Positronium Formation in Positron-Helium Scattering

An approximation method developed by Chen and Mittleman has been used to investigate the process of positronium formation in positron-helium scattering. The energy range in which only ground-state positronium may be formed is considered. This method leads to an approximation made on a projection-operator technique, and further includes a coordinate change which allows the expression of the entire problem in terms of the positron coordinate. The result is two coupled ordinary differential equations, of second order, which may be solved numerically. The projection-operator technique leads naturally to the inclusion of the polarizability of both helium and positronium in the potentials which appear in the final equations, and a thorough investigation is made of the effects of various forms for the polarization potentials. The results await a comparison with experimental data, which are expected to be made available in the near future.