Imaging Resonance Effects in C + H2 Collisions Using a Zeeman Decelerator.

An intriguing phenomenon in molecular collisions is the occurrence of scattering resonances, which originate from bound and quasi-bound states supported by the interaction potential at low collision energies. The resonance effects in the scattering behavior are extraordinarily sensitive to the interaction potential, and their observation provides one of the most stringent tests for theoretical models. We present high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated C(3P1) atoms and para-H2 molecules at collision energies ranging from 77 cm-1 down to 0.5 cm-1. Rapid variations in the angular distributions were observed, which can be attributed to the consecutive reduction of contributing partial waves and effects of scattering resonances. The measurements showed excellent agreement with distributions predicted by ab initio quantum scattering calculations. However, discrepancies were found at specific collision energies, which most likely originate from an incorrectly predicted quasi-bound state. These observations provide exciting prospects for further high-precision and low-energy investigations of scattering processes that involve paramagnetic species.

Low-Energy Collisions of Zeeman-Decelerated NH Radicals with He Atoms.

We report an experimental study of state-to-state inelastic scattering of NH (X 3Σ-, N = 0, j = 1) radicals with He atoms. Using a crossed molecular beam apparatus that combines a Zeeman decelerator and velocity map imaging, we study both integral and differential cross sections in the N = 0, j = 1 → N = 2, j = 3 inelastic channel. We developed various new REMPI schemes to state-selectively detect NH radicals, and tested their performance in terms of sensitivity and ion recoil velocity. We found a 1 + 2' + 1' REMPI scheme using the A 3Π â† X 3Σ- resonant transition, which yields acceptable recoil velocities and is more than an order of magnitude more sensitive than conventional one-color REMPI schemes to detect NH. We used this REMPI scheme to probe state-to-state integral and differential cross sections around the channel opening at 97.7 cm-1, as well as at higher energies where structure in the scattering images could be resolved. The experimental results are in excellent agreement with the predictions from quantum scattering calculations which are based on an ab initio NH-He potential energy surface.

Quantum state-resolved molecular dipolar collisions over four decades of energy.

Collisions between cold polar molecules represent a fascinating research frontier but have proven hard to probe experimentally. We report measurements of inelastic cross sections for collisions between nitric oxide (NO) and deuterated ammonia (ND3) molecules at energies between 0.1 and 580 centimeter-1, with full quantum state resolution. At energies below the ~100-centimeter-1 well depth of the interaction potential, we observed backward glories originating from peculiar U-turn trajectories. At energies below 0.2 centimeter-1, we observed a breakdown of the Langevin capture model, which we interpreted in terms of a suppressed mutual polarization during the collision, effectively switching off the molecular dipole moments. Scattering calculations based on an ab initio NO-ND3 potential energy surface revealed the crucial role of near-degenerate rotational levels with opposite parity in low-energy dipolar collisions.

Correlated rotational excitations in NO-CO inelastic collisions.

We present a joint experimental and theoretical study of rotationally inelastic collisions between NO (X2Π1/2, ν = 0, j = 1/2, f) radicals and CO (X1Σ+, ν = 0, j = 0) molecules at a collision energy of 220 cm-1. State-to-state scattering images for excitation of NO radicals into various final states were measured with high resolution by combining the Stark deceleration and velocity map imaging techniques. The high image resolution afforded the observation of correlated rotational excitations of NO-CO pairs, which revealed a number of striking scattering phenomena. The so-called "parity-pair" transitions in NO are found to have similar differential cross sections, independent of the concurrent excitation of CO, extending this well-known effect for collisions between NO and rare gas atoms into the realm of bimolecular collisions. Forward scattering is found for collisions that induce a large amount of rotational energy transfer (in either NO, CO, or both), which require low impact parameters to induce sufficient energy transfer. This observation is interpreted in terms of the recently discovered hard collision glory scattering mechanism, which predicts the forward bending of initially backward receding trajectories if the energy uptake in the collision is substantial in relation to the collision energy. The experimental results are in good agreement with the predictions from coupled-channels quantum scattering calculations based on an ab initio NO-CO potential energy surface.

Glory scattering in deeply inelastic molecular collisions.

For molecular collisions, the deflection of a molecule's trajectory provides one of the most sensitive probes of the interaction potential and there are general rules of thumb that relate the direction of deflection to precollision conditions. Following intuition, forward scattering results from glancing collisions, whereas near head-on collisions result in back scattering. Here we present the observation of forward scattering in inelastic processes that defies this common wisdom. For deeply inelastic collisions between NO radicals and CO or HD molecules, we observed forward scattering in fully resolved pair-correlated differential cross-sections, despite the low impact parameters that are needed to induce a sufficient energy transfer. We rationalized these findings by extending the textbook model of hard-sphere scattering-taking inelastic energy transfer into account-and attribute the forward scattering to glory-type trajectories caused by attractive forces. This phenomenon, which we refer to as hard-collision glory scattering, is predicted to be ubiquitous. We derive under which conditions hard-collision glory scattering occurs and retrospectively identify such behaviour in previously studied systems.

