Dunn, Joel Thomas; (2002) Theoretical studies of low-energy positron-atom and atom-antiatom collisions. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Theoretical studies of low-energy positron collisions with various one-electron models of the helium atom have been made using the Kohn variational method in order to find out if such a model atom is capable of yielding accurate cross sections for elastic scattering, positronium (Ps) formation and annihilation. For positron-helium scattering, comparisons are made with the accurate results obtained from the ab initio variational calculations of Van Reeth and Humberston. All the models provide qualitatively accurate results over some energy intervals. Although one model gives excellent values for the elastic scattering cross section up to the Ps formation threshold, it is affected by a resonance near the threshold. None of the models yields very accurate results for the annihilation cross section, although a comparatively crude model reproduces the accurate distribution function for the Doppler broadening of the annihilation γ-ray energy spectrum. A correlation has been found by Van Reeth et al between the Ps formation cross section and the associated threshold energy for the noble gas atoms. A parameter in the correlation equation has been interpreted as the Ps formation cross section for an atom with a zero threshold energy, so Ps formation cross sections have been calculated for such a model atom. The results obtained compare reasonably favourably with the energy dependence of this parameter obtained from experimental data. An adiabatic model has also been used to study hydrogen-antihydrogen collisions, and further studies may involve a model one-electron atom in the study of helium-antihydrogen collisions. The results are satisfactory, but further investigations are needed to include the rearrangement of the atom-antiatom system into positronium and protonium.

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