Cold collisions of hot molecules

In this Perspective, we review our recent work on rotationally inelastic collisions of highly vibrationally excited NO molecules prepared in single rotational and parity levels at v = 10 using stimulated emission pumping (SEP). This state preparation is employed in a recently developed crossed molecular beam apparatus where two nearly copropagating molecular beams achieve an intersection angle of 4° at the interaction region. This near-copropagating beam geometry of the molecular beams permits very wide tuning of the collision energy, from far above room temperature down to 2 K where we test the theoretical treatment of the attractive part of the potentials and the difference potential for the first time. We have obtained differential cross sections for state-to-state collisions of NO (v = 10) with Ar and Ne in both spin-orbit manifolds using velocity map imaging. Overall good agreement of the experimental results was seen with quantum mechanical close-coupling calculations done on both coupled-cluster and multi-reference configuration interaction potential energy surfaces. Probing cold collisions of NO carrying ∼2 eV of vibrational excitation allows us to test state-of-the-art theory in this extreme nonequilibrium regime.

Imaging rotational energy transfer: comparative stereodynamics in CO + N2 and CO + CO inelastic scattering

State-to-state rotational energy transfer in collisions of ground ro-vibrational state ¹³CO molecules with N₂ molecules has been studied using the crossed molecular beam method under kinematically equivalent conditions used for ¹³CO + CO rotationally inelastic scattering described in a previously published report (Sun et al., Science, 2020, 369, 307-309). The collisionally excited ¹³CO molecule products are detected by the same (1 + 1' + 1'') VUV (Vacuum Ultra-Violet) resonance enhanced multiphoton ionization scheme coupled with velocity map ion imaging. We present differential cross sections and scattering angle resolved rotational angular momentum alignment moments extracted from experimentally measured ¹³CO + N₂ scattering images and compare them with theoretical predictions from quasi-classical trajectories (QCT) on a newly calculated ¹³CO-N₂ potential energy surface (PES). Good agreement between experiment and theory is found, which confirms the accuracy of the ¹³CO-N₂ potential energy surface for the 1460 cm^-1 collision energy studied by experiment. Experimental results for ¹³CO + N₂ are compared with those for ¹³CO + CO collisions. The angle-resolved product rotational angular momentum alignment moments for the two scattering systems are very similar, which indicates that the collision induced alignment dynamics observed for both systems are dominated by a hard-shell nature. However, compared to the ¹³CO + CO measurements, the primary rainbow maximum in the DCSs for ¹³CO + N₂ is peaked consistently at more backward scattering angles and the secondary maximum becomes much less obvious, implying that the ¹³CO-N₂ PES is less anisotropic. In addition, a forward scattering component with high rotational excitation seen for ¹³CO + CO does not appear for ¹³CO-N₂ in the experiment and is not predicted by QCT theory. Some of these differences in collision dynamics behaviour can be predicted by a comparison between the properties of the PESs for the two systems. More specific behaviour is also predicted from analysis of the dependence on the relative collision geometry of ¹³CO + N₂ trajectories compared to ¹³CO + CO trajectories, which shows the special 'do-si-do' pathway invoked for ¹³CO + CO is not effective for ¹³CO + N₂ collisions.

Tomography of Feshbach resonance states

Feshbach resonances are fundamental to interparticle interactions and become particularly important in cold collisions with atoms, ions, and molecules. In this work, we present the detection of Feshbach resonances in a benchmark system for strongly interacting and highly anisotropic collisions: molecular hydrogen ions colliding with noble gas atoms. The collisions are launched by cold Penning ionization, which exclusively populates Feshbach resonances that span both short- and long-range parts of the interaction potential. We resolved all final molecular channels in a tomographic manner using ion-electron coincidence detection. We demonstrate the nonstatistical nature of the final-state distribution. By performing quantum scattering calculations on ab initio potential energy surfaces, we show that the isolation of the Feshbach resonance pathways reveals their distinctive fingerprints in the collision outcome.

Field-linked resonances of polar molecules

Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances¹, which have been extensively studied in various platforms^1-7, are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance^8-10. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances^11-14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium-potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole-dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids¹⁵ and molecular supersolids¹⁶, as well as assembling ultracold polyatomic molecules.

