Masters Thesis Defense - CI-Kohn Method of Positron-Atom Scattering

Who: Scott Young

Time: 1:00pm, Monday 6th August, 2007

Place: P-250

Abstract: Computationally, one of the most challenging problems in quantum mechanics is the scattering problem. The elastic positron-atom scattering problem is studied here by the use of the non-relativistic configuration-interaction method (CI), with plane wave boundary conditions imposed via the Kohn variational method. This work follows on from previous scattering calculations which demonstrated that Kohn calculations are able to avoid singularities without resorting to the complex Kohn method. Here, the method’s convergence and stability are investigated and applied to positron-hydrogen scattering.

The method was first validated using potential scattering from the Woods-Saxon, “static” potentials, along with simple hydrogen models. Scattering lengths, annihilation rates and phase shifts are calculated for increasingly large basis sets, and exhibit complicated convergence patterns (including periodic “shoulders”, and odd/even basis set dependence).

Calculations for s-wave positron-hydrogen scattering, however, showed excellent convergence in the scattering lengths, phase shifts and annihilation rates at the threshold limit as well as finite energy. At threshold, the scattering length and annihilation rate are each comprised of two convergent series, based on the total number of orbitals included in the basis set requiring a larger basis set to be used. Extrapolations of the scattering length, phase shift and annihilation rate to the complete basis set limit are reported for the threshold limit and finite energy cases.

Extrapolating finite energy calculations of p-wave positron-hydrogen system did not return consistent results for the phase shift or annihilation rate, and any future works will start with the exploration of the p-wave finite energy scattering problem. This research lays the foundation for future application of the method to other one and two valence electron systems such as Mg, Zn and Cd. These atoms are known to have resonant structures in their annihilation rates due to p-wave positron-atom scattering.

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