Kinematic Apse Research Articles

Differential cross sections and collision-induced rotational alignment in inelastic scattering of NO(X) by Xe

Fully Λ-doublet resolved differential cross sections and collision-induced rotational alignment moments have been measured for the NO(X)–Xe collision system at a collision energy of 519 cm−1. The experiments combine initial quantum state selection, employing a hexapole inhomogeneous electric field, with quantum state resolved detection, using (1+1′) resonantly enhanced multiphoton ionization and velocity map ion imaging. The differential cross sections and polarization dependent differential cross sections are shown to agree well with quantum mechanical scattering calculations performed on ab initio potential energy surfaces [J. Kłos et al. J. Chem. Phys. 137, 014312 (2012)]. By comparison with quasi-classical trajectory calculations, quantum mechanical scattering calculations on a hard-shell potential, and kinematic apse model calculations, the effects of the attractive part of the potential on the measured differential cross sections and collision-induced rotational alignment moments are assessed.

Rotational alignment effects in NO(X) + Ar inelastic collisions: A theoretical study

Rotational angular momentum alignment effects in the rotational inelastic scattering of NO(X) with Ar have been investigated by means of close-coupled quantum mechanical, quasi-classical trajectory, and Monte Carlo hard shell scattering calculations. It has been shown that the hard shell nature of the interaction potential at a collision energy of Ecoll = 66 meV is primarily responsible for the rotational alignment of the NO(X) molecule after collision. By contrast, the alternating trend in the quantum mechanical parity resolved alignment parameters with change in rotational state Δj reflects differences in the differential cross sections for NO(X) parity conserving and changing collisions, rather than an underlying difference in the collision induced rotational alignment. This suggests that the rotational alignment and the differential cross sections are sensitive to rather different aspects of the scattering dynamics. The applicability of the kinematic apse model has also been tested and found to be in excellent agreement with exact quantum mechanical scattering theory provided the collision energy is in reasonable excess of the well depth of the NO(X)-Ar potential energy surface.

A general scaling rule for the collision energy dependence of a rotationally inelastic differential cross-section and its application to NO(X) + He

The quasi-quantum treatment (QQT) (Gijsbertsen et al., J. Am. Chem. Soc., 2006, 128, 8777) provides a physically compelling framework for the evaluation of rotationally inelastic scattering, including the differential cross sections (DCS). In this work the QQT framework is extended to treat the DCS in the classically forbidden region as well as the classically allowed region. Most importantly, the QQT is applied to the collision energy dependence of the angular distributions of these DCSs. This leads to an analytical formalism that reveals a scaling relationship between the DCS calculated at a particular collision energy and the DCS at other collision energies. This scaling is shown to be exact for QM calculated or experimental DCSs if the magnitude of the (kinematic apse frame) underlying scattering amplitude depends solely on the projection of the incoming momentum vector onto the kinematic apse vector. The QM DCSs of the NO(X)-He collision system were found to obey this scaling law nearly perfectly for energies above 63 meV. The mathematical derivation is accompanied by a mechanistic description of the Feynman paths that contribute to the scattering amplitude in the classically allowed and forbidden regions, and the nature of the momentum transfer during the collision process. This scaling relationship highlights the nature of (and limits to) the information that is obtainable from the collision-energy dependence of the DCS, and allows a description of the relevant angular range of the DCSs that embodies this information.

The k-j-j′ vector correlation in inelastic and reactive scattering

Quasi-classical trajectory (QCT) methods are presented which allow characterization of the angular momentum depolarization of the products of inelastic and reactive scattering. The particular emphasis of the theory is on three-vector correlations, and on the connection with the two-vector correlation between the initial and final angular momenta, j and j', which is amenable to experimental measurement. The formal classical theory is presented, and computational results for NO(A) + He are used to illustrate the type of mechanistic information provided by analysis of the two- and three-vector correlations. The classical j-j' two-vector correlation results are compared with quantum mechanical calculations, and are shown to be in good agreement. The data for NO(A) + He support previous conclusions [M. Brouard, H. Chadwick, Y.-P. Chang, R. Cireasa, C. J. Eyles, A. O. L. Via, N. Screen, F. J. Aoiz, and J. Kłos, J. Chem. Phys. 131, 104307 (2009)] that this system is only weakly depolarizing. Furthermore, it is shown that the projection of j along the kinematic apse is nearly conserved for this system under thermal collision energy conditions.

