The configuration interaction (CI) method using orbitals centered on the nucleus has recently been applied to calculate the interactions of positrons interacting with atoms. Computational investigations of the convergence properties of binding energy, phase shift, and annihilation rate with respect to the maximum angular momentum of the orbital basis for the and PsH bound states, and the scattering system were completed. The annihilation rates converge very slowly with angular momentum, and moreover the convergence with radial basis dimension appears to be slower for high angular momentum. A number of methods of completing the partial wave sum are compared; an approach based on a ΔXJ=a(J+ 12 )−n+b(J+ 12 )−(n+1) form [with for phase shift (or energy) and for the annihilation rate] seems to be preferred on considerations of utility and underlying physical justification.