Thesis (Ph. D.)--University of Wisconsin--Madison, 1954. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1959. / Typescript with manuscript equations. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

<p dir="ltr">Complex physical systems provide a fertile ground for exploring various phenomena owing to the quantum nature inherent in their structure. Atoms and molecules not only serve as realistic systems for experimental investigation, but also exhibit a complexity stemming from their many-body interactions which is of significant theoretical interest. This thesis delves into the domain of ultracold collisions between different interacting species (where temperature T < 1mK), and introduces novel applications for probing such systems, particularly focusing on molecular formation via photoassociation. Molecular interactions, in comparison to their atomic counterparts, present heightened complexity. The interplay of electrostatic forces among electrons and nuclei intricately couples all degrees of freedom within a single molecule. Historically, the exploration of quantum dynamics between molecules was pioneered by Born and Oppenheimer. Their seminal work involved solving Schrödinger’s equation in two steps. First step is addressing a portion of the molecular Hamiltonian where the nuclei are clamped in space (adiabatic). This adiabatic solution yields effective potentials between nuclei, encapsulating the integrated influence of the surrounding electronic cloud. The second step is to solve for the nuclear degrees of freedom in the vicinity of the effective potentials. The validity of the Born-Oppenheimer approximation stems from the substantial mass disparity between electrons and nuclei, enabling a quasi-separation of the electronic and nuclear Hamiltonians. The first order Born-Oppenheimer approximation assumes a partial separation of the molecular wave function Ψmolecule ≈ ΞvibrationYrotationalΦelectronic.</p><p dir="ltr"> A comprehensive treatment is provided for systems with numerous degrees of freedom, elucidating how the Born-Oppenheimer approximation manifests when applied to molecules. This chapter also encapsulates the principal findings from collision theory and photoassociation spectroscopy, as well as foundational techniques underpinning this thesis. Spectroscopic investigations encompass four relevant transition types: boundbound (Rabi oscillations), bound-free (photoionization), free-free (elastic scattering), and free-bound (photoassociation) transitions. Photoassociation (PA) spectroscopy probes laserinduced processes where the reactants interact through a channel |i〉, and can absorb one or more photons causing a transition to a bound state in an excited channel |f〉. The excited complex usually decays with a high probability to the ground state of the formed molecule. The same process can be utilized experimentally to prepare a cold molecule in its vibrational ground state . Diatomic PA has been of great theoretical and experimental interest in recent years. Herein, we present a theoretical inquiry into photoassociation within triatomic systems, with a particular focus on alkali atom-dimer systems, and introduce a method for calculating PA rates.</p><p dir="ltr">Moreover, this thesis presents different methods for shielding polar molecules from their short-range interactions where inelastic collisions and chemical reactions can occur with high probability. Shielding polar molecules has been shown to suppress inelastic collisions substantially between two molecules. A technique to shield two polar molecules in their ground state is studied and applied to model collisions in a gas of ground state (NaCs) molecules at temperatures T ≈ 100nK. The results show a region of interactions between two polar molecules that has an extremely long-range nature and is well isolated from the short-range losses, allowing for long-range spectroscopic studies. A new long-range regime of molecular physics arises in the study of shielded molecules where long-range vibrational tetramer states form. Different tetramer formation pathways are studied within a range of different shielding parameters. In fact, microwave shielding provides a region to study collisions between polar molecules, and controls their dynamics without worrying about shortrange losses. It has also been applied in the observation of a Bose gas of polar molecules.</p>