Collisional angular momentum depolarization of OH(A) and NO(A) by Ar: A comparison of mechanisms

This paper discusses the contrasting mechanisms of collisional angular momentum depolarization of OH(A(2)Σ(+)) and NO(A(2)Σ(+)) by Ar. New experimental results are presented for the collisional depolarization of OH(A) + Ar under both thermal and superthermal collision conditions, including cross sections for loss of both angular momentum orientation and alignment. Previous work on the two systems is summarized. It is shown that NO(A) + Ar depolarization is dominated by impulsive events in which the projection of the angular momentum, j, along the kinematic apse, a, is nearly conserved, and in which the majority of the trajectories can be described as "nearside." By contrast, at the relatively low collision energies sampled at 300 K, OH(A) + Ar depolarization is dominated by attractive collisions, which show a preponderance of "farside" trajectories. There is also evidence for very long-lived, complex type trajectories in which OH(A) and Ar orbit each other for several rotational periods prior to separation. Nevertheless, there is still a clear preference for conservation of the projection of j along the kinematic apse for both elastic and inelastic collisions. Experimental and theoretical results reveal that, as the collision energy is raised, the depolarization of OH(A) by Ar becomes more impulsive-like in nature.

Two-photon spectroscopy of aligned acetaldehyde

We reinvestigate the two-photon absorption of the (3s-n) transition in acetaldehyde and its implications for the observation of collision-induced alignment. The two-photon spectroscopy of an aligned ensemble of acetaldehyde produced in collisions with He provides clear evidence for the quantum interference of tensors of different rank. The observed polarization effect can be understood in terms of the non-vanishing tensor components Z 0 (0)=1.0, Z 0 (2)=0.4±0.1 and | Z ±2 (2)|=0.3±0.1. For a collision energy of 916 cm −1, the alignment is largely consistent with the predictions of the kinematic apse model.

REMPI detection of alignment in NO collisions

Abstract The detection of collision induced alignment in ensembles of NO molecules scattered from He or Ne is investigated. The alignment is probed through (2 + 1) resonance enhanced multiphoton ionization of NO via different Rydberg states: E 2 Σ , F 2 Δ , and H 2 Σ , H ′ 2 Π . Transitions belonging to the first two electronic systems yield identical polarization effects consistent with the fact that the two-photon transition is characterized by a single second rank tensor component Z (2) ±1 . The electronic system involving the H-state is considerably more complicated because of the state mixing due to L-uncoupling and the simultaneous presence of zeroth and second rank tensor components for the two-photon transition. Alignment moments extracted from TOF spectra measured through different electronic systems are identical within the experimental uncertainty. The alignment is consistent with predictions of either the kinematic apse or the geometric apse models. These models indicate further that higher moments have a negligible influence on the polarization effect if the alignment is derived from spectra measured with laser light polarized parallel and perpendicular to the molecular beam axis.

Ion imaging measurement of collision-induced rotational alignment in Ar-NO scattering

Collision-induced rotational alignment of NO X 2Π1/2(v=0,j=8.5) is measured for rotationally inelastic scattering of NO X 2Π1/2(v=0,j=0.5) with Ar at 65 meV collision energy. The experiments are performed by velocity-mapped ion imaging with polarized 1+1′ REMPI probing of the scattered NO products. It is shown that the azimuthal information intrinsic to imaging detection allows the measurement of additional alignment moments not previously reported. The measured alignment shows only qualitative agreement with the predictions of the kinematic apse conservation model.

Polarization of emission from asymmetric rotors. II. Vector reorientation through intramolecular coupling and inelastic collisions

We report measurements of the linear and circular polarization ratios from fully resolved rotational levels of the asymmetric rotor NH2 populated by collisions with H atoms. The results compare well with a theoretical model that includes the depolarizing effects of intramolecular coupling of rotational angular momentum N to nuclear and to electron spin. These have a very significant influence on fluorescence polarization. The model also incorporates the tilting of the N vector in the molecule frame that occurs when inter-k stack transitions take place. Changes in N vector orientation are described with the aid of the angular momentum sphere, a classical representation of the motion of the N vector in a molecule fixed frame. The theoretical treatment assumes the classically impulsive limit for the collisional interaction with conservation of the m quantum number along the kinematic apse. This description of the fate of the N vector under the influence of intra- and intermolecular interactions allows stereodynamical conclusions to be drawn from experimental observations of fluorescence polarization.

