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<p>This dissertation discusses theoretical methods for describing photoionization in different systems in the context of time-dependent and time-independent non-relativistic and time-independent relativistic systems. We introduce a multichannel quantum defect theory (MQDT) model for describing photoionization in the context of pump-probe experiments. The basics of MQDT are introduced and specialized to the argon atom. Two energy regimes are studied in detail and compared to the experiment: (i) a perturbative calculation describing the dynamics of an autoionizing wave packet, (ii) a time-resolved calculation describing the two-photon ionization of a deeply bound wave packet. In both cases, the model accurately describes the relative ionization with respect to the two spin-orbit split thresholds of the ion and the oscillations shown in the delay between the pump and probe. We finalize with a brief presentation, which is primarily pedagogical, of how to use MQDT inside a finite box.</p> <p>Next, we use MQDT to describe the ytterbium atom in different energy regimes and varying degrees of approximation. The motivation behind this lies in the context of quantum information science, but our study is only concerned with calculating atomic properties. We start with a minimal MQDT model to describe the data observed in the experiment, followed by the presentation of an ab initio two-electron model. Both models compare very well to the experiment, and the ab initio method compares favorably with older spectroscopic results. In addition, we show unpublished results that incorporate the hyper-fine effects into the approximate model.</p> <p>Finally, we present an implementation of the two-electron variational R-matrix method for the Dirac equation, including the complete derivation of the solution of the Dirac equation in a central potential. We provide explicit analytic forms for the solutions of the Coulomb potential and use them to derive the generalized quantum defect parameters. A discussion of the variational R-matrix method for the Dirac equation in single and multichannel contexts is presented, with sample calculations for the beryllium and radium atoms. A chapter that summarizes and points to future work for each one of the projects concludes the work.</p>

Deux stratégies sont présentées à utiliser des effets de couplage de modes pour l’amplification de l’atténuation du son dans les conduits acoustiques. La première est de coupler le mode incident propagatif avec un mode localisé, aussi appelé résonance de Fano. Cette stratégie est présentée et validée dans un système conduit-cavité et un guide d’onde partiellement traité en paroi avec un matériau à réaction locale. La méthode “R-matrix” est introduite pour résoudre le problème de propagation d’onde. Une annulation de la transmission se produit quand un mode piégé (qui est formé par les interférences de deux modes voisins) est excité dans le système ouvert. Ce phénomène est aussi lié au croisement évité des valeurs propres et à un point exceptionnel. Dans la seconde stratégie, un réseau d’inclusions rigides périodiques est intégré dans une couche poreuse pour améliorer l’atténuation du son à basse fréquence. Le couplage de modes est du à la présence de ces inclusions. Le théorème de Floquet-Bloch est proposé pour analyser l’atténuation du son dans un guide d’onde périodique en 2D. Un croisement de l’atténuation de deux ondes de Bloch est observé. Ce phénomène est utilisé pour expliquer le pic de pertes en transmission observé expérimentalement et numériquement dans un guide 3D partiellement traitée par un matériau poreux avec des inclusions périodiques. Enfin, le comportement acoustique d’un liner purement réactif dans un conduit rectangulaire avec et sans écoulement est étudié. Dans une certaine gamme de fréquence, aucune onde ne peut se propager à contre sens de l’écoulement. Par analyse des différent modes à l’aide de la relation de dispersion, il est démontré que le son peut être ralenti et même arrêté. / Two strategies are presented to use the mode coupling effects to enhance sound attenuation in acoustic ducts. The strategy is to couple the incoming propagative mode with the localized mode, which is also called Fano resonance. This strategy is presented and validated in a duct-cavity system and a waveguide partially lined with a locally reacting material. The R-matrix method is introduced to solve the propagation problems. A zero in the transmission is present, due to the excitation of a trapped mode which is formed by the interferences of two neighboured modes. It is also linked to the avoided crossing of the eigenvalues and exceptional point. In the second strategy, a set of periodic rigid inclusions are embedded in a porous lining to enhance sound attenuation at low frequencies. The mode coupling is due to the presence of the embedded inclusions. Floquet - Bloch theorem is proposed to investigate the attenuation in a 2D periodic waveguide. Crossing is observed between the mode attenuations of two Bloch waves. The most important and interesting figure is that near the frequency where the crossing appears, an attenuation peak is observed. This phenomenon can be used to explain the transmission loss peak observed numerically and experimentally in a 3D waveguide partially lined by a porous material embedded with periodic inclusions. Finally, the acoustical behaviours of a purely reacting liner in a duct in absence and presence of flow are investigated. The results exhibit an unusual acoustical behaviour : for a certain range of frequencies, no wave can propagate against the flow. a negative group velocity is found, and it is demonstrated that the sound can be slowed down and even stopped.