Quantum-Controlled Collisions of H2 Molecules

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H₂ and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

Differential Cross Sections for Cold, State-to-State Spin-Orbit Changing Collisions of NO(v = 10) with Neon

Inelastic scattering processes have proven a powerful means of investigating molecular interactions, and much current effort is focused on the cold and ultracold regime where quantum phenomena are clearly manifested. Studies of collisions of the open shell nitric oxide (NO) molecule have been central in this effort since the pioneering work of Houston and co-workers in the early 1990s. State-to-state scattering of vibrationally excited molecules in the cold regime introduces challenges that test the suitability of current theoretical methods for ab initio determination of intermolecular potentials, and concomitant electronically nonadiabatic processes raise the bar further. Here we report measurements of differential cross sections for state-to-state spin-orbit changing collisions of NO (v = 10, Ω″ = 1.5, and j″ = 1.5) with neon from 2.3 to 3.5 cm^-1 collision energy using our recently developed near-copropagating beam technique. The experimental results are compared with those obtained from quantum scattering calculations on a high-level set of coupled cluster potential energy surfaces and are shown to be in good agreement. The theoretical results suggest that distinct backscattering in the 2.3 cm^-1 case arises from overlapping resonances.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Evidence for the association of triatomic molecules in ultracold 23Na40K + 40K mixtures

Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics and quantum simulation with molecules^1-3. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in a mixture of ultracold atoms and diatomic molecules by using a Feshbach resonance between them^4,5. Although ultracold atom-diatomic-molecule Feshbach resonances have been observed recently^6,7, using these resonances to form triatomic molecules remains challenging. Here we report on evidence of the association of triatomic molecules near the Feshbach resonance between ²³Na⁴⁰K molecules in the rovibrational ground state and ⁴⁰K atoms. We apply a radio-frequency pulse to drive the free-bound transition in ultracold mixtures of ²³Na⁴⁰K and ⁴⁰K and monitor the loss of ²³Na⁴⁰K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature. The observation that the distance between the association feature and the atomic transition changes with the magnetic field provides strong evidence for the formation of triatomic molecules. The binding energy of the triatomic molecules is estimated from the measurements. Our work contributes to the understanding of the complex ultracold atom-molecule Feshbach resonances and may open up an avenue towards the preparation and control of ultracold triatomic molecules.

Enhanced Coupling of Electron and Nuclear Spins by Quantum Tunneling Resonances

Noble-gas spins feature hours-long coherence times, owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically excited potassium atoms and reveal the formation of quasibound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to 6 orders of magnitude and 2 orders of magnitude enhancement for the thermally averaged, polarization rate coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.

Fully quantum calculations of O2-N2 scattering using a new potential energy surface: Collisional perturbations of the oxygen 118 GHz fine structure line

A proper description of the collisional perturbation of the shapes of molecular resonances is important for remote spectroscopic studies of the terrestrial atmosphere. Of particular relevance are the collisions between the O₂ and N₂ molecules-the two most abundant atmospheric species. In this work, we report a new highly accurate O₂(X³Σ_g ^-)-N₂(X¹Σ_g ⁺) potential energy surface and use it for performing the first quantum scattering calculations addressing line shapes for this system. We use it to model the shape of the 118 GHz fine structure line in O₂ perturbed by collisions with N₂ molecules, a benchmark system for testing our methodology in the case of an active molecule in a spin triplet state. The calculated collisional broadening of the line agrees well with the available experimental data over a wide temperature range relevant for the terrestrial atmosphere. This work constitutes a step toward populating the spectroscopic databases with ab initio line shape parameters for atmospherically relevant systems.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

Shape resonance determined from angular distribution in D2 (v = 2, j = 2) + He → D2 (v = 2, j = 0) + He cold scattering

We find an l = 2 shape resonance fingerprinted in the angular distribution of the cold (∼1 K) Δj = 2 rotationally inelastic collision of D₂ with He in a single supersonic expansion. The Stark-induced adiabatic Raman passage is used to prepare D₂ in the (v = 2, j = 2) rovibrational level with control of the spatial distribution of the bond axis of the molecule by magnetic sublevel selection. We show that the rate of Δj = 2 D₂-D₂ relaxation is nearly two orders of magnitude weaker than that of D₂-He. This suggests that the strong D₂-He scattering is caused by an orbiting resonance that is highly sensitive to the shape of the long-range potential.

Resonant collisional shielding of reactive molecules using electric fields

Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. We demonstrate extreme tunability of ultracold chemical reaction rates by inducing resonant dipolar interactions by means of an external electric field. We prepared fermionic potassium-rubidium molecules in their first excited rotational state and observed a modulation of the chemical reaction rate by three orders of magnitude as we tuned the electric field strength by a few percent across resonance. In a quasi-two-dimensional geometry, we accurately determined the contributions from the three dominant angular momentum projections of the collisions. Using the resonant features, we shielded the molecules from loss and suppressed the reaction rate by an order of magnitude below the background value, thereby realizing a long-lived sample of polar molecules in large electric fields.

