Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Also available online.

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.

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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

Master of Science / Department of Physics / Brett D. Esry / The two-state field-aligned (1-D) model has been employed to investigate the dissociation dynamics of a hydrogen molecular ion and its isotopes under the Born-Oppenheimer approximation without rotation. The emphasis of this work was on the role of mass during the dynamical dissociation processes and on the laser-induced branching ratios between different photon pathways. Firstly, we have found that scaling the pulse duration of the laser pulse, applied to H[subscript]2+ and D[subscript]2+ , by the square root of the mass ratio of these isotopes will produce similar structure in the nuclear kinetic energy release (KER) spectra. In fact, the similarity of the spectra is enhanced by including some averaging that is necessary for comparison with experiment. For this to occur, the same broad initial vibrational distribution and a short pulse are preferred. Using this scaling idea, it is possible to produce effectively shorter laser pulses by studying heavier isotopes, like D[subscript]2+. Secondly, we have demonstrated analytically and numerically that there is a carrier-envelope phase effect in the total dissociation probability (TDP) of H[subscript]2+, and this effect grows with nuclear mass. We further show that under the same laser conditions, the CEP effect in the asymmetry between breakup channels decreases with mass. Our analytic expressions enhance the idea that CEP effects can be understood as an interference between different n-photon processes. Thirdly, the trends in the dissociation dynamics of H[subscript]2+ and D[subscript]2+ in a 800nm ultra short intense laser field were demonstrated by studying the dissociation branching ratios of multiphoton processes as a function of the laser peak intensity (from 8[times]10[superscript]9 to 10[superscript]14 W/cm[superscript]2) or pulse length (5fs-7.5fs). Based on the two-state approximation, an energy-analysis method (EAM) was employed to separate multiphoton processes. The results show that the one-photon dissociation process dominates over all other photon processes under all the laser conditions applied in the calculations and that the zero-photon process contributes to a surprisingly large fraction of the total dissociation. Two- and three- photon dissociation are weaker processes, but become more and more important as the laser peak intensity and pulse length increases. A two-state Floquet method was used to check the accuracy of the EAM, and good agreement between the two methods was found, demonstrating the reliability of the EAM. In comparison with H[subscript]2+, D[subscript]2+ displays stronger two and three photon branching ratios (above-threshold dissociation - ATD), which can be attributed to the late arrival of D[subscript]2+ to the critical distance for ATD to occur due to its heavier mass. Therefore, this "mass" effect can be used to steer the molecular dissociation pathways.