Mapping partial wave dynamics in scattering resonances by rotational de-excitation collisions.

One of the most important parameters in a collision is the 'miss distance' or impact parameter, which in quantum mechanics is described by quantized partial waves. Usually, the collision outcome is the result of unavoidable averaging over many partial waves. Here we present a study of low-energy NO-He collisions that enables us to probe how individual partial waves evolve during the collision. By tuning the collision energies to scattering resonances between 0.4 and 6 cm-1, the initial conditions are characterized by a limited set of partial waves. By preparing NO in a rotationally excited state before the collision and by studying rotational de-excitation collisions, we were able to add one quantum of angular momentum to the system and trace how it evolves. Distinct fingerprints in the differential cross-sections yield a comprehensive picture of the partial wave dynamics during the scattering process. Exploiting the principle of detailed balance, we show that rotational de-excitation collisions probe time-reversed excitation processes with superior energy and angular resolution.

High-Resolution Imaging of C + He Collisions using Zeeman Deceleration and Vacuum-Ultraviolet Detection.

High-resolution measurements of angular scattering distributions provide a sensitive test for theoretical descriptions of collision processes. Crossed beam experiments employing a decelerator and velocity map imaging have proven successful to probe collision cross sections with extraordinary resolution. However, a prerequisite to exploit these possibilities is the availability of a near-threshold state-selective ionization scheme to detect the collision products, which for many species is either absent or inefficient. We present the first implementation of recoil-free vacuum ultraviolet (VUV) based detection in scattering experiments involving a decelerator and velocity map imaging. This allowed for high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated carbon C(3P1) atoms and helium atoms. We fully resolved diffraction oscillations in the angular distributions, which showed excellent agreement with the distributions predicted by quantum scattering calculations. Our approach offers exciting prospects to investigate a large range of scattering processes with unprecedented precision.

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.

Imaging the onset of the resonance regime in low-energy NO-He collisions.

At low energies, the quantum wave-like nature of molecular interactions results in distinctive scattering behavior, ranging from the universal Wigner laws near 0 kelvin to the occurrence of scattering resonances at higher energies. It has proven challenging to experimentally probe the individual waves underlying these phenomena. We report measurements of state-to-state integral and differential cross sections for inelastic NO-He collisions in the 0.2 to 8.5 centimeter-1 range with 0.02 centimeter-1 resolution. We studied the onset of the resonance regime by probing the lowest-lying resonance dominated by s and p waves only. The highly structured differential cross sections directly reflect the increasing number of contributing waves as the energy is increased. Only with CCSDT(Q) level of theory was it possible to reproduce our measurements.

Correlations in rotational energy transfer for NO-D2 inelastic collisions.

We present a combined experimental and theoretical study of state-to-state inelastic collisions between NO (X 2Π1/2, j = 1/2, f) radicals and D2 (j = 0, 1, 2, 3) molecules at collision energies of 100 cm-1 and 750 cm-1. Using the combination of Stark deceleration and velocity map imaging, we fully resolve pair-correlated excitations in the scattered molecules. Both spin-orbit conserving and spin-orbit changing transitions in the NO radical are measured, while the coincident rotational excitation (j = 0 → j = 2) and rotational de-excitation (j = 2 → j = 0 and j = 3 → j = 1) in D2 are observed. De-excitation of D2 shows a strong dependence on the spin-orbit excitation of NO. We observe translation-to-rotation energy transfer as well as direct rotation-to-rotation energy transfer at the lowest collision energy probed. The experimental results are in good agreement with cross sections obtained from quantum coupled-channels calculations based on recent NO-D2 potential energy surfaces. The observed trends in the correlated scattering cross sections are understood in terms of the NO-D2 quadrupole-quadrupole interaction.

High-resolution imaging of molecular collisions using a Zeeman decelerator.

We present the first crossed beam scattering experiment using a Zeeman decelerated molecular beam. The narrow velocity spreads of Zeeman decelerated NO (X2Π3/2, j = 3/2) radicals result in high-resolution scattering images, thereby fully resolving quantum diffraction oscillations in the angular scattering distribution for inelastic NO-Ne collisions and product-pair correlations in the radial scattering distribution for inelastic NO-O2 collisions. These measurements demonstrate similar resolution and sensitivity as in experiments using Stark decelerators, opening up possibilities for controlled and low-energy scattering experiments using chemically relevant species such as H and O atoms, O2 molecules, or NH radicals.

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.

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 (ΔjD2 = 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.

Energy dependent parity-pair behavior in NO + He collisions.

Colliding molecules behave fundamentally differently at high and low collision energies. At high energies, a collision can be described to a large extent using classical mechanics, and the scattering process can be compared to a billiard-ball-like collision. At low collision energies, the wave character of the collision partners dominates, and only quantum mechanics can predict the outcome of an encounter. It is, however, not so clear how these limits evolve into each other as a function of the collision energy. Here, we investigate and visualize this evolution using a special feature of the differential cross sections for inelastic collisions between NO radicals and He atoms. The so-called "parity-pair" transitions have similar differential cross sections at high collision energies, whereas their cross sections are significantly different in the quantum regime at low energies. These transitions can be used as a probe for the quantum nature of the collision process. The similarity of the parity-pair differential cross sections at high energies could be theoretically explained if the first-order Born approximation were applicable. We found, however, that the anisotropy of the NO-He interaction potential is too strong for the first-order Born approximation to be valid, so higher-order perturbations must be taken into account.