Rotational polarisation effects have been investigated in the rotationally inelastic collisions of NO(X) and Ar by means of theoretical and experimental methods. Rotational polarisation describes the correlation between the <strong>k</strong>–<strong>k'</strong>–<strong>j'</strong> vectors, that is the initial and final relative velocities of the colliding partners and the final rotational angular momentum of the diatom, respectively. The simplest types of polarisation are the rotational orientation, or preferred sense of rotation, and the rotational alignment, or preferred plane of rotation. They are quantised by the renormalised polarisation dependent differential cross sections (PDDCSs) In this thesis the theoretical methods included exact quantum mechanical, quasi- classical trajectory and Monte Carlo classical hard shell calculations. Various features of the interaction potential influence differently the polarisation dynamics. The effects of attraction and soft repulsion were elucidated employing a number of differently modified potentials. The rotational alignment is primarily determined by a classical impulsive, or hard shell mechanism at a collision energy of 66 meV. The attractive and soft repulsive forces only perturb this underlying mechanism. On the other hand, the parity dependent oscillations of the open shell alignment moments are due to differences between the quantum mechanical differential cross sections. It has been shown the bigger the well depth compared to the collision energy, the less applicable becomes the classical hard shell model to describe rotational alignment. The quantum mechanical rotational alignment in the collisions of hard shells was also calculated. The classical and quantum mechanical hard shell models predict different rotational alignment. Nevertheless, the classical alignment is a good approximation to the exact quantum mechanical results. The rotational orientation is much more sensitive to the details of the interaction potential. It does not exist in the classical description of hard shell collisions, if the system exhibits certain symmetry properties. The attraction and finite range repulsion break this symmetry and leads to the molecule having a preferred sense of rotation. In general there is non-vanishing rotational orientation in the collisions of a hard shell in the framework of quantum mechanics. This is due to the finite spatial and temporal interaction of the colliding partners. Quantum mechanical interference effects also play an important role in this phenomenon. The rotational alignment was experimentally determined in the collisions of NO(X) and Ar at collision energy of 66meV with a hexapole state selective ion-imaging apparatus. An algorithm was developed based on the Fourier moment analysis to extract rotational polarisation information from the experimental ion images. It is fast and robust and can also be of used to simulate experimental images. This algorithm was used to retrieve the experimental renormalised PDDCSs ion images. The measurements confirmed that a classical, impulsive dynamics is mainly responsible for the rotational alignment in these collisions.

Inelastic collisions between dipolar molecules, assumed to be trapped in a static electric field at cold (> 10−3K) temperatures, are investigated and compared with elastic collisions. For molecules with a Λ-doublet energy-level structure, a dipole moment arises because of the existence of two nearly degenerate states of opposite parity, and the collision of two such dipoles can be solved entirely analytically in the energy range of interest. Cross sections and rate constants are found to satisfy simple, universal formulas. In contrast, for molecules in a Σ electronic ground state, the static electric field induces a dipole moment in one of three rotational sublevels. Collisions between two rotor dipoles are calculated numerically; the results scale simply with molecule mass, rotational constant, dipole moment, and field strength. It might be expected that any particles interacting only under the influence of the dipole-dipole interaction would show similar behavior; however, the most important and general result of this research is that at cold temperatures inelastic rate constants and cross sections for dipoles depend strongly upon the internal structure of the molecules. The most prominent difference between the Λ-doublet and rotor molecules is variation of the inelastic cross section with applied field strength. For Λ-doublet dipoles, cross sections decrease with increasing field strength. For rotor dipoles, cross sections increase proportionally with the square of field strength. Furthermore, the rate constants of the two types of molecules depend very differently on the angular orientations of the dipoles in the electric field.

Nous avons étudié les collisions réactives O(1D) + CH4 et O(1D) + H2O d’intérêt atmosphérique et astrophysique à l’aide de méthodes de chimie quantique et de dynamique réactionnelle. Pour la première réaction, des calculs de dynamique quantique à l’aide d’une méthode indépendante du temps ont été entrepris sur une surface d’énergie potentielle existante en considérant CH3 comme un pseudo-atome. Cette approche à dimensionnalité réduite, qualifiée ici de modèle pseudo-triatomique, a permis d’obtenir les probabilités de réaction à un moment angulaire total nul (J=0), puis de calculer les sections efficaces et les taux de réaction par une méthode approchée de type J-shifting. Nos résultats quantiques ont été comparés aux résultats obtenus par une méthode quasi-classique de trajectoires et aux prédictions expérimentales. Ces comparaisons ont, entre autre, validé le fait que la voie de sortie OH + CH3 était la voie principale pour cette réaction. La seconde réaction O(1D) + H2O a été abordée d’un point de vue structure électronique. Nous avons caractérisé les grandes lignes de la surface d’énergie potentielle de H2O2 en tenant compte de tous les degrés de liberté avec une méthode de calcul de haut niveau (MRCI : Multi Reference Configuration Interaction). Ainsi, nous avons pu déterminer avec une grande précision les géométries, les fréquences et les énergies des isomères du système H2O2 ainsi que son diagramme énergétique. A l’avenir, il faudra construire une surface d’énergie potentielle qui sera utilisée pour décrire la dynamique de cette réaction. / We have studied the reactive collisions, O (1D) + CH4 and O (1D) + H2O, of atmospheric and astrophysical interest, using different quantum chemistry methods and reaction dynamics approaches. For the first reaction, quantum dynamical calculations using a time-independent method were carried out on an existing potential energy surface by considering CH3 as a pseudo-atom. This reduced dimensionality approach, i.e. a pseudo triatomic model, yielded the calculation of the reaction probabilities at zero total angular momentum (J = 0). The cross sections and reaction rates have been computed by the approximate J-shifting method. Our quantum results were compared with results obtained by a quasi-classical trajectory method and experimental predictions. These comparisons, among others, have enabled the fact that the channel CH3 + OH was the main exit channel for this reaction. The second reaction O(1D) + H2O has been studied at the level of electronic structure. We have characterized the outline of the potential energy surface of H2O2 , taking into account all the degrees of freedom at a high level calculation (MRCI: Multi Reference Configuration Interaction). Thus, we were able to determine with great accuracy the geometries, frequencies and energies of isomers of the H2O2 system and its energy diagram. In the future, a potential energy surface has to be built to be used in the dynamical calculations for this reaction.

