collision energies in the 0.3–15 K could be readily achieved, as demonstrated by the group of van de Meerakker.9, 11 The technique of merged beams makes use of the ability to bend one of the beams by a magnetic or electric field such that the crossing angle becomes zero, thereby affording collision energies in the range 0.1 K–10 K. Merging beams have been used in studies of Penning ionization by the groups of Narevicius5, 12 and Osterwalder18 and made it possible to unravel shape and Feshbach resonances arising in this process. The techniques mentioned so far require the reactants to be polar or paramagnetic. For reactants that are neither, collision energies as low as 5 K could be achieved by taking advantage of a favorable combination of low intersection angles and low reduced mass of the reactants. This approach has been demonstrated by Bergeat, Costes, Naulin, and coworkers in a series of reactive3, 19 and inelastic collision experiments8, 20 of H 2 $_2$ . Yet, another approach to achieving low relative collision velocities relies on the coexpansion of the collision partners in a single molecular beam.21 If their masses are similar, both partners will end up with nearly the same velocities, within a few ms − 1 $^{-1}$ . Using this technique, Zare, Mukherjee, and coworkers carried out a series of experiments in which rotational quenching of HD by H 2 $_2$ , D 2 $_2$ , and He was investigated. Moreover, in these experiments, the HD molecule was prepared in v $v$ =1 and j $j$ =2 using Stark-field-induced adiabatic Raman passage that allowed, in addition, to align the rotational angular momentum of the HD reactant molecule with respect to the initial relative velocity of the HD + He reactants.22-24 Collisional energy transfer between rotation and translation, in which a molecule is excited or relaxed via scattering by an atom or another molecule, has been of particular significance for developing our understanding of inelastic collisions. Most notably, the scattering of NO molecules by rare gas (Rg) atoms has served as a benchmark system for both experimentalists and theorists for decades. In its ground electronic state, NO is a 2 Π $^2\Pi$ molecule with a single unpaired electron in an antibonding π ∗ $\pi ^*$ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω | $|\Omega |$ ( = 1 2 $=\frac{1}{2}$ or 3 2 $\frac{3}{2}$ ) of the electronic angular momentum (orbital and spin) on the internuclear axis. The rotational levels with the same j $j$ in the two manifolds are separated by approximately 123 cm − 1 $^{-1}$ for v $v$ =0 (117 cm − 1 $^{-1}$ for v $v$ =10). In addition, each rotational level within each manifold is further split into two Λ $\Lambda$ -doublet states ( ε = ± 1 $\epsilon = \pm 1$ , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2 $p = (-1)^{j-\epsilon /2}$ . As the Rg atom approaches the NO molecule, the degeneracy of the Λ $\Lambda$ doublets is lifted, giving rise to two PESs, A ′ $A^{\prime }$ and A ′ ′ $A^{\prime \prime }$ , in which the orbital of the unpaired electron lies, respectively, in the plane of the three atoms or perpendicular to it. In computational practice, it is more convenient to use linear combinations (sums and differences) of the A ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ PESs. Using hexapole focusing or Stark deceleration combined with detection via velocity ion imaging, fully state-to-state-resolved integral and differential cross sections for rotationally elastic and inelastic collisions could be measured with high resolution.9, 11, 25, 26 More than that, the orientation and alignment of the scattered (outgoing) NO molecules could be measured as a function of the scattering angle27-30 and, quite recently, the effects of orientation of the reactant (incoming) NO molecules on the differential cross section in collisions with Rg, mostly Ar, could be established.31-35 On the theory side, quantum mechanical close coupling (QMCC) scattering calculations on accurate two-dimensional ab initio PESs using the benchmark coupled-cluster, CCSD(T), method with the NO internuclear distance fixed at its equilibrium value36 were performed and found to account for all the details revealed by the experiments. Although state of the art, most of these experiments except for those described in Refs. 9, 11 were carried out at thermal energies for NO molecules in their lowest level, | v = 0 , j = 1 2 , Ω = 1 2 , f ⟩ $|v=0, j=\frac{1}{2}, \Omega =\frac{1}{2}, f\rangle$ . Scattering of highly vibrationally excited molecules in the cold energy regime remained an unexplored frontier until the recent work by the groups of Arthur Suits, Ad van der Avoird, Gerrit Groenenboom, and Hua Guo who added spin–orbit and rotational state selection and looked for spin- and rotational-state changing collisions to boot. Published in the current issue of Natural Sciences,37 this work is a culmination of a 3-year collaboration that included both implementation of new experimental techniques and boosting of theoretical methods. Working with the NO+Ar system, the authors made use of stimulated emission pumping via the electronically excited A 2 Σ + $A^2\Sigma ^+$ state to promote NO( 2 Π 1 2 $^2\Pi _{\frac{1}{2}}$ ) molecules to the vibrationally excited state with v = 10 $v=10$ and a selected spin–orbit state | Ω | $|\Omega |$ and rotational state j $j$ , | v = 10 , j , Ω , f ⟩ $|v=10, j,\Omega , f\rangle$ .38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘ $^{\circ }$ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′ $^{\prime }$ REMPI with the ionization laser tuned just above the ionization threshold. Fully state-resolved angular distributions of the scattered NO molecules were measured by velocity ion slice imaging and detected by a charge-coupled device (CCD). In order to be able to detect the product (outgoing) molecules resulting from the cold NO + Ar collisions, some excess energy had to be made available to the products. This came in the form of the initial spin–orbit and/or rotational state energy. In the study highlighted herein,37 angular distributions leading to the spin–orbit changing transition | v = 10 , Ω = 3 2 , j = 3 2 f ⟩ → | v ′ = 10 , Ω ′ = 1 2 , j ′ = 9 2 , e ⟩ $|v=10, \Omega =\frac{3}{2}, j=\frac{3}{2} f\rangle \rightarrow |v^{\prime }=10, \Omega ^{\prime }=\frac{1}{2}, j^{\prime }=\frac{9}{2}, e \rangle$ were measured at energies in the 2 K–5 K range. Although intrabeam scattering could have been used as an alternative as it had been in previous work,21 the authors demonstrated that a dual-beam setup provides a superior angular and energy resolution. The highlighted experiment challenged the existing theoretical treatments of the NO+ Rg systems: first, the approximation of fixing NO at its equilibrium distance was bound to fail for NO in v = 10 $v=10$ due to the concomitant elongation of the NO bond. Second, for such a highly excited vibrational state, both the long- and short-range interactions are affected, triggering nonadiabatic effects involving rotational and spin–orbit degrees of freedom. The above rendered the single-reference coupled-cluster method used in previous treatments of NO( 2 Π 1 2 , v = 0 $^2\Pi _{\frac{1}{2}},v=0$ ) inadequate. Therefore, the authors of the highlighted paper37 constructed a new coupled-cluster PES as well as a multireference configuration-interaction (MRCI) PES and carried out full-fledged (3D) QMCC calculations on both PESs. These tour-de-force calculations reproduced quite well the experimental differential cross sections and defined a new state of the art in scattering calculations. However, some discrepancies remain as at low collision energies, and the accuracy of the long-range potential needed is a challenge for any ab initio method. Moreover, treating spin-changing collisions that are dominated by the essentially attractive difference potential, V A ′ ′ − V A ′ $V_{A^{\prime \prime }}-V_{A^{\prime }}$ , puts additional demands on the accuracy of the A ′ ′ $A^{\prime \prime }$ and A ′ $A^{\prime }$ PESs. The calculated integral cross section in the 3–4 cm − 1 $^{-1}$ energy interval exhibits a bump that may indicate the presence of resonances that show up as backscattering in the measured differential cross section. A partial-wave analysis points to overlapping resonances associated with contributions from several of the highest partial waves involved. In any case, tracing the resonances may require additional improvements of the existing PESs. All in all, the highlighted combined experimental and theoretical study sets a new standard for our understanding of cold collisions. There is no conflict of interest. The peer review history for this article is available at https://publons.com/publon/10.1002/ntls.20210088. This Highlight has been internally reviewed and edited by Bretislav Friedrich and Gerard Meijer. No data available.