Correlated energy transfer in rotationally and spin-orbit inelastic collisions of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-).

We present a combined experimental and theoretical study of state-to-state inelastic scattering of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-) molecules at a collision energy of 480 cm-1, focusing in particular on the observation and interpretation of correlated excitations in both NO and O2. Various final states of the NO radical, in both spin-orbit manifolds, were measured with high resolution using a crossed molecular beam apparatus which employs a combination of Stark deceleration and velocity map imaging. Velocity map imaging directly measures both the angular distribution and the radial velocity distribution of the scattered NO molecules, which probes the kinetic energy uptake or release and hence correlated excitations of NO-O2 pairs. Simultaneous excitations of NO and O2 were resolved for all studied final states of NO. In all cases, the experimental results excellently agree with the results of simulations based on quantum scattering calculations. Trends are discussed by analyzing the scattering wave functions from the calculations.

Cold Collisions in a Molecular Synchrotron.

We study collisions between neutral, deuterated ammonia molecules (ND_{3}) stored in a 50 cm diameter synchrotron and argon atoms in copropagating supersonic beams. The advantages of using a synchrotron in collision studies are twofold: (i) By storing ammonia molecules many round-trips, the sensitivity to collisions is greatly enhanced; (ii) the collision partners move in the same direction as the stored molecules, resulting in low collision energies. We tune the collision energy in three different ways: by varying the velocity of the stored ammonia packets, by varying the temperature of the pulsed valve that releases the argon atoms, and by varying the timing between the supersonic argon beam and the stored ammonia packets. These give consistent results. We determine the relative, total, integrated cross section for ND_{3}+Ar collisions in the energy range of 40-140 cm^{-1}, with a resolution of 5-10 cm^{-1} and an uncertainty of 7%-15%. Our measurements are in good agreement with theoretical scattering calculations.

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.

Observation of correlated excitations in bimolecular collisions.

Although collisions between atoms and molecules are largely understood, collisions between two molecules have proven much harder to study. In both experiment and theory, our ability to determine quantum-state-resolved bimolecular cross-sections lags behind their atom-molecule counterparts by decades. For many bimolecular systems, even rules of thumb-much less intuitive understanding-of scattering cross sections are lacking. Here, we report the measurement of state-to-state differential cross sections on the collision of state-selected and velocity-controlled nitric oxide (NO) radicals and oxygen (O2) molecules. Using velocity map imaging of the scattered NO radicals, the full product-pair correlations of rotational excitation that occurs in both collision partners from individual encounters are revealed. The correlated cross sections show surprisingly good agreement with quantum scattering calculations using ab initio NO-O2 potential energy surfaces. The observations show that the well-known energy-gap law that governs atom-molecule collisions does not generally apply to bimolecular excitation processes, and reveal a propensity rule for the vector correlation of product angular momenta.

State-to-State Differential Cross Sections for Inelastic Collisions of NO Radicals with para-H2 and ortho-D2.

We present state-to-state differential cross sections for collisions of NO molecules (X2Π1/2, j = 1/2f) with para-H2 and ortho-D2 molecules, at a collision energy of 510 and 450 cm-1, respectively. The angular scattering distributions for various final states of the NO radical are measured with high resolution using a crossed molecular beam apparatus that employs the combination of Stark deceleration and velocity map imaging. Rotational rainbows as well as diffraction oscillations are fully resolved in the scattering images. The observed angular scattering distributions are in excellent agreement with the cross sections obtained from quantum close-coupling scattering calculations based on recently computed NO-H2 potential energy surfaces, except for excitation of NO into the j = 7/2f channel. For this particular inelastic channel, a significant discrepancy with theory is observed, despite various additional measurements and calculations, at present, not understood.

Imaging diffraction oscillations for inelastic collisions of NO radicals with He and D2.

We present state-to-state differential cross sections for collisions of NO molecules (X2Π1/2,j=1/2,f) with He atoms and ortho-D2 (j = 0) molecules as a function of collision energy. A high angular resolution obtained using the combination of Stark deceleration and velocity map imaging allows for the observation of diffraction oscillations in the angular scattering distributions. Differences in the differential cross sections and, in particular, differences in the angular spacing between individual diffraction peaks are observed. Since the masses of D2 and He are almost equal and since D2(j = 0) may be considered as a pseudo-atom, these differences directly reflect the larger size of D2 as compared to He. The observations are in excellent agreement with the cross sections obtained from quantum close-coupling scattering calculations based on accurate ab initio NO-He and NO-D2 potential energy surfaces. For the latter, we calculated a new NO-D2 potential energy surface.