Towards chemistry at absolute zero

The prospect of cooling matter down to temperatures that are close to absolute zero raises intriguing questions about how chemical reactivity changes under these extreme conditions. Although some types of chemical reaction still occur at 1 μK, they can no longer adhere to the conventional picture of reactants passing over an activation energy barrier to become products. Indeed, at ultracold temperatures, the system enters a fully quantum regime, and quantum mechanics replaces the classical picture of colliding particles. In this Review, we discuss recent experimental and theoretical developments that allow us to explore chemical reactions at temperatures that range from 100 K to 500 nK. Although the field is still in its infancy, exceptional control has already been demonstrated over reactivity at low temperatures.

Ion-Molecule Reactions below 1 K: Strong Enhancement of the Reaction Rate of the Ion-Dipole Reaction He^{+}+CH_{3}F

The reaction between He^{+} and CH_{3}F forming predominantly CH_{2}^{+} and CHF^{+} has been studied at collision energies E_{coll} between 0 and k_{B}·10  K in a merged-beam apparatus. To avoid heating of the ions by stray electric fields, the reaction was observed within the orbit of a highly excited Rydberg electron. Supersonic beams of CH_{3}F and He(n) Rydberg atoms with principal quantum number n=30 and 35 were merged and their relative velocity tuned using a Rydberg-Stark decelerator and deflector, allowing an energy resolution of 150 mK. A strong enhancement of the reaction rate was observed below E_{coll}/k_{B}=1  K. The experimental results are interpreted with an adiabatic capture model that accounts for the state-dependent orientation of the polar CH_{3}F molecules by the Stark effect as they approach the He^{+} ion. The enhancement of the reaction rate at low collision energies is primarily attributed to para-CH_{3}F molecules in the J=1, KM=1 high-field-seeking states, which represent about 8% of the population at the 6 K rotational temperature of the supersonic beam.

Experimental and theoretical investigation of resonances in low-energy NO-H2 collisions

The experimental characterization of scattering resonances in low energy collisions has proven to be a stringent test for quantum chemistry calculations. Previous measurements on the NO-H₂ system at energies down to 10 cm^-1 challenged the most sophisticated calculations of potential energy surfaces available. In this report, we continue these investigations by measuring the scattering behavior of the NO-H₂ system in the previously unexplored 0.4 cm^-1-10 cm^-1 region for the parity changing de-excitation channel of NO. We study state-specific inelastic collisions with both para- and ortho-H₂ in a crossed molecular beam experiment involving Stark deceleration and velocity map imaging. We are able to resolve resonance features in the measured integral and differential cross sections. Results are compared to predictions from two previously available potential energy surfaces, and we are able to clearly discriminate between the two potentials. We furthermore identify the partial wave contributions to these resonances and investigate the nature of the differences between collisions with para- and ortho-H₂. Additionally, we tune the energy spreads in the experiment to our advantage to probe scattering behavior at energies beyond our mean experimental limit.

Determining the nature of quantum resonances by probing elastic and reactive scattering in cold collisions

Scattering resonances play a central role in collision processes in physics and chemistry. They help build an intuitive understanding of the collision dynamics due to the spatial localization of the scattering wavefunctions. For resonances that are localized in the reaction region, located at short separation behind the centrifugal barrier, sharp peaks in the reaction rates are the characteristic signature, observed recently with state-of-the-art experiments in low-energy collisions. If, however, the localization occurs outside of the reaction region, mostly the elastic scattering is modified. This may occur due to above-barrier resonances, the quantum analogue of classical orbiting. By probing both elastic and inelastic scattering of metastable helium with deuterium molecules in merged-beam experiments, we differentiate between the nature of quantum resonances-tunnelling resonances versus above-barrier resonances-and corroborate our findings by calculating the corresponding scattering wavefunctions.

Probing the location of the unpaired electron in spin-orbit changing collisions of NO with Ar

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

Rotational-vibrational resonance states

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L², square integrable) or non-Hermitian (non-L²) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

A versatile molecular beam apparatus for cold/ultracold collisions

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.