New dynamical applications of quantum beat spectroscopy (QBS) to molecular dynamics are employed to probe the angular momentum polarization effects in photodissociation and molecular collisions. The magnitude and the dynamical behaviour of angular momentum alignment and orientation, two types of polarization, can be measured via QBS technique on a shot-by-shot basis. The first part of this thesis describes the experimental studies of collisional angular momentum depolarization for the electronically excited state radicals in the presence of the collider partners. Depolarization accompanies both inelastic collisions, giving rise to rotational energy transfer (RET), and elastic collisions. Experimental results also have a fairly good agreement with the results of quasi-classical trajectory scattering calculations. Chapter 1 provides the brief theories about the application of the QBS technique and collisional depolarization. Chapter 2 describes the method and instrumentation employed in the experiments of this work. In Chapter 3, the QBS technique is used to measure the total elastic plus elastic depolarization rate constants under thermal conditions for NO(A,v=0) in the presence of He, Ar, N2, and O2. In the case of NO(A) with Ar, and particularly with He, collisional depolarization is significantly smaller than RET, reflecting the weak long-range forces in these systems. In the case of NO(A)+N2/O2, collisional depolarization and RET are comparable, reflecting the relatively strong long-range forces in these systems. In Chapter 4, the QBS technique is used to measure the elastic and inelastic depolarization and total RET rate constants for OH(A,v=0) under thermal conditions in the presence of He and Ar, as well as the total depolarization rate constants under superthermal conditions. In the case of OH(A)+He, elastic depolarization is sensitive to the N rotational state, and inelastic depolarization is strongly dependent on the collision energy. In the case of OH(A)+Ar, elastic depolarization is insensitive to N, and inelastic depolarization is less sensitive to the collision energy, reflecting that the relatively strong long-range force in OH(A)+Ar system. The second part of this thesis describes the experimental studies of photodissociation under thermal conditions. Chapter 5 provides a brief introduction about several polarization parameter formalisms used for photodissociation, and the incorporation of the QBS technique to measure these polarization parameters. In this thesis, most polarization parameters of the molecular photofragments are measured using the LIF method, and the QBS technique is used as a complementary tool to probe these polarization parameters. In Chapter 6, rotational orientation in the OH(X,v=0) photofragments from H2O2 photodissociation using circularly polarized light at 193 nm is observed. Although H2O2 can be excited to both the A and B electronic states by 193 nm, the observed orientation is only related to the A state dynamics. A proposed mechanism about the coupling between a polarized photon and the H2O2 parent rotation is simulated, and the good agreement between the experimental and simulation results further confirms the validity of this mechanism. In Chapter 7, rotational orientation in the NO(X,v) photofragments from NO2 photodissociation using circularly polarized light at 306 nm (v=0,1,2) and at 355 nm (v=0,1) is observed. Two possible mechanisms, the parent molecular rotation and the coherent effect between multiple electronic states, are discussed. NOCl is photodissociated using circularly polarized light at 306 nm, and NO(X,v) rotational distributions (v=0,1) and rotational orientation (v=0) are measured. For the case of NOCl, the generation of orientation is attributed to the coherent effect.