A theoretical study of elastic electron positronium scattering and photo-absorption by the positronium negative ion

Abstract

This thesis describes both a theoretical study of low-energy electron scattering by positronium (Ps), below the n=2 threshold and the photo detachment of the positronium negative ion (Ps-.) E+/- + Ps(1s) → e+/- + Ps(1s) Ps- + hv → Ps(1s) + e- The importance of the photodetachment of Ps- was recognized by Mills (in 1981) since it can be used as a possible mechanism of producing a slow monoenergetic Ps beam. Accurate 1,3S and 1,3P phase shifts were evaluated by the Kohn and inverse Kohn variational methods in which very flexible trial functions were used. Higher order phase shifts were determined by the static exchange and adiabatic ex-change models in order to obtain the total elastic, momentum-transfer, ortho-para conversion and elastic differential cross sections for the scattering process. In the variational calculation, the lowest 1S, 1P and the two lowest 3P resonances, which lie just below the n=2 threshold were revealed. The scattering results for ea-Ps were compared with those for ea-H. Using a variational bound-state wave function, which contained 95 linear and 2 non-linear parameters, and a p-wave continuum function, which contained 220-linear and 3 non-linear parameters, the photo detachment cross section was calculated in both the length and velocity formulation. The agreement between the length and velocity forms was to better than 1.6% for lambda 27.5 x 103A, and the sum-rule was satisfied to within 2%. By systematically improving both the bound-state and continuum wave functions separately, the reliability of the cross section was determined. A comparison of the photo detachment of Ps- was made with the corresponding atomic ion, H-.