The transition amplitude for electron-positron annihilation during positron
-hydrogen scattering is formulated in terms of the half-shell T-matrix elem
ents obtained from a solution of the momentum space Lippmann-Schwinger equa
tion. The derived expression is well defined at energies below the positron
ium (Ps) formation threshold. However, singularities in the transition ampl
itude exist at energies above the Ps-formation threshold. The annihilation
parameter for positron-hydrogen scattering is computed in a variety of mode
ls at energies below the Ps-formation threshold. Calculations with the larg
est basis reproduce previous variational calculations of Z(eff)(J) for the
J = 0 and 1 partial waves. Accurate values of Z(eff)(J) were also given for
the J = 2, 3 and 4 partial waves to give a summed Z(eff) that is probably
the most accurate so far reported.