An experimental and theoretical study of the dynamics of atom-molecule scattering
Keywords: inelastic
scattering
collisions
reaction dynamics

In this thesis, a joint experimental and theoretical study of the dynamics of atom- molecule collisions will be presented. The focus of this study will be conducted towards the precise, quantitative theoretical description of the collision dynamics in terms of the vectors k, k', j, and j' (the incoming and outgoing relative momenta associated with the collision, and the initial and final rotational angular momentum of the target diatom respectively) that define the collision, and on the experimental measurement of these vector correlations.
Chapter 1 is introductory, providing an overview of the field of reaction dynamics, and the experimental and theoretical methods that exist to treat the collisions of atoms and molecules. This work focusses on the collisions of the spherically symmetric rare gas atoms Ar and He with the open-shell heteronuclear diatomic radicals NO and OH. In particular, the fully quantum state-to-state resolved differential cross-sections for the collisions of NO(X) with Ar (reflecting the k - k' vector correlation), and the collisional cross-sections for the depolarisation of the rotational angular momenta of the NO(A) and OH(A) radicals (reflecting the j - j' vector correlation) have been determined experimentally and theoretically, and the results have been discussed and interpreted in terms of the mechanistic aspects of the collision dynamics, and the features of the potential energy surface that give rise to these.
In Chapter 2, the atom-molecule systems that constitute the subject of this work will be introduced in detail. The close-coupled quantum mechanical and quasi-classical trajectory scattering calculations performed as part of this work will be discussed in greater detail, providing a greater insight into molecular scattering theory. The explicit calculation of the quantities of interest (most significantly the differential cross-section, and the tensor/depolarisation cross-sections) will be presented for the quasi-classical and quantum cases, offering the most transparent definitions of these quantities. Finally the mathematical description of the spatial probability distribution of a single vector, a pair of correlated vectors, and three correlated vectors is described in detail, including a discussion of the quantum mechanical nature of the vectors in question.
Chapter 3 describes the experimental measurement of the differential cross-sections for the collisions of NO(X) with Ar. A hexapole was used to select uniquely those NO molecules in the |Ω = 0.5; j = 0.5, f> quantum state, allowing full experimental quantum state-to-state selection for the first time. A crossed molecular beam apparatus with (1+1') resonantly enhanced multi-photon ionisation detection coupled with velocity mapped ion- imaging was employed to measure the differential cross-section, and the details of the experimental set-up are provided. The accurate extraction of the true, centre of mass frame differential cross-section from the laboratory frame information yielded by the experiment is something of an involved process, and much of this Chapter will be concerned with the development of a Monte Carlo method to achieve this end.
In Chapter 4, the experimental and theoretical fully quantum state-to-state resolved differential cross-sections for the collisions of NO(X) with Ar are presented, having been measured for the first time. Full resolution of the initial parity of the rotational wave- function of the NO molecule has enabled the observation of parity dependent structures within the differential cross-section, and the origin of these structures has been investi- gated, employing quasi-classical, quantum mechanical and semi-classical methods in order to elucidate the mechanism by which they arise.
Chapter 5 introduces the measurement of the collisional depolarisation of the rotational angular momentum of the diatom. Rate constants for the collisional depolarisation of j were measured by monitoring the time dependence of the amplitude of Zeeman and hyperfine quantum beats in the (1+1) laser induced fluorescence decays of an ensemble of NO(A) or OH(A) radicals in the presence of a series of background pressures of a collision partner. The creation and subsequent evolution of the polarisation of j induced by the absorption of polarised laser light is described, and the magnitude of this polarisation is linked to the amplitude of the quantum beat in the laser induced fluorescence decay. The extraction of the depolarisation cross-sections from the raw experimental data is discussed, and a Monte Carlo simulation of the experiment is described to account for any additional unwanted experimental factors that may contribute to the loss of polarisation of j. A formalism is also introduced that makes use of the tensor opacities to recover spin- rotation conserving and spin-rotation changing open-shell rotational energy transfer and depolarisation cross-sections from the intrinsically closed shell quasi-classical trajectory scattering calculations.
In Chapter 6, the experimentally determined collisional depolarisation cross-sections for the collisions of NO(A) with He/Ar, and of OH(A) with Ar at collision energies of 39 meV/757meV are presented along with their theoretical counterparts. The relative magnitudes of the cross-sections are rationalised in terms of the potential energy surface over which the collision takes place, and the importance of spin-rotation conserving and spin-rotation changing transitions in the depolarisation process is assessed. A detailed study of the ensemble of quasi-classical trajectories is performed to determine the character of the various atom-molecule collisions, and to identify which conditions lead to the most efficient depolarisation of j. The relative importance of the potential energy surface and the collision kinematics is also assessed at this point.
The results presented in this thesis thus investigate two complementary expressions of the collision dynamics, the k - k' and j - j' vector correlations, and encompass a variety of collision partners exhibiting vastly differing collision characteristics. As such, this work serves as an illustrative overview of atom-molecule scattering dynamics, containing both experimental and theoretical reflections of the collision dynamics, and relating this information back to the fundamentals of scattering theory.