[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This thesis presents the successful implementation of a slice velocity map imaging apparatus capable of performing molecular beam scattering experiments at collision energies from well above the room temperature to below 1 K. The novel techniques introduced here offers a platform to study collisions at a regime where the scattering is mainly governed by quantum mechanics. Experimental developments of low energy collisions will challenge the theoretical description of molecular interactions, and aid in validating the accuracy of the calculated potential energy surfaces. Scattering studies involving two different configurations of the apparatus, intrabeam and near-copropagating beam configurations are reported in this thesis. The intrabeam scattering approach exploits beam slippage, the velocity difference of different species in the same beam, to establish the relative velocity. The beam slippage in the current setup was created by a pulsed electric discharge which induced a velocity upchirp in the excited species. Implementing a unique dual-slit chopper that can separately fix the velocities of the excited and non-excited species at the interaction region, we achieve precise control over the relative velocity and narrow its spread. With this configuration l-changing collisions occurring between Xe Rydberg atoms and Xe ground state atoms at subKelvin temperatures have been observed. The near-copropagating beam apparatus coupled with the stimulated emission pumping method and sliced velocity map imaging detection enabled us to measure the state-to-state differential cross sections for inelastic collisions between vibrationally excited NO molecules and Ar at broadly tunable energies. Experimentally measured rotationally inelastic state-to-state differential cross sections have enjoyed excellent agreement with quantum scattering calculations performed on state-of-the-art coupled-cluster potential energy surfaces. In contrast, state-to-state differential cross sections obtained for collision-induced multiplet changing transitions at collision energies near 1 K have showed better agreement with quantum scattering calculations involving multireference potential energy surfaces compared to coupled-cluster surfaces. This study provided a platform to validate the accuracy of the potential energy surfaces for collisions which are mainly governed by the attractive part of the interaction potential.
We have developed an apparatus capable of performing intrabeam and near-copropagating beam scattering experiments at collision energies from room temperature to below 1 K where interesting quantum phenomena can be observed. A detailed description of the major components of the apparatus, single and dual molecular beam valves, high speed chopper, and the discharge source, is presented. With the intrabeam scattering setup, a novel dual-slit chopper permits collision energies down to millikelvins with a collision energy spread of 20%. With the near-copropagating beam configuration, state-to-state differential cross sections for rotationally inelastic collisions of highly vibrationally excited NO molecules with Ar have been measured at broadly tunable energies documenting the versatility of the instrument. Future applications in stereodynamics and cold state-to-state collisions of vibrationally excited polyatomic molecules are briefly discussed.
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.
Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.
We present two methods for studying reactive collisions between two atomic or molecular species: a collinear merged-beam method in which two gas pulses from a single supersonic beam source are coalesced and an intrabeam-scattering technique in which a single gas pulse is used. Both approaches, which rely on the laser cooling and deceleration of a laser-coolable species inside a Zeeman slower, can be used for a wide range of scattering studies. Possible experimental implementations of the proposed methods are outlined for autoionizing collisions between helium atoms in the metastable 2 3 S 1 state and a second, atomic or molecular species. Using numerical trajectory calculations, we provide estimates of the expected on-axis detection efficiency, collision-energy range, and collision-energy resolution of the approaches. We have experimentally tested the feasibility of such an experiment by producing two gas pulses at very short time intervals, and the results of these measurements are also detailed.
Collisions of molecules in a thermal gas are difficult to control. Thermal motion randomizes molecular encounters and diminishes the effects of external radiation or static electromagnetic fields on intermolecular interactions. The effects of the thermal motion can be reduced by cooling molecular gases to low temperatures. At temperatures near or below 1 K, the collision energy of molecules becomes less significant than perturbations due to external fields. At the same time, inelastic scattering and chemical reactions may be very efficient in low-temperature molecular gases. The purpose of this article is to demonstrate that collisions of molecules at temperatures below 1 K can be manipulated by external electromagnetic fields and to discuss possible applications of cold controlled chemistry. The discussion focuses on molecular interactions at cold (0.001-2 K) and ultracold (<0.001 K) temperatures and is based on both recent theoretical and experimental work. The article concludes with a summary of current challenges for theory and experiment in the research of cold molecules and cold chemistry.