The question of convergence in two-centre expansions is addressed via the s
tudy of positron-hydrogen scattering within the s-wave model. Direct scatte
ring, positronium formation, and breakup cross sections are found to conver
ge if a sufficient number of states, centred on the hydrogen atom and posit
ronium, are used to expand the total scattering wavefunction. Moreover, thi
s occurs only if pseudostate expansions are applied to both the atomic and
positronium centres.