POSITRONIUM SCATTERING BY HELIUM Jennifer Blackwood$^+$, C.P.Campbell$^+$, Mary T.McAlinden$^*$ and H.R.J.Walters$^+$ ${}^+$Department of Applied Mathematics, Queen's University, Belfast BT7 1NN, UK. ${}^*$ School of Computing, Staffordshire University, Beaconside, Stafford ST18 0DG, UK. We report results of extensive calculations of positronium - helium scattering within the coupled - pseudostate formalism. These calculations give a complete picture of all the main processes over the energy range 0 to 40eV.