Although the collisions of electrons and atomic hydrogen has been studied for several decades, there is still neither a complete database of scattering data, nor a universal method that would let generate such data. For astronomical and other purposes the cross sections of electron-hydrogen collisions are necessary, in a broad range of energies - from tenths of electronvolt to millions of electronvolts. In this work the author concentrates on several established approaches to electron-atom scattering and confronts results of his own implementations of these methods against the published data and results of freely available computer codes. A special attention is given to the overlaps of different methods, so that in the end a database with easy user interface can be offered for common practical usage of scattering data in applied fields.

In this thesis, We study the driven Morse system in a strong time-periodic field. We are interested in the quasi-bound states, which live in the driven system with limit life-times, with an increasing field strength in a low frequency region. We found those states by using Floquet theory, and the exterior complex scaling method (ECCS), which widely use in the resonance system. Choosing the Morse potential with supports 3 bound states, we found that as we increase the time-periodic external field, the number of the quasi-bound states decrease to 2. The distributions of the quasi-bound states which represented by the Husimi distribution were also studied, and compared with the Poincaré surface of section plots of the system. / text

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.

Jakub Benda Astrophysically important processes in collisions of electrons with hydrogen atoms This thesis focuses on calculations of the cross sections and other scattering quantities that characterize the outcome of collisions of electrons with hydro- gen atoms. For the chosen energy range and atomic transitions the scattering process is solved within the non-relativistic quantum mechanics by discretiz- ation of the Schr¨odinger equation in the basis of B-splines, which transforms the equation into a linear-algebraic problem. The thesis discusses the boundary conditions, methods of solution of the linear system, preconditioning of the sys- tem and interpretation of results, including several original ideas that proved to be very beneficient for the calculations. The calculated data are provided by means of graphs at the end of the thesis. Also, a custom web-based scattering database containing the results has been set up, freely available to the expected audience of this project. 1

The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H$_2^+$ by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics. Powered by TCPDF (www.tcpdf.org)