  We perform a momentum-space calculation of the reaction $pp \rightarrow pp\pi
^0$ near threshold. Direct production and pion rescattering are taken into
account. For the latter a T-matrix obtained from a microscopic model of the
$\pi N$ interaction is employed. The effects of some approximations commonly
used in studies of $ pp \rightarrow pp\pi ^0$ \ are discussed. We find that
those approximations overestimate the cross section and also modify its energy
dependence. We obtain a significant contribution from rescattering, but not
nearