Resonant states are multiply excited states in atoms and ions that have enough energy to decay by emitting an electron. The ability to emit an electron and the strong electron correlation (which is extra strong in negative ions) makes these states both interesting and challenging from a theoretical point of view. The main contribution in this thesis is a method, which combines the use of B splines and complex rotation, to solve the three-electron Schrödinger equation treating all three electrons equally. It is used to calculate doubly excited and triply excited states of 4S symmetry with even parity in He-. For the doubly excited states there are experimental and theoretical data to compare with. For the triply excited states there is only theoretical data available and only for one of the resonances. The agreement is in general good. For the triply excited state there is a significant and interesting difference in the width between our calculation and another method. A cause for this deviation is suggested. The method is also used to find a resonant state of 4S symmetry with odd parity in H2-. This state, in this extremely negative system, has been predicted by two earlier calculations but is highly controversial. Several other studies presented here focus on two-electron systems. In one, the effect of the splitting of the degenerate H(n=2) thresholds in H-, on the resonant states converging to this threshold, is studied. If a completely degenerate threshold is assumed an infinite series of states is expected to converge to the threshold. Here states of 1P symmetry and odd parity are examined, and it is found that the relativistic and radiative splitting of the threshold causes the series to end after only three resonant states. Since the independent particle model completely fails for doubly excited states, several schemes of alternative quantum numbers have been suggested. We investigate the so called DESB (Doubly Excited Symmetry Basis) quantum numbers in several calculations. For the doubly excited states of He- mentioned above we investigate one resonance and find that it cannot be assigned DESB quantum numbers unambiguously. We also investigate these quantum numbers for states of 1S even parity in He. We find two types of mixing of DESB states in the doubly excited states calculated. We also show that the amount of mixing of DESB quantum numbers can be inferred from the value of the cosine of the inter-electronic angle. In a study on Li- the calculated cosine values are used to identify doubly excited states measured in a photodetachment experiment. In particular a resonant state that violates a propensity rule is found.

This thesis presents quantum chemical calculations, applications of the response function formalism recently implemented within the framework of density functional theory by our research group. The purpose of the calculations is to assess the performance of this perturbative approach to determining heavy atom effects on magnetic resonance parameters. Relativistic corrections can be generated by spin-orbit interactions or by scalar relativistic effects due to high velocity electrons in the atomic core region of heavy atoms. In this work, the evaluation of nuclear magnetic resonance parameters is considered, the nuclear shielding tensor and the indirect nuclear spin-spin coupling tensor. For series of homologous compounds, it is found that both types of corrections to these parameters are increasing in size upon substitution of a constituent atom by a heavier element, but that their relative importance is system dependent. The obtained results are compatible with the ones provided by electron correlated ab initio methods, and a qualitative agreement with experimentally determined parameters is overall achieved. The methodology presented in this thesis aims to be a practical approach which can be applied in the study of molecular properties of large systems. This thesis also addresses the calculation of hyperfine coupling constants, and evaluates a novel approach to the treatment of spin-polarization in spin restricted calculations without the spin contamination associated with spin unrestricted calculations / QC 20100811

We look at the theory of ionization of atoms and molecules in the presence of a strong laser field. The history of ionization of atoms is reviewed and the methods used to calculate the ionization rates are examined in detail. In particular the quasi-classical methods used to solve for atomic rates are examined in detail. Early work on the ionization of molecules is also examined. A new method of calculating ionization rates is developed which allows for clear, analytic descriptions of atoms and molecules in intense light fields. The results and implications of this new theory are also examined in both atoms and molecules. The results are compared against known analytic results in the case of atoms and against numerical computation for molecules. Finally, applications of the study of atoms and molecules in intense fields are examined. We show how processes such as high harmonic generation and laser induced electron diffraction occur in strong fields and give an overview of the current state of the art and likely goals for the future. The process of laser induced electron diffraction is given close examination and ways of optimizing the diffraction patterns are discussed. The use of two-color orthogonal fields is shown to greatly increase contrast and efficiency when the carrier phases are tuned correctly.

The ACME collaboration aims to measure the eEDM via Ramsey spectroscopy of a cryogenic beam of ThO molecules in their metastable H state. This thesis describes the launch of this new experimental effort. A set of diode lasers has been built to address all the necessary ThO transitions. The laser frequencies were stabilized to a stable reference laser via a \(Fabry-P\acute{e}rot\) transfer cavity. A measurement of the magnetic dipole moment of the H state has been performed that is complementary to a previous measurement by the collaboration. This value is important for determining the sensitivity of the H state to magnetic fields, which can be a source of noise and systematic errors in the eEDM measurement. Experimental efforts to prepare the coherent superposition of the \(M = \pm1\) Zeeman sublevels in the H,J = 1 state that is the starting point of the eEDM experiment using transitions to the G state resulted in a better understanding of transitions between \(\Omega\)-doublet states in an electric field. This led to a new technique for normalizing out shot-to-shot fluctuations in the molecular beam flux, which has also been demonstrated experimentally. / Physics

Many bulk properties of gases depend linearly on the gas density at lower densities, but as the density increases departures from linearity are observed. The density dependence of a bulk property Q may often be discussed systematically by expanding Q as a power series in l/Vm, to yield: Q=Aq+Bq/Vm+Cq/V2m+..., where Bq is known as the second virial coefficient of the property Q. Aq is the ideal gas value of Q, and Bq describes the contribution of molecular pair interactions to Q. Theories of Q may be regarded as having two main components, one describing how the presence of a neighbour of a given molecule can enhance or detract from its contribution to Q, and the other the molecular interaction energy which determines the average geometry of a pair encounter. The latter component is common to all theories, and the former requires detailed derivations for each specific bulk property Q. In this work we consider the second virial coefficients of five effects, namely the second pressure virial coefficient B(T), and also the second dielectric, refractivity, Kerr-effect and light-scattering virial coefficients, Be, Br, Bk, and Bp, respectively. Using a powerful computer algebraic manipulation package we have extended the existing dipole-induced-dipole (DID) theories of the second dielectric, refractivity and Kerr-effect virial coefficients to sufficiently high order to establish convergence in the treatment of both linear and non-linear gases. Together with the established linear theory of the second pressure virial coefficient, the extended theory of the second light- scattering virial coefficient developed by Couling and Graham, and their new non-linear theory of the second pressure and light-scattering virial coefficients, our new theories provide a comprehensive base from which to calculate numerical values for the various effects for comparison with experiment. We have collected as much experimental data of the various second virial coefficients as possible, for a wide range of gases. The ten gases chosen for detailed study comprise a selection of polar and non-polar, linear and non-linear gases: the linear polar gases fluoromethane, trifluoromethane, chloromethane and hydrogen chloride; the non-polar linear gases nitrogen, carbon dioxide and ethane; the non-linear polar gases sulphur dioxide and dimethyl ether; and the non-linear non-polar gas ethene. Using the best available measured or calculated molecular parameter data for these gases, together with the complete theories for the second virial coefficients, we have attempted to find unique sets of molecular parameters for each gas which explain all the available experimental data. In general, reliable measured or calculated molecular properties are regarded as fixed, and only the Lennard-Jones and shape parameters in the molecular interaction energy are treated as best-fit parameters within the constraints of being physically reasonable. Many of the apparent failures of second virial coefficient theories have been due to the lack of convergence in the series of terms evaluated. It is essential to work to sufficiently high orders in the polarizabilities and various multipole moments to ensure convergence for meaningful comparison with experiment. This often requires the manipulation of extremely long and complicated expressions, not possible by the manual methods of our recent past. The advent of computer manipulation packages and fast processors for numerical integration have now enabled calculation to high orders, where the degree of convergence can be sensibly followed. Our efforts to describe all of the effects for which data is available met with mixed success. For four of the gases, fluoromethane, chloromethane, dimethyl ether and ethene, a unique parameter set was found for each which described all of the available effects reasonably well. For the three gases, trifluoromethane, nitrogen and sulphur dioxide, one interaction parameter set explained all but one of the effects for which data was available to within experimental uncertainty. For trifluoromethane the parameter set which yielded good agreement for B(T), Be, and Bk could not explain the observed values of Br, while for nitrogen one parameter set produced reasonable agreement for all of the effects except Bp and a different set, which yielded good agreement for Bp, did not explain the remaining four effects as well as the first set. The parameter set which explained B(T), Bk and Bp very well for sulphur dioxide, yielded a value for Be, which was much larger than the experimental value, although of the correct sign and order of magnitude. Hydrogen chloride posed a special problem as data was only available for two of the effects, B(T) and Be. It was possible to find a set of interaction parameters in good agreement with the measured values of B(T), but the experimental data for Be was an order of magnitude larger than the largest calculated values. Since the remaining effects have not been measured for this gas it was not possible to test the theory more rigorously. For the remaining gases carbon dioxide and ethane, it was impossible, based on the existing measured values, to select a unique parameter set which explained all of the effects. In many of the cases where definite conclusions could not be drawn, it was not possible to decide whether the disagreement between theory and experiment was due to the large scatter and uncertainty of the experimental data or failure of the theory. However, there were very few instances of complete failure of the theory to explain experiment, and no one effect showed consistent disagreement, so that in general it may be said that the mechanisms of the second virial coefficients under study are reasonably well understood. It would require more precise measurements of the various effects, as well as more measured or calculated molecular property tensor components, such as the hyperpolarizability and the A- and C-tensors , to test the DID molecular interaction model more stringently. / Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 1997.

