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.

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.

Unraveling Cold Molecular Collisions: Stark Decelerators in Crossed-Beam Experiments.

In the last two decades, enormous progress has been made in the manipulation of molecular beams. In particular, molecular decelerators have been developed with which advanced control over neutral molecules in a beam can be achieved. By using arrays of inhomogeneous and time-varying electric (or magnetic) fields, bunches of molecules can be produced with a tunable velocity, narrow velocity spreads, and almost perfect quantum-state purity. These monochromatic or "tamed" molecular beams are ideally suited to be used in crossed-molecular-beam scattering experiments. Here, we review the first generation of these "cold and controlled" scattering experiments that have been conducted in the last decade and discuss the prospects for this emerging field of research in the years to come.

High-resolution imaging of velocity-controlled molecular collisions using counterpropagating beams.

We present ultrahigh-resolution measurements of state-to-state inelastic differential cross sections for NO-Ne and NO-Ar collisions, obtained by combining the Stark deceleration and velocity map imaging techniques. We show that for counterpropagating crossed beam geometries, the effect of the velocity spreads of the reagent beams on the angular resolution of the images is minimized. Furthermore, the counterpropagating geometry results in images that are symmetric with respect to the relative velocity vector. This allows for the use of inverse Abel transformation methods that enhance the resolution further. State-resolved diffraction oscillations in the differential cross sections are measured with an angular resolution approaching 0.3°. Distinct structures observed in the cross sections gauge the quality of recent ab initio potential energy surfaces for NO-rare-gas atom collisions with unprecedented precision.

Molecular collisions coming into focus.

The Stark deceleration method exploits the concepts of charged particle accelerator physics to produce beams of neutral polar molecules with an almost perfect quantum state purity, a tunable velocity and a narrow velocity distribution. These monochromatic molecular beams offer interesting perspectives for precise studies of molecular scattering processes, in particular when used in conjunction with state-of-the-art laser-based detection techniques such as velocity map imaging. Here, we describe crossed beam scattering experiments in which the Stark deceleration method is combined with the velocity map imaging technique. The narrow velocity spread of Stark-decelerated molecular beams results in scattering images with unprecedented velocity and angular resolution. We demonstrate this by resolving quantum diffraction oscillations in state-to-state inelastic differential scattering cross sections for collisions between NO radicals and rare gas atoms. We describe the future prospects of this "best-of-two-worlds" combination, ranging from scattering studies at low collision energies to bimolecular scattering using two decelerators, and discuss the challenges that lie ahead to achieve these goals.

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.

Imaging quantum stereodynamics through Fraunhofer scattering of NO radicals with rare-gas atoms.

Stereodynamics describes how the vector properties of molecules, such as the directions in which they move and the axes about which they rotate, affect the probabilities (or cross-sections) of specific processes or transitions that occur on collision. The main aspects of stereodynamics in inelastic atom-molecule collisions can often be understood from classical considerations, in which the particles are represented by billiard-ball-like hard objects. In a quantum picture, however, the collision is described in terms of matter waves, which can also scatter into the region of the geometrical shadow of the object and reveal detailed information on the pure quantum-mechanical contribution to the stereodynamics. Here we present measurements of irregular diffraction patterns for NO radicals colliding with rare-gas atoms that can be explained by the analytical Fraunhofer model. They reveal a hitherto overlooked dependence on (or 'propensity rule' for) the magnetic quantum number m of the molecules, and a previously unrecognized type of quantum stereodynamics that has no classical analogue or interpretation.

Optimal beam sources for Stark decelerators in collision experiments: a tutorial review.

With the Stark deceleration technique, packets of molecules with a tunable velocity, a narrow velocity spread, and a high state purity can be produced. These tamed molecular beams find applications in high resolution spectroscopy, cold molecule trapping, and controlled scattering experiments. The quality and purity of the packets of molecules emerging from the decelerator critically depend on the specifications of the decelerator, but also on the characteristics of the molecular beam pulse with which the decelerator is loaded. We consider three frequently used molecular beam sources, and discuss their suitability for molecular beam deceleration experiments, in particular with the application in crossed beam scattering in mind. The performance of two valves in particular, the Nijmegen Pulsed Valve and the Jordan Valve, is illustrated by decelerating ND 3 molecules in a 2.6 meter-long Stark decelerator. We describe a protocol to characterize the valve, and to optimally load the pulse of molecules into the decelerator. We characterize the valves regarding opening time duration, optimal valve-to-skimmer distance, mean velocity, velocity spread, state purity, and relative intensity.

Imaging resonances in low-energy NO-He inelastic collisions.

In molecular collisions, resonances occur at specific energies at which the colliding particles temporarily form quasibound complexes, resulting in rapid variations in the energy dependence of scattering cross sections. Experimentally, it has proven challenging to observe such scattering resonances, especially in differential cross sections. We report the observation of resonance fingerprints in the state-to-state differential cross sections for inelastic NO-He collisions in the 13 to 19 centimeter(-1) energy range with 0.3 centimeter(-1) resolution. The observed structures were in excellent agreement with quantum scattering calculations. They were analyzed by separating the resonance contributions to the differential cross sections from the background through a partitioning of the multichannel scattering matrix. This revealed the partial-wave composition of the resonances and their evolution during the collision.

State-resolved diffraction oscillations imaged for inelastic collisions of NO radicals with He, Ne and Ar.

Just as light scattering from an object results in diffraction patterns, the quantum mechanical nature of molecules can lead to the diffraction of matter waves during molecular collisions. This behaviour manifests itself as rapid oscillatory structures in measured differential cross-sections, and such observable features are sensitive probes of molecular interaction potentials. However, these structures have proved challenging to resolve experimentally. Here, we use a Stark decelerator to form a beam of state-selected and velocity-controlled NO radicals and measure state-to-state differential cross-sections for inelastic collisions of NO with He, Ne and Ar atoms using velocity map imaging. The monochromatic velocity distribution of the NO beam produced scattering images with unprecedented sharpness and angular resolution, thereby fully resolving quantum diffraction oscillations. We found excellent agreement with quantum close-coupling scattering calculations for these benchmark systems.