Asymptotic cross section and scaling law: positronium formation in Rydberg states in positron-hydrogen collisions

Positronium formation in Rydberg states from the ground state of the hydrogen atom by positron impact has been studied within the framework of a distorted wave theory which includes static dipole polarization potential. The distorted wave scattering amplitude has been obtained in a closed form. A detailed investigation has been made on the differential and total cross sections in the energy range 25-300 eV of incident positron. It has been found that asymptotic cross sections for the positronium formation into different angular momentum states obey a simple law.