Natural Sciences•Nov 11, 2021•0 citations

Cold magnetically trapped 2Dg scandium atoms. II. Scattering dynamics

Tijs Karman, Gerrit C. Groenenboom

The binary collision dynamics of ${}^{2}{D}_{g,3/2}$ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.

Physical Review A•Nov 5, 2014•6 citations

Cold and ultracold NH–NH collisions: The field-free case

Liesbeth M. C. Janssen, Piotr Szymon Żuchowski, Ad van der Avoird +2 more

We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.

arXiv:1012.0804•The Journal of Chemical Physics•Mar 28, 2011•25 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

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

Spin-Orbit Interactions and Quantum Spin Dynamics in Cold Ion-Atom Collisions

Timur V. Tscherbul, Paul W. Brumer, Alexei A. Buchachenko

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.

arXiv:1511.08237•Physical Review Letters•Sep 27, 2016•28 citations
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 last decade has seen substantial advances in the exploration of inelastic and reactive collisions at collision energies in the cold ( < <<< 1 K) and ultracold ( < 1 <1<1<1 mK) regime.1-13 These advances ushered in an understanding of cold and ultracold collisions that is impacting research areas ranging from molecular spectroscopy to quantum simulation and computation to quantum control of chemical reaction dynamics. Cold collisions are dominated by resonances, as amply manifest in most of the systems studied.1, 14 Resonances are also present in the thermal ( > >>> 100 K) and hyperthermal ( > >>> 1000 K) collision energy regimes,15 but obscured by background (non-resonant) scattering and the presence of many partial waves pertaining to higher angular momenta that blur the partial waves' individual contributions. Moreover, the outcome of thermal and hyperthermal collisions is somewhat insensitive to the details of the interaction potential – the potential energy surface (PES) – especially to its attractive long-range region. Only in a handful of cases, such as the F+HD exchange reaction, resonances in the thermal regime have been experimentally detected and theoretically accounted for by quantum mechanical scattering calculations.16, 17 In contrast, in the cold regime, collisions are dominated by only a few partial waves whose effects on the integral and differential scattering cross-sections can be singled out and linked to particular resonances. The cold collision energy regime has been attained by making use of crossed molecular beams that were either Stark- or Zeeman-decelerated or whose intersection angle could be reduced all the way down to the merging-beams limit. A beam emerging from a Stark or Zeeman decelerator has a variable, well-defined laboratory velocity. When crossed with a secondary beam at small angles (5 ∘ ∘^{\circ }∘ –10 ∘ ∘^{\circ }∘ ), collision energies in the 0.3–15 K could be readily achieved, as demonstrated by the group of van de Meerakker.9, 11 The technique of merged beams makes use of the ability to bend one of the beams by a magnetic or electric field such that the crossing angle becomes zero, thereby affording collision energies in the range 0.1 K–10 K. Merging beams have been used in studies of Penning ionization by the groups of Narevicius5, 12 and Osterwalder18 and made it possible to unravel shape and Feshbach resonances arising in this process. The techniques mentioned so far require the reactants to be polar or paramagnetic. For reactants that are neither, collision energies as low as 5 K could be achieved by taking advantage of a favorable combination of low intersection angles and low reduced mass of the reactants. This approach has been demonstrated by Bergeat, Costes, Naulin, and coworkers in a series of reactive3, 19 and inelastic collision experiments8, 20 of H 2 2_22​ . Yet, another approach to achieving low relative collision velocities relies on the coexpansion of the collision partners in a single molecular beam.21 If their masses are similar, both partners will end up with nearly the same velocities, within a few ms − 1 −1^{-1}−1 . Using this technique, Zare, Mukherjee, and coworkers carried out a series of experiments in which rotational quenching of HD by H 2 2_22​ , D 2 2_22​ , and He was investigated. Moreover, in these experiments, the HD molecule was prepared in v vvv =1 and j jjj =2 using Stark-field-induced adiabatic Raman passage that allowed, in addition, to align the rotational angular momentum of the HD reactant molecule with respect to the initial relative velocity of the HD + He reactants.22-24 Collisional energy transfer between rotation and translation, in which a molecule is excited or relaxed via scattering by an atom or another molecule, has been of particular significance for developing our understanding of inelastic collisions. Most notably, the scattering of NO molecules by rare gas (Rg) atoms has served as a benchmark system for both experimentalists and theorists for decades. In its ground electronic state, NO is a 2 Π 2Π^2\Pi2Π molecule with a single unpaired electron in an antibonding π ∗ π∗\pi ^*π∗ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω | ∣Ω∣|\Omega |∣Ω∣ ( = 1 2 =12=\frac{1}{2}=21​ or 3 2 32\frac{3}{2}23​ ) of the electronic angular momentum (orbital and spin) on the internuclear axis. The rotational levels with the same j jjj in the two manifolds are separated by approximately 123 cm − 1 −1^{-1}−1 for v vvv =0 (117 cm − 1 −1^{-1}−1 for v vvv =10). In addition, each rotational level within each manifold is further split into two Λ Λ\LambdaΛ -doublet states ( ε = ± 1 ϵ=±1\epsilon = \pm 1ϵ=±1 , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2 p=(−1)j−ϵ/2p = (-1)^{j-\epsilon /2}p=(−1)j−ϵ/2 . As the Rg atom approaches the NO molecule, the degeneracy of the Λ Λ\LambdaΛ doublets is lifted, giving rise to two PESs, A ′ A′A^{\prime }A′ and A ′ ′ A′′A^{\prime \prime }A′′ , in which the orbital of the unpaired electron lies, respectively, in the plane of the three atoms or perpendicular to it. In computational practice, it is more convenient to use linear combinations (sums and differences) of the A ′ ′ A′′A^{\prime \prime }A′′ and A ′ A′A^{\prime }A′ PESs. Using hexapole focusing or Stark deceleration combined with detection via velocity ion imaging, fully state-to-state-resolved integral and differential cross sections for rotationally elastic and inelastic collisions could be measured with high resolution.9, 11, 25, 26 More than that, the orientation and alignment of the scattered (outgoing) NO molecules could be measured as a function of the scattering angle27-30 and, quite recently, the effects of orientation of the reactant (incoming) NO molecules on the differential cross section in collisions with Rg, mostly Ar, could be established.31-35 On the theory side, quantum mechanical close coupling (QMCC) scattering calculations on accurate two-dimensional ab initio PESs using the benchmark coupled-cluster, CCSD(T), method with the NO internuclear distance fixed at its equilibrium value36 were performed and found to account for all the details revealed by the experiments. Although state of the art, most of these experiments except for those described in Refs. 9, 11 were carried out at thermal energies for NO molecules in their lowest level, | v = 0 , j = 1 2 , Ω = 1 2 , f ⟩ ∣v=0,j=12,Ω=12,f⟩|v=0, j=\frac{1}{2}, \Omega =\frac{1}{2}, f\rangle∣v=0,j=21​,Ω=21​,f⟩ . Scattering of highly vibrationally excited molecules in the cold energy regime remained an unexplored frontier until the recent work by the groups of Arthur Suits, Ad van der Avoird, Gerrit Groenenboom, and Hua Guo who added spin–orbit and rotational state selection and looked for spin- and rotational-state changing collisions to boot. Published in the current issue of Natural Sciences,37 this work is a culmination of a 3-year collaboration that included both implementation of new experimental techniques and boosting of theoretical methods. Working with the NO+Ar system, the authors made use of stimulated emission pumping via the electronically excited A 2 Σ + A2Σ+A^2\Sigma ^+A2Σ+ state to promote NO( 2 Π 1 2 2Π12^2\Pi _{\frac{1}{2}}2Π21​​ ) molecules to