Two related lines of research in experimental electron density determination are reported in this thesis. In the first case, the well-proven and popular multipole modeling technique is applied to three high resolution, single-crystal X-ray diffraction data sets. The preliminary part of this thesis (Chapters 2-5) deals with the theoretical aspects of the multipole model, and also some of the theoretical and practical aspects of data collection and reduction. Chapter 6 reports an experimental charge density determination of a nitrogen ylide. Chapter 7 contains details of the treatment of data from a large, pendant-arm macrocyclic complex of nickel, while Chapter 8 reports the characteristics of the experimentally determined charge density for a substituted acetylene molecule which exhibits interesting intramolecular interactions. The charge densities for all three cases are analysed using Bader's Theory of Atoms in Molecules. The latter part of this thesis deals with more novel ways of treating experimental data. Chapter 9 gives a thorough review of the literature on the application of Maximum Entropy techniques to image reconstruction in general and charge density determination in particular, followed in Chapter 10 by an application to diffraction data from the cubic phase of acetylene. The novel approach of removing core scattering from the data is developed and gives improved results. Chapter 11 reviews some aspects of fermion density matrices and their relationship to electron density functions and X-ray scattering, followed in Chapter 12 by results from the density matrix refinement method applied to diffraction data from formamide. Particular emphasis is placed upon basis set effects, idempotency and various N-representable approximations to the experimentally determined density matrix.

This thesis presents an extensive computational study of electron-impact scattering and ionisation of atomic hydrogen and hydrogenic ions, which are fundamental to many diverse disciplines, from astrophysics and nuclear fusion to atmospheric physics. The non-relativistic Schrodinger equation describes these collisions, though finding solutions for even hydrogen, the simplest electron-atom collision, has proven to be a monumental task. Recently, Rescigno et al [Science 286, 2474 (1999)] solved this equation in coordinate space using exterior complex scaling (ECS), and presented the first electron-hydrogen differential cross sections for ionisation that matched with experiment without requiring uncontrolled approximation. This method has significant potential for extension to larger collision systems, but its large computational demand has limited its energy range and target configurations, and its application to discrete final-state collisions has been largely unexplored. Using radically different numerical algorithms, this thesis develops methods that improve the computational efficiency of ECS by two orders of magnitude. It extends the method to calculate discrete final-state scattering cross sections and enhances the target description to include hydrogenic ions and excited initial states. In combination, these developments allow accurate solutions over a broad range of energies and targets, for both scattering and ionisation, including the important near-threshold energy region where accurate calculations have been unavailable. The refined ECS method implemented in this work now offers complete numerical solutions of electron-hydrogen collisions, and its computational efficiency will facilitate its future application to more complex targets. The thesis culminates with the first ab initio quantum mechanical confirmation of ionisation threshold laws for electron-hydrogen collisions [Bartlett and Stelbovics, 2004, Phys. Rev. Lett. 93, 233201], which have resisted confirmation through the complete solution of the Schrodinger equation for more than half a century.

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Com a crescente disponibilidade de luz síncrotron tem-se utilizado cada vez mais a dispersão anômala (f´) no estudo de materiais. Apesar dos vários métodos já empregados na medida do fator de espalhamento atômico, ainda é pequeno o número de elementos abrangidos. Este trabalho apresenta uma contribuição à ampliação da gama de elementos mensuráveis através de um método interferométrico diferencial para a determinação experimental de f´. A sua demonstração é feita através de medidas em Selênio obtendo-se o mesmo nível de precisão do método &#933-&#933/2 usado em trabalhos anteriores. Esses dois métodos são criticados quanto ao limite de erro atingível devido à sua natureza não-absoluta. Uma técnica de preparação de amostras para materiais de baixo ponto de fusão é explorada, permitindo determinar f´absolutamente, com erro de 0,03 elétron. A medida do fator de espalhamento atômico através do desvio angular entre as reflexões de Bragg e Laue é proposta e testada com resultados de qualidade bastante inferior às técnicas interferométricas. A construção de interferômetros de raios X estáveis e de alto contraste é estudada quanto à seleção dos monocristais de silício e tratamento após o corte do dispositivo, atingindo-se contraste de 80% com estabilidade de uma milifranja por hora. / The use of anomalous dispersion (f\') in the study of materials has been increasing with the availability of synchrotron radiation. Although many methods have been designed for the measurement of the atomic scattering factor, the number of elements the cover is still small. This work presents a contribution to the widening of the range of measurable elements through a Differential interferometric method for the determination of f´. Its demonstration is achieved by measurements on Selenium, reaching the same level of accuracy obtained by the &#933-&#933/2 method used in previous work. These two methods are criticized in terms of the achievable errors due to its non-absolute nature. A technique for the preparation of samples with low melting point materials is developed, allowing the determination of f´ absolutely, with an error of 0,03 electron. The measurement of atomic scattering factor through the angular offset between Bragg and Laue reflections is proposed and tested, with low quality results compared to interferometric methods. The construction of high stability and good contrast X-ray interferometers is studied in terms of silicon single crystal selection and its treatment after device cutting. 80% contrast was achieved with a stability of one milifringe per hour.

Com a crescente disponibilidade de luz síncrotron tem-se utilizado cada vez mais a dispersão anômala (f´) no estudo de materiais. Apesar dos vários métodos já empregados na medida do fator de espalhamento atômico, ainda é pequeno o número de elementos abrangidos. Este trabalho apresenta uma contribuição à ampliação da gama de elementos mensuráveis através de um método interferométrico diferencial para a determinação experimental de f´. A sua demonstração é feita através de medidas em Selênio obtendo-se o mesmo nível de precisão do método &#933-&#933/2 usado em trabalhos anteriores. Esses dois métodos são criticados quanto ao limite de erro atingível devido à sua natureza não-absoluta. Uma técnica de preparação de amostras para materiais de baixo ponto de fusão é explorada, permitindo determinar f´absolutamente, com erro de 0,03 elétron. A medida do fator de espalhamento atômico através do desvio angular entre as reflexões de Bragg e Laue é proposta e testada com resultados de qualidade bastante inferior às técnicas interferométricas. A construção de interferômetros de raios X estáveis e de alto contraste é estudada quanto à seleção dos monocristais de silício e tratamento após o corte do dispositivo, atingindo-se contraste de 80% com estabilidade de uma milifranja por hora. / The use of anomalous dispersion (f\') in the study of materials has been increasing with the availability of synchrotron radiation. Although many methods have been designed for the measurement of the atomic scattering factor, the number of elements the cover is still small. This work presents a contribution to the widening of the range of measurable elements through a Differential interferometric method for the determination of f´. Its demonstration is achieved by measurements on Selenium, reaching the same level of accuracy obtained by the &#933-&#933/2 method used in previous work. These two methods are criticized in terms of the achievable errors due to its non-absolute nature. A technique for the preparation of samples with low melting point materials is developed, allowing the determination of f´ absolutely, with an error of 0,03 electron. The measurement of atomic scattering factor through the angular offset between Bragg and Laue reflections is proposed and tested, with low quality results compared to interferometric methods. The construction of high stability and good contrast X-ray interferometers is studied in terms of silicon single crystal selection and its treatment after device cutting. 80% contrast was achieved with a stability of one milifringe per hour.