Comparison of positronium, positron and electron collisions with hydrogen at low velocities

Recent experimental findings indicate that at equal velocity electron and ortho-positronium scattering cross sections are similar over a wide range of velocities and targets where both elastic and inelastic processes can take place. We present a comparative study of positronium, positron and electron elastic scattering from atomic hydrogen in order to investigate if a similar behaviour occurs for this target at low velocities where inelastic channels are closed. We calculate elastic cross sections for the three projectiles using Kohn-type variational methods which allows us to make a detailed study of the differences and similarities. We find a qualitative similarity in the spin-weighted elastic integrated cross sections for positronium and electron scattering and a good agreement between the singlet integrated cross sections. However, this agreement does extend to the low velocity region and where the agreement is found in the integrated cross sections we show that it is not present in the individual partial waves cross sections. Interestingly, given the agreement we find in the singlet integrated cross section for electron and positronium scattering, when comparing the overall shapes of the corresponding singlet differential cross sections we find different angular and velocity dependencies. (paper)