A pseudostate method for computing photon-atom scattering cross-sections

A computational method is developed for photon-atom scattering cross-sections given by the p.A interaction, which dominates scattering at low frequencies. Our method is simple and intuitive, and has the advantage of being extremely adaptable - it can be extended to higher-order scattering processes and applied to any atom. The scattering cross-sections calculated in this thesis provide a more complete picture of the photon-atom interaction than is currently available, which is useful for high-precision atomic, molecular and optical (AMO) experiments and has applications in astrophysics and spectroscopy. Our method utilises the atomic structure data produced by the non-relativistic code patom, developed by M. W. J. Bromley. This code models the atom to be in a box, which effectively discretises the continuum. The set of positive energy states that describe the continuum are referred to as pseudostates. The single-photon scattering cross-section calculations in this thesis are based on the computation of transition polarisabilities, which are also known as the Kramers-Heisenberg matrix elements. These describe the process where an atom initially in state i transitions to state j through the absorption and emission of one photon. We develop a method that uses the pseudostate information to compute the complex transition polarisabilities at frequencies both below and above ionisation energy. Our pseudostate method is first applied to atomic hydrogen, and compared with the results of our semi-analytical calculations and literature values. These transition polarisabilities are then used to compute the various single photon scattering cross-sections off atomic hydrogen - Rayleigh and Raman scattering, as well as the photoionisation cross-section. Rayleigh scattering describes the elastic process where a photon of equal energy is absorbed and emitted. We show that the Rayleigh scattering cross-sections given by our pseudostate method are completely converged even for frequencies far above threshold. On the other hand, the Raman scattering cross-section is the inelastic process where an atom initially in state i transitions to a bound state j through the absorption and emission of photons of different energies. Though Raman scattering is often used in spectroscopy, there is only very little data for the cross-sections of Raman scattering off atomic hydrogen. Here we show that our method is able to calculate the various Raman scattering cross-sections. We also investigate the calculation of Compton scattering cross-sections with detailed convergence studies. We demonstrate that our total and differential Compton scattering cross-sections exhibit unresolved convergence issues related to box size and the use of free-to-free transition matrix elements. Our pseudostate method is extended to higher-order processes as well, such as the calculation of two-photon ionisation cross-section and complex hyperpolarisability. Though the same free-to-free transition matrix elements are used in the hyperpolarisability calculation as in our calculation of Compton scattering cross-sections, we find that our hyperpolarisability results are converged and in agreement with literature. Our method is extremely adaptable, as it can not only be extended to multi-photon scattering calculations, but also easily be applied to atoms other than hydrogen. We present calculations of one valence electron systems - hydrogen isotopes, positronium, metastable helium, lithium and sodium. Finally, we show that our pseudostate method is limited to frequencies below the second ionisation threshold in the case of multi-photon processes. Further limitations and possible extensions to our method to more than one active electron are discussed.