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 ∘
∘ –10 ∘
∘ ), 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
2Π molecule with a single unpaired electron in an antibonding π ∗
π∗ orbital. In this state, the rotational levels are split into two spin–orbit manifolds, defined by the projection | Ω |
∣Ω∣ ( = 1 2
=21 or 3 2
23 ) 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
Λ -doublet states ( ε = ± 1
ϵ=±1 , e/f), which are nearly degenerate, but differ in parity, p = ( − 1 ) j − ε / 2
p=(−1)j−ϵ/2 . As the Rg atom approaches the NO molecule, the degeneracy of the Λ
Λ doublets is lifted, giving rise to two PESs, A ′
A′ and A ′ ′
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′′ and A ′
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=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+ state to promote NO( 2 Π 1 2
2Π21 ) molecules to the vibrationally excited state with v = 10
v=10 and a selected spin–orbit state | Ω |
∣Ω∣ and rotational state j
j , | v = 10 , j , Ω , f ⟩
∣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 ∘
∘ and intersected by the pump and dump laser beams of the stimulated-emission pumping scheme. Downstream, the collision products were probed using 1+1 ′
′ 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=23,j=23f⟩→∣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=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
2Π21,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′ , puts additional demands on the accuracy of the A ′ ′
A′′ and A ′
A′ 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.
The key features of the cross sections for electron-impact excitation out of the ground levels of the rare-gas atoms are summarized and application of these cross section data is shown. This is followed by discussions of recent experiments on determination of electron-impact cross sections for excitation out of the metastable levels of He and Ar. The metastiable atom targets are produced by two different methods, i.e., hollow-cathode discharges and charge-exchange collisions of rare-gas ions with Cs atoms. The former method is simple but is limited to low electron energies because of the very small metastable concentration, whereas the latter method yields a fast target beam with predominantly metastable atoms allowing measurements up to the keV range. The measured cross sections show features very different from those of excitation out of the ground levels. Another new development in electron-atom collision is the use of atom traps for measuring ionization cross sections. The experiment is conducted by passing an electron beam pulse through magneto-optically trapped Rb atoms while the trap is momentarily turned off. Turning the trap back on immediately after the electron beam pulse recaptures the unionized atoms allowing only the ions to escape. The ionization cross section is determined bymore » measuring the electron beam current density at the trapped atom region and the fractional loss of trapped atoms due to the electron beam. This method avoids measurements of the absolute number of the target atoms and the overlap between the atomic and electron beams and therefore eliminates the major sources of uncertainty associated with the crossed-beam method for measuring ionization cross section.« less
Potassium atoms in selected high-lying np Rydberg states (80 {<=} n {<=} 400) are being used as a tool to examine electron-polar molecule collisions at ultra-low energies ({approximately}80 {mu}eV - 1 meV). This energy regime has not been investigated previously and is of interest because the corresponding electron de Broglie wavelength is large, {approximately}1300 - 330 {Angstrom}, and because the collision time is comparable to the period of molecular rotation. A variety of target molecules has been studied, including simple rotors such as HF, and more complex species such as NH{sub 3}, CH{sub 3}I, CH{sub 2}Br{sub 2} and C{sub 6}H{sub 5}NO{sub 2}. These targets encompass a range of dipole moments and rotational behavior, but analysis of the data shows that in each case the cross section {sigma}({epsilon}) for rotationally-inelastic electron-polar molecule scattering varies approximately as 1/{epsilon} where {epsilon} is the electron energy. Such threshold behavior is not predicted by the Born approximation and possible reasons for this discrepancy will be discussed. In the case of NH{sub 3}, the data show that near-resonant energy transfer associated with transitions between different inversion levels is an important process leading to collisional state changing.
We review the experimental findings on scattering resonances in molecular collisions occurring in the energy domain equivalent to temperatures of a few Kelvin. We discuss the conditions required to observe shape (or orbiting) and Feshbach resonances, the crucial factor being in all cases the number of partial waves involved in the process. This implies operating with supersonic beams with matched and low velocities, high velocity resolution and low beam-intersection angle. This is exemplified for elastic, inelastic and reactive collisions, where different strategies, thence experimental arrangements, are used. We review the first observation of resonances in elastic collisions from the 1970s and the recent results in inelastic and reactive collisions. The most striking result is obtained for O2 + para-H2 inelastic collisions for which rotational excitation occurs through a pure quantum process, yielding a well-resolved structure in the integral cross section assigned to definite well-separated partial waves.
Research of cold and ultracold molecules is currently a burgeoning field in experimental and theoretical physics. New experimental techniques, involving an increasingly large set of molecule types under high levels of control, are currently opening up new avenues of research with a vast array of potential applications. From understanding the role of quantum mechanics in molecular scattering and cold chemistry, to testing the fundamental symmetries of nature and realizing quantum computing with dipolar molecular qubits, experiments are accessing regimes not dreamed of even a few years ago. Theoretical interest and computing capabilities are also at an all time high, spurred on by the possibility of creating ultracold dipolar gases as tunable realizations of strongly interacting quantum Hamiltonians, creating exotic phases of matter, and the investigation of controlling molecular interactions with applied electromagnetic fields.\nLess than a decade ago, cold molecule experiments had seemingly reached a technological plateau, being capable of creating moderate densities of 106-107 molecules/cm3 at temperatures of 10-100 mK. With many applications requiring colder temperatures and higher densities, the field was ripe for new advances. Today, via a plethora of methods such as direct molecular laser cooling, electro-optical cooling, magneto- and photo-association, and new molecular beam deceleration techniques, the field is just beginning to have the tools capable of producing truly interesting systems for study.\nThis work will discuss a couple of major steps taken in the direction of achieving scientific goals using cold molecules. The first experimental advancement discussed will be the development of a co-trap environment for studying interactions and collisions between ultracold atoms and Stark decelerated cold polar molecules. In this experiment, rubidium atoms are trapped using magnetic fields, and ammonia atoms are decelerated and trapped using electric fields. The two traps are spatially overlapped in order to investigate inter-species interactions. The co-trap environment provides exceedingly long interaction times, many orders of magnitude longer than typical beam-based interaction studies. As a result, it provides extremely high sensitivity to weak interaction mechanisms. The second experimental advancement discussed will be the development and construction of a new style of Stark decelerator, capable of producing much larger densities of cold molecules. This apparatus has the potential to expand the realm of possible experiments with chemically interesting species, and provide an unprecedented amount of control over molecular beams and traps. The gains haven't come easily though, as a new class of custom high-voltage amplifiers have needed to be developed. This part of the experiment alone took approximately two years of consistent effort to bring to fruition. After many years of development, this experiment is poised to come online, finally fulfilling its potential.