Polarization ratio velocity dependence dips: A collision frame model relating spectroscopic observables to the differential cross section

We present a model that accounts for the observation described in the first paper of this series (I) of a dip in the polarization ratio profile observed in certain rotationally inelastic processes as a narrow line laser is tuned across the Doppler profile. The model is based on conservation of the projection of j along the kinematic apse [Khare, Kouri, and Hoffmann, J. Chem. Phys. 74, 2275 (1981)], a consequence of rotational angular momentum transfer in the impulsive limit. As an illustration, we present calculations of lab frame observations expected for several examples of scattering behavior in the collision frame and conclude that information on the state-to-state differential scattering cross section is contained in the polarization profile. We display a number of figures that make explicit the relationship between the relative momentum and rotational angular momentum vectors in the experiment and illustrate the ‘‘stereochemical dynamics’’ responsible for the polarization dip.

Propensities for preserving polarization in rotationally inelastic He-O2collisions

The occurrence of M-preserving propensities is investigated in He-O2 rotationally inelastic collisions. Close-coupling calculations are used to obtain the M-dependent integral cross sections in several common quantization frames. A strong propensity for conserving e/f symmetry in JM = 0ε → J′M′ = 0ε′ transitions is observed regardless of the quantization frame. The polarized cross sections in the kinematic and geometric apse frames (as defined by Khare et al.) are found to be almost diagonal in M. It is argued that this approximate δM = 0 selection rule in both apse frames is due to the dominance of large-angle scattering which occurs if the significant atom-molecule interaction is strongly repulsive.

Born approximation for collisional alignment

It is shown that the first order Born approximation is in qualitative agreement with many of the experimental observations on the angular momentum alignment of Na 2 molecules produced during collisions with He. A model for certain aspects of the second order Born approximation is introduced which is able to predict the observed deviation of the orientation of the alignment from being directed along the kinematic apse. As well, exact expressions for the alignment cross section are given in terms of reduced T-matrix elements.

M-preserving propensities for rotationally inelastic NH3-He collisions. In the kinematic apse frame

Abstract Semiclassical calculations are used to obtain integral cross sections in both the initial velocity, or collision-fixed, frame and the kinematic apse frame (defined by Khare et al.) for rotational excitation in the NH 3 -He system at a collision energy of 100 cm − . A comparison with earlier close-coupling calculations in the initial velocity frame. using the same interaction potential, shows that the semiclassical method predicts relative M -dependence quite accurately. The kinematic apse cross sections, unlike those in the initial velocity frame, are highly diagonal in the quantum number M . An examination of the M -dependent transition probabilities as a function of impact parameter indicates that the propensity for conservation of M in the kinematic apse frame is due to the dominance of backward, or high-angle, scattering in the cross section. The propensity for conservation of M breaks down for large impact parameters where the interaction is attractive.

The kinematic apse and j z-preserving propensities for nonreactive, dissociative, and reactive polyatomic collisions

We consider the generalization of the kinematic apse to nonreactive polyatom–polyatom impulsive collisions, dissociative atom–molecule impulsive collisions, and (partially) impulsive reactive atom–diatom collisions. Appropriate generalizations of the kinematic apse are obtained along which there is a classical propensity for preserving the projection of the total intrinsic spin. In the case of reactive scattering, we discuss several different situations for which such a propensity occurs. For reactive systems in which no such propensity exists, the analysis may still provide a basis for classifying reactions.

On j z-preserving propensities in molecular collisions. I. Quantal coupled states and classical impulsive approximations

The occurrence of jz-preserving propensities in atom–linear molecule collisions is considered within the contexts of the quantum mechanical CS approximation and of a classical model collision system. The latter involves an impulsive interaction which is the extreme limit of the class of potentials for which the CS approximation is expected to be valid. The classical model results in exact conservation of jz along a ’’kinematic apse.’’ Quantum mechanically, the CS approximation is reformulated in a manner that clearly shows the relationship between the ℓ̄ choice and the degree and direction of jz preservation. Away from the forward direction, the simplest choice obeying time reversal symmetry ℓ̄=(ℓ+ℓ′)/2, is shown to result in a propensity for preserving jz along a ’’geometric apse’’ which coincides with the kinematic apse in the energy sudden limit, and for nonenergy sudden systems only differs significantly from it close to the forward direction.