Quantum resonances near absolute zero

Ultralow-energy atom-molecule collisions reveal quasi-bound state quantum resonances

The Leiden Atomic and Molecular Database (LAMDA): Current Status, Recent Updates, and Future Plans

The Leiden Atomic and Molecular Database (LAMDA) collects spectroscopic information and collisional rate coefficients for molecules, atoms, and ions of astrophysical and astrochemical interest. We describe the developments of the database since its inception in 2005, and outline our plans for the near future. Such a database is constrained both by the nature of its uses and by the availability of accurate data: we suggest ways to improve the synergies among users and suppliers of data. We summarize some recent developments in computation of collisional cross sections and rate coefficients. We consider atomic and molecular data that are needed to support astrophysics and astrochemistry with upcoming instruments that operate in the mid- and far-infrared parts of the spectrum.

Cold and controlled chemical reaction dynamics

State-to-state chemical reaction dynamics, with complete control over the reaction parameters, offers unparalleled insight into fundamental reactivity.

Direct observation of product-pair correlations in rotationally inelastic collisions of ND3 with D2

We present a combined experimental and theoretical study of state-to-state inelastic scattering of ND₃(j = 1₁^-) with D₂ (j = 0, 1, 2, 3) molecules at collision energies around 800 cm^-1. Using a crossed molecular beam apparatus which employs the combination of Stark deceleration and velocity map imaging, we observe the correlated rotational excitations of both collision partners. For D₂, both elastic (Δj_D2 = 0), inelastic excitation (j = 0 →j = 2) and inelastic de-excitation (j = 2 →j = 0) processes are observed. For a number of final ND₃ states, inelastic channels in which D₂ is rotationally excited or de-excited appear surprisingly strong. The experimental results are in excellent agreement with the predictions from quantum scattering calculations which are based on an ab initio ND₃-D₂ potential energy surface.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

Differential Cross Sections for State-to-State Collisions of NO( v = 10) in Near-Copropagating Beams

State-to-state differential cross sections for rotationally inelastic collisions of vibrationally excited NO with Ar have been measured in a near-copropagating crossed beam experiment at collision energies of 530 and 30 cm^-1. Stimulated emission pumping (SEP) to prepare NO in specific rovibrational levels is coupled with direct-current slice velocity map imaging to obtain a direct measurement of the differential cross sections. The use of nearly copropagating beams to achieve low NO-Ar collision energies and broad collision energy tuning capability are also demonstrated. The experimental differential cross sections (DCSs) for NO in v = 10 in specific rotational and parity states are compared with the corresponding DCSs predicted for NO in v = 0 obtained from quantum mechanical close coupling calculations to highlight the differences between the NO( v = 10)-Ar and NO( v = 0)-Ar interaction potentials.

Quantum Behavior of Spin-Orbit Inelastic Scattering of C-Atoms by D2 at Low Energy

Fine-structure populations and collision–induced energy transfer in atoms are of interest for many fields, from combustion to astrophysics. In particular, neutral carbon atoms are known to play a role in interstellar media, either as probes of physical conditions (ground state ³P_j spin-orbit populations), or as cooling agent (collisional excitation followed by radiative decay). This work aims at investigating the spin-orbit excitation of atomic carbon in its ground electronic state due to collisions with molecular deuterium, an isotopic variant of H₂, the most abundant molecule in the interstellar medium. Spin-orbit excitations of C(³P_j) by H₂ or D₂ are governed by non-adiabatic and spin-orbit couplings, which make the theoretical treatment challenging, since the Born-Oppenheimer approximation no longer holds. Inelastic collisional cross-sections were determined for the C(³P₀) + D₂ → C(³P_j) + D₂ (with j = 1 and 2) excitation process. Experimental data were acquired in a crossed beam experiment at low collision energies, down to the excitation thresholds (at 16.42 and 43.41 cm⁻¹, respectively). C-atoms were produced mainly in their ground spin-orbit state, ³P₀, by dissociation of CO in a dielectric discharge through an Even-Lavie pulsed valve. The C-atom beam was crossed with a D₂ beam from a second valve. The state-to-state cross-sections were derived from the C(³P_j) (j = 1 or 2) signal measured as a function of the beam crossing angle, i.e., as a function of the collision energy. The results show different quantum behaviors for excitation to C(³P₁) or C(³P₂) when C(³P₀) collides with ortho-D₂ or normal-D₂. These experimental results are analyzed and discussed in the light of highly accurate quantum calculations. A good agreement between experimental and theoretical results is found. The present data are compared with those obtained for the C-He and C-H₂ collisional systems to get new insights into the dynamics of collision induced spin-orbit excitation/relaxation of atomic carbon.

Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ K_max, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (K_max = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.

Observation of magnetically tunable Feshbach resonances in ultracold 23Na40K + 40K collisions

Resonances in ultracold collisions involving heavy molecules are difficult to simulate theoretically and have proven challenging to detect. Here we report the observation of magnetically tunable Feshbach resonances in ultracold collisions between potassium-40 (40K) atoms and sodium-23–potassium-40 (23Na40K) molecules in the rovibrational ground state. We prepare the atoms and molecules in various hyperfine levels of their ground states and observe the loss of molecules as a function of the magnetic field. The atom-molecule Feshbach resonances are identified by observing an enhancement of the loss. We have observed 11 resonances in the magnetic field range of 43 to 120 gauss. The observed atom-molecule Feshbach resonances at ultralow temperatures probe the three-body potential energy surface with exceptional resolution and will help to improve understanding of ultracold collisions.

Design and construction of a multistage Zeeman decelerator for crossed molecular beams scattering experiments

Zeeman deceleration is a relatively new technique used to obtain full control over the velocity of paramagnetic atoms or molecules in a molecular beam. We present a detailed description of a multistage Zeeman decelerator that has recently become operational in our laboratory [Cremers et al., Phys. Rev. A 98, 033406 (2018)] and that is specifically optimized for crossed molecular beams scattering experiments. The decelerator consists of an alternating array of 100 solenoids and 100 permanent hexapoles to guide or decelerate beams of paramagnetic atoms or molecules. The Zeeman decelerator features a modular design that is mechanically easy to extend to arbitrary length and allows for solenoid and hexapole elements that are convenient to replace. The solenoids and associated electronics are efficiently water cooled and allow the Zeeman decelerator to operate at repetition rates exceeding 10 Hz. We characterize the performance of the decelerator using various beams of metastable rare gas atoms. Imaging of the atoms that exit the Zeeman decelerator reveals the transverse focusing properties of the hexapole array in the Zeeman decelerator.

Probing Nonadiabatic Effects in Low-Energy C(3 P j) + H2 Collisions

Nonadiabatic effects are of fundamental interest in collision dynamics. In particular, inelastic collisions between open-shell atoms and molecules, such as the collisional excitation of C(³ P _j) by H₂, are governed by nonadiabatic and spin-orbit couplings that are the sole responsible of collisional energy transfer. Here, we study collisions between carbon in its ground state C(³ P _j=0) and molecular hydrogen (H₂) at low collision energies that result in spin-orbit excitation to C(³ P _j=1) and C(³ P _j=2). State-to-state integral cross sections are obtained experimentally from crossed-beam experiments with a source of almost pure beam of C(³ P _j=0) and theoretically from highly accurate quantum calculations. We observe very good agreement between experimental and theoretical data that demonstrates our ability to model nonadiabatic dynamics. New rate coefficients at temperatures relevant to astrochemical modeling are also provided. They should lead to an increase of the abundance of atomic C(³ P) derived from the observations of interstellar clouds and a decrease of the efficiency of the cooling of the interstellar gas due to carbon atoms.

Quantum-state-controlled channel branching in cold Ne(3P2)+Ar chemi-ionization

A prerequisite to gain a complete understanding of the most basic aspects of chemical reactions is the ability to perform experiments with complete control over the reactant degrees of freedom. By controlling these, details of a reaction mechanism can be investigated and ultimately manipulated. Here, we present a study of chemi-ionization-a fundamental energy-transfer reaction-under completely controlled conditions. The collision energy of the reagents was tuned from 0.02 K to 1,000 K, with the orientation of the excited Ne atom relative to Ar fully specified by an external magnetic field. Chemi-ionization of Ne(³P₂) and Ar in these conditions enables a detailed investigation of how the reaction proceeds, and provides us with a means to control the branching ratio between the two possible reaction outcomes. The merged-beam experimental technique used here allows access to a low-energy regime in which the atoms dynamically reorient into a favourable configuration for reaction, irrespective of their initial orientations.