The research presented in this thesis was carried out as part of a collaboration between the groups of Dr Tanja van Mourik at the School of Chemistry, University of St Andrews and Professor Jonathan Tennyson at the Department of Physics and Astronomy at University College London. This thesis presents State-Averaged Complete Active Space Self Consistent Field (SA-CASSCF) calculations on nucleic acid bases, deoxyribose and phosphoric acid H₃PO₄). In the case of uracil, for comparison, Multireference Configuration Interaction calculations were also performed. The SA-CASSCF orbitals were subsequently used in R-matrix electron scattering calculations using the close-coupling model. Of major importance for obtaining accurate SA-CASSCF results is the choice of the active space and the number of calculated states. Properties such as the electronic energy, number of configurations, excitation energy and dipole moment were considered in the choice of active space. Electron-collision calculations were performed on two of the most stable isomers of phosphoric acid, a weakly dipolar form with all OH groups pointing up and a strongly dipolar form where one OH group points down. A broad shape resonance at about 7 eV was found for both isomers. Ten-state close-coupling calculations suggest the presence of narrow, Feshbach resonances in a similar energy region. Elastic and electronically inelastic cross sections were calculated for both isomers. The R-matrix calculations on uracil were done by the group from UCL. R-matrix calculations are currently being done on guanine. Scattering calculations on the other DNA bases will be performed in the near future.

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In this thesis we review some aspects of Yang-Baxter deformations of semi-symmetric space sigma models. We start by giving a short review of the sigma model description of superstrings and then we offer a self contained introduction to the Yang-Baxter deformation technique. We then show how to obtain an integrable deformation of the hybrid sigma model. Also, we show that the gravity dual of beta-deformed ABJM theory can be obtained as a Yang-Baxter deformation. This is done by selecting a convenient combination of Cartan generators in order to construct an Abelian r-matrix satisfying the classical Yang-Baxter equation. / Nesta tese revisamos alguns aspectos das deformações de Yang-Baxter de modelos sigma em espaços semi-simétricos. Damos uma breve revisão do modelo sigma de supercordas e, em seguida, oferecemos uma introdução ao método de deformação de Yang-Baxter. Em seguida, mostramos como obter uma deformação integrável do modelo sigma híbrido. Além disso, mostramos que o dual gravitacional da teoria ABJM beta-deformada pode ser obtida como uma deformação de Yang-Baxter. Isso é feito selecionando-se uma combinação conveniente de geradores de Cartan para construir uma matriz r Abeliana satisfazendo a equação clássica de Yang-Baxter.

This thesis presents a set of measurements of spin asymmetries from the heavy atoms krypton and rubidium. These investigations allow examination of the spin orbit interaction for electron scattering from the target atoms. These measurements utilise spin polarized electrons in a crossed beam experiment to measure the Sherman function from krypton and the A2 parameter from the 52P state of rubidium. The measurements utilise a new spin polarized electron energy spectrometer which is designed to operate in the 20-200 eV range. The apparatus consists of a standard gallium arsenide polarized electron source, a 180 degrees hemispherical electron analyser to detect scattered electrons and a Mott detector to measure electron polarization. A series of measurements of the elastic Sherman function were performed on krypton at incident electron energies of 20, 50, 60, 65, 100, 150 and 200 eV. Scattered electrons are measured over an angular range of 30-130 degrees. These measurements are compared with calculations of the Sherman function which are obtained by solution of the Dirac-Fock equations. These calculations include potentials to account for dynamic polarization and loss of flux into inelastic channels. At the energies 50, 60 and 65 eV, experimental agreement with theory is seen to be extremely dependent on the theoretical model used. Measurement of the A2 parameter from the combined 52P1/2,3/2 state of rubidium are performed at an incident energy of 20 eV. The scattered electrons are measured over an angular range of 30-110 degrees. This measurement represents the first such measurement of this parameter for rubidium. Agreement with preliminary calculations performed using the R-matrix technique are good and are expected to improve with further theoretical development.

In this thesis work, the K-shell photoionization of multi-charged ions has been studied as well as the valence photoionization of atomic and small molecular ions. The K-shell photoionization cross sections were measured for nitrogen iso-nuclear series, from N+ to N4+ ions using the ion-photon merged beam technique and the valence photoionization cross sections for Xe+ and Kr+ ions and the small molecular ions CO_2^+ and N_2^+ using both the merged beam and ion trap techniques at the SOLEIL synchrotron radiation facility in Saint-Aubin, France. Combination of the two techniques allows for the measurement of the pure ground state ionization cross section on an absolute scale.The experimental K-shell photoionization cross sections are compared with theoretical results obtained from the multi-configuration Dirac-Fock (MCDF), R-matrix and the Screening Constant by Unit Nuclear Charge (SCUNC) methods. The interplay between experiment and theory enables the identification and characterization of the strong 1s→2p and 1s→3p resonances observed in the spectra. The experimental valence photoionization cross sections for Xe+ and Kr+ ions are compared with MCDF calculations results obtained for the direct photoionization process. The quality of the absolute cross section measurements using the merged beam techniques is strongly dependent on the performance of Electron Cyclotron Resonance Ion Source (ECRIS). In order to improve the current of ions in the interaction region, the ions extraction system and transport was simulated by using IGUN program and ECRopt.