The molecular theory of the second light-scattering virial coefficient Bp describing the effects of interacting pairs of molecules on the depolarization ratio p of Rayleigh-scattered light is reviewed, both for interacting linear and nonlinear molecules. The molecular tensor theory of Bp for nonlinear molecules is extended for the first time to include in the scattered intensity p those contributions arising from field gradient effects and induced quadrupole moments in the molecular interactions. The expressions for contributions to Bp are evaluated numerically for the nonlinear polar molecule dimethyl ether. We have used an existing light-scattering apparatus to investigate the pressure-dependence of the depolarization ratio p for dimethyl ether, allowing Bp to be extracted. The measured value is compared with the calculated value, theory and experiment being found to agree to within 9%. This success in modelling Bp for dimethyl ether spurred us on to extend our investigation to the second Kerr-effect virial coefficient BK • The molecular-tensor theory of BK for nonlinear molecules is reviewed, and is applied in this work to dimethyl ether. The calculated BK values generally lie within the uncertainty limits of the available measured data over their full range of temperatures. We have used a recently-commissioned Kerr cell to undertake our own measurement of BK for dimethyl ether at room temperature. This value is in good agreement with the findings of our molecular model, and is in reasonable agreement with the other measured data. This thesis serves to reaffirm recent claims that comprehensive dipole-induced-dipole theories of molecular interaction effects explain the observed phenomena adequately provided one works to higher orders in the molecular tensors so that the series of contributing terms has converged to a meaningful numerical result, and provided the full symmetry of the molecules is allowed for. / Thesis (M.Sc.) - University of Natal, Pietermaritzburg, 2000.

We look at the theory of ionization of atoms and molecules in the presence of a strong laser field. The history of ionization of atoms is reviewed and the methods used to calculate the ionization rates are examined in detail. In particular the quasi-classical methods used to solve for atomic rates are examined in detail. Early work on the ionization of molecules is also examined. A new method of calculating ionization rates is developed which allows for clear, analytic descriptions of atoms and molecules in intense light fields. The results and implications of this new theory are also examined in both atoms and molecules. The results are compared against known analytic results in the case of atoms and against numerical computation for molecules. Finally, applications of the study of atoms and molecules in intense fields are examined. We show how processes such as high harmonic generation and laser induced electron diffraction occur in strong fields and give an overview of the current state of the art and likely goals for the future. The process of laser induced electron diffraction is given close examination and ways of optimizing the diffraction patterns are discussed. The use of two-color orthogonal fields is shown to greatly increase contrast and efficiency when the carrier phases are tuned correctly.

- / -

- / -

Neste trabalho elaboramos estudos teóricos sobre colisões frias mediadas por fótons em armadilhas magnéto-ópticas. Para isto implementamos algorítimos numéricos de alto desempenho para o cálculo das formas de linha do espectro de fotoassociação do 88Sr. O principal algorítimo utilizado foi o de Numerov renormalizado. Também foram implementados sistemas de construção dos elementos da matriz hamiltoniana para estudos de colisões atômicas levando em consideração a estrutura fina dos potenciais de interação. Por último introduzimos o método de Monte Carlo de Integrais sobre Trajetórias como ferramenta para o estudo da termodinâmica do condensado de Bose-Einstein em armadilhas 2D considerando a interação entre os átomos / In this work we present theoretical studies of cold collisions mediated by photons in magneto-optical traps. We have implemented high-performance numerical algorithms to calculate the photoassociation spectral line shapes of 88Sr. We have mainly utilized the renormalized Numerov algorithm. We have also implemented schemes to write down the Hamiltonian matrix elements to study atomic collisions taking into account the fine structure of the interaction potentials. Finally, we have introduced the Path Integral Monte Carlo method as a tool for studying the thermodynamics of the Bose-Einstein condensate in two-dimensional traps, considering the binary atomic interactions