Rotational (de-)excitation of isocyanogen by collision with helium at low energies

Isocyanogen, CNCN, was discovered very recently in the interstellar medium (ISM). At present, the rate coefficients for the rotational (de-)excitation of CNCN by collisions with He are determined. First, we mapped the interaction potential between CNCN and He in Jacobi coordinates using highly correlated ab initio methodology. Then, an analytical expansion of the CNCN-He potential energy surface is derived. Later on, quantum dynamical treatments of nuclear motions are performed using the close coupling technique. We obtained the cross sections for the rotational (de-)excitation of CNCN after a collision by He up to 2000 cm^-1 total energies. These cross sections are used to deduce the collision rates in the 10-300 K range. These data are needed for modeling the CNCN abundances in the ISM. This work should help for determining the abundance of such non-symmetrical dicyanopolyynes in astrophysical media and indirectly the symmetric one [Cyanogen (NCCN)].

A detailed account of the measurements of cold collisions in a molecular synchrotron

We have recently demonstrated a general and sensitive method to study low energy collisions that exploits the unique properties of a molecular synchrotron (Van der Poel et al., Phys Rev Lett 120:033402, 2018). In that work, the total cross section for ND3 + Ar collisions was determined from the rate at which ammonia molecules were lost from the synchrotron due to collisions with argon atoms in supersonic beams. This paper provides further details on the experiment. In particular, we derive the model that was used to extract the relative cross section from the loss rate, and present measurements to characterize the spatial and velocity distributions of the stored ammonia molecules and the supersonic argon beams.

First-order symmetry-adapted perturbation theory for multiplet splittings

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S² approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S² approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Cold chemistry with two atoms

Two atoms react to form a molecule in an optical “beaker”

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation

Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H₂ and D₂ using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0-5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H₂/HD and D₂/HD scattering suggest the presence of anisotropically sensitive resonances.

Scattering resonances in bimolecular collisions between NO radicals and H2 challenge the theoretical gold standard

Over the last 25 years, the formalism known as coupled-cluster (CC) theory has emerged as the method of choice for the ab initio calculation of intermolecular interaction potentials. The implementation known as CCSD(T) is often referred to as the gold standard in quantum chemistry. It gives excellent agreement with experimental observations for a variety of energy-transfer processes in molecular collisions, and it is used to calibrate density functional theory. Here, we present measurements of low-energy collisions between NO radicals and H₂ molecules with a resolution that challenges the most sophisticated quantum chemistry calculations at the CCSD(T) level. Using hitherto-unexplored anti-seeding techniques to reduce the collision energy in a crossed-beam inelastic-scattering experiment, a resonance structure near 14 cm^-1 is clearly resolved in the state-to-state integral cross-section, and a unique resonance fingerprint is observed in the corresponding differential cross-section. This resonance structure discriminates between two NO-H₂ potentials calculated at the CCSD(T) level and pushes the required accuracy beyond the gold standard.

Intrabeam Scattering for Ultracold Collisions

We demonstrate a method to probe cold and ultracold chemistry in a single molecular beam. The approach exploits beam slippage, the velocity difference of different species in the same beam, to establish the relative velocity. Average collision energies of 2.5 mK are achieved but with a spread of 100% or more. However, by implementing a dual-slit chopper that can separately fix the velocities of the two species at the interaction region, we achieve precise control over the relative velocity and narrow its spread. Relative velocities of 7-10 ± 1.1 m/s are achieved with an angular divergence less than 0.25°. In the present study, we observe l-changing collisions occurring between Xe Rydberg atoms and Xe ground state atoms at subKelvin temperatures. We show that in this case the collision energies are tunable between 200 to 450 mK with a root-mean-square deviation of ∼18%. Application of the method to other species and access to much lower energies is straightforward.

Angular distributions for the inelastic scattering of NO(X2Π) with O2(X3Σg-)

The inelastic scattering of NO(X²Π) by O₂(X³Σ_g^-) was studied at a mean collision energy of 550 cm^-1 using velocity-map ion imaging. The initial quantum state of the NO(X²Π, v = 0, j = 0.5, Ω=0.5, 𝜖 = -1, f) molecule was selected using a hexapole electric field, and specific Λ-doublet levels of scattered NO were probed using (1+1^') resonantly enhanced multiphoton ionization. A modified "onion-peeling" algorithm was employed to extract angular scattering information from the series of "pancaked," nested Newton spheres arising as a consequence of the rotational excitation of the molecular oxygen collision partner. The extracted differential cross sections for NO(X) f→f and f→e Λ-doublet resolved, spin-orbit conserving transitions, partially resolved in the oxygen co-product rotational quantum state, are reported, along with O₂ fragment pair-correlated rotational state population. The inelastic scattering of NO with O₂ is shown to share many similarities with the scattering of NO(X) with the rare gases. However, subtle differences in the angular distributions between the two collision partners are observed.