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 wavefunctions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the 1,3 H-wave and obtain highly accurate 1,3 Sand 1,3 P-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 1 F-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.

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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.