Detailed Investigation Of Low-Energy Positronium-Hydrogen Scattering

We investigate the four-body Coulomb process of low-energy elastic positronium-hydrogen (Ps-H) scattering below the Ps(n = 2) excitation threshold using scattering wave functions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the H-1,H-3 wave and obtain highly accurate S-1,S-3- and P-1,P-3-wave phase shifts. The complex Kohn variational results compare well to a number of other calculations for this system. We present elastic differential, elastic integrated, and momentum transfer cross sections, and for the singlet, resonances through the F-1 wave. The differential cross section exhibits interesting features, including a change from slightly backward peaked to forward peaked scattering as the energy of the incident positronium increases and rich structure due to multiple resonances near the Ps(n = 2) threshold. We also give a detailed analysis of the scattering lengths and effective ranges using multiple effective range theories.