the vibrationally excited state with v = 10 v=10v=10v=10 and a selected spin–orbit state | Ω | ∣Ω∣|\Omega |∣Ω∣ and rotational state j jjj , | v = 10 , j , Ω , f ⟩ ∣v=10,j,Ω,f⟩|v=10, j,\Omega , f\rangle∣v=10,j,Ω,f⟩ .38, 39 Low (cold) collision energies were achieved in a novel experimental setup of two beams (dual-beam arrangement) crossing at 4 ∘ ∘^{\circ }∘ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′ ′^{\prime }′ REMPI with the ionization laser tuned just above the ionization threshold. Fully state-resolved angular distributions of the scattered NO molecules were measured by velocity ion slice imaging and detected by a charge-coupled device (CCD). In order to be able to detect the product (outgoing) molecules resulting from the cold NO + Ar collisions, some excess energy had to be made available to the products. This came in the form of the initial spin–orbit and/or rotational state energy. In the study highlighted herein,37 angular distributions leading to the spin–orbit changing transition | v = 10 , Ω = 3 2 , j = 3 2 f ⟩ → | v ′ = 10 , Ω ′ = 1 2 , j ′ = 9 2 , e ⟩ ∣v=10,Ω=32,j=32f⟩→∣v′=10,Ω′=12,j′=92,e⟩|v=10, \Omega =\frac{3}{2}, j=\frac{3}{2} f\rangle \rightarrow |v^{\prime }=10, \Omega ^{\prime }=\frac{1}{2}, j^{\prime }=\frac{9}{2}, e \rangle∣v=10,Ω=23​,j=23​f⟩→∣v′=10,Ω′=21​,j′=29​,e⟩ were measured at energies in the 2 K–5 K range. Although intrabeam scattering could have been used as an alternative as it had been in previous work,21 the authors demonstrated that a dual-beam setup provides a superior angular and energy resolution. The highlighted experiment challenged the existing theoretical treatments of the NO+ Rg systems: first, the approximation of fixing NO at its equilibrium distance was bound to fail for NO in v = 10 v=10v=10v=10 due to the concomitant elongation of the NO bond. Second, for such a highly excited vibrational state, both the long- and short-range interactions are affected, triggering nonadiabatic effects involving rotational and spin–orbit degrees of freedom. The above rendered the single-reference coupled-cluster method used in previous treatments of NO( 2 Π 1 2 , v = 0 2Π12,v=0^2\Pi _{\frac{1}{2}},v=02Π21​​,v=0 ) inadequate. Therefore, the authors of the highlighted paper37 constructed a new coupled-cluster PES as well as a multireference configuration-interaction (MRCI) PES and carried out full-fledged (3D) QMCC calculations on both PESs. These tour-de-force calculations reproduced quite well the experimental differential cross sections and defined a new state of the art in scattering calculations. However, some discrepancies remain as at low collision energies, and the accuracy of the long-range potential needed is a challenge for any ab initio method. Moreover, treating spin-changing collisions that are dominated by the essentially attractive difference potential, V A ′ ′ − V A ′ VA′′−VA′V_{A^{\prime \prime }}-V_{A^{\prime }}VA′′​−VA′​ , puts additional demands on the accuracy of the A ′ ′ A′′A^{\prime \prime }A′′ and A ′ A′A^{\prime }A′ PESs. The calculated integral cross section in the 3–4 cm − 1 −1^{-1}−1 energy interval exhibits a bump that may indicate the presence of resonances that show up as backscattering in the measured differential cross section. A partial-wave analysis points to overlapping resonances associated with contributions from several of the highest partial waves involved. In any case, tracing the resonances may require additional improvements of the existing PESs. All in all, the highlighted combined experimental and theoretical study sets a new standard for our understanding of cold collisions. There is no conflict of interest. The peer review history for this article is available at https://publons.com/publon/10.1002/ntls.20210088. This Highlight has been internally reviewed and edited by Bretislav Friedrich and Gerard Meijer. No data available.
The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.
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.
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 accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.