Master of Science / Department of Physics / Carlos Trallero / Over the past four decades, the single-electron ionization of atoms has been a subject of great interest within the ultra-fast community. While contemporary atomic ionization models tend to agree well with experiment across a wide range of intensities (10[superscript]13-10[superscript]15 W/cm[superscript]2), analogous models for the ionization of molecules are currently lacking in accuracy. The deficiencies present in molecular ionization models constitute a formidable barrier for experimentalists, who wish to model the single-electron ionization dynamics of molecules in intense laser fields. The primary motivation for the work presented in this thesis is to provide a comprehensive data set which can be used to improve existing models for the strong-field ionization of molecules. Our approach is to simultaneously measure the singly-charged ion yield of a diatomic molecule paired with a noble gas atom, both having commensurate ionization potentials. These measurements are taken as a function of the laser intensity, typically spanning two orders of magnitude (10[superscript]13-10[superscript]15 W/cm[superscript]2). By taking the ratio of the molecular to atomic yields as a function of laser intensity, it is possible to "cancel out" systematic errors which are common to both species, e.g. from laser instability, or temperature fluctuations. This technique is very powerful in our ionization studies, as it alludes to the distinct mechanisms leading to the ionization of both molecular and atomic species at the same intensity which are not a function of the experimental conditions. By using the accurate treatments of atomic ionization in tandem with existing molecular ionization models as a benchmark, we can use our experimental ratios to modify existing molecular ionization theories. We hope that the data procured in this thesis will be used in the development of more accurate treatments describing the strong-field ionization of molecules.

The electron-electron coincidence (e,2e) technique yields complete kinematical information about the electron impact ionization process. The (e,2e) technique has been widely used to study dynamical effects in ionizing collisions with atomic targets, however studies of molecular ionization using this technique have been very limited. Recently further experimental studies of small molecules have been proposed, as the cross sections of small molecules are now computable using sophisticated theoretical approaches [77, 24]. This thesis presents dynamical investigations for the electron impact ionization of the molecular targets H2O and H2, employing the (e,2e) technique to experimentally measure the triple differential cross section (TDCS). The TDCS is defined as the probability that a bound electron will be ejected from the target atom or molecule (into a particular direction with a defined energy) and the initial electron will be scattered into a particular direction with a particular energy. All TDCSs presented within this thesis were performed using an electron coincidence spectrometer in the coplanar asymmetric geometry at intermediate incident electron energies. This thesis presents the electron impact ionization TDCSs of H2O. A series of measurements were performed using H2O in the vapour form. Measurements of the TDCS are presented for the 2a1 atomic-like orbital and the 1b2, 3a1 and 1b1 molecular orbitals at a common incident electron energy of 250eV, ejected electron energy of 10eV and scattering angle of -15o. The experimental TDCSs are compared with theoretical cross sections that were calculated by Champion et al [25, 26] using a distorted wave Born approach (DWBA). TDCS measurements for the single ionization of the hydrogen molecule, H2 were performed as in recent years there has been evidence that indicates the ejected electron angular distribution is perturbed due to Young-type interference effects. The oscillatory structure which is predicted in the cross section is due to the two-centred nature of the molecule [27, 29]. This thesis presents experimental TDCSs for the ionization of H2 which are compared to TDCSs of helium. A series of measurements for the TDCSs of H2 and He are presented at a common incident electron energy of 250eV and scattering angle of -15o, for a range of ejected electron energies between 10eV and 100eV. The experimental TDCSs are compared with two types of theoretical calculations.

For the first time, a full-dimensional quantum-mechanical description of excitation, dissociation and ionization of H2+ in intense laser fields is presented. The quantum-mechanical propagation of the nuclei is carried out approximately using time-dependent Floquet surfaces and the Coulomb surface, switching between these surfaces is possible stochastically (”hopping”). The impact of quantum effects in the nuclear dynamics on dissociation and ionization as well as their interplay is investigated in detail. The results are in excellent agreement with experimental data. It is shown in particular that quantum effects in the nuclear dynamics are essential for the description and interpretation of the experiments.:1 Introduction 1 2 Theory 3 2.1 Methods for the description of H+ 3 2.2 Hopping between potential surfaces 5 2.3 Equations of motion 9 2.3.1 The classical equations of motion for the nuclei 11 2.3.2 The Schr¨odinger equation for the electronic part 12 2.3.3 The connection between classical and quantum mechanical propagation 13 2.4 Calculation and discussion of required quantities 15 2.4.1 Born-Oppenheimer states and Born-Oppenheimer surfaces 15 2.4.2 Floquet states and Floquet surfaces 16 2.4.3 Initial conditions 22 2.5 Dissociation 24 2.5.1 Hopping between Floquet surfaces 25 2.5.2 Comparison with full quantum-mechanical results 29 2.6 Ionization 32 2.6.1 Hopping to the Coulomb surface 32 2.6.2 Comparison with NA-QMD results 37 3 Application: Fragmentation dynamics of H+ in short, intense laser pulses 41 3.1 Dissociation and ionization probabilities 43 3.1.1 Time resolved probabilities 43 3.1.2 Intensity resolved probabilities 44 3.1.3 Angular resolved probabilities 48 3.2 Kinetic energy release (KER) 50 3.2.1 Angular integrated KER 50 3.2.2 Angular resolved KER 54 3.2.3 Distribution of the ionization hops 56 3.3 The role of rotationally excited initial conditions 57 3.4 Comparison with experimental data 61 3.4.1 Dissociation KER 62 3.4.2 Angular distribution of dissociating fragments 64 3.4.3 ionization KER 65 Summary, conclusion, and outlook 67 Appendices 69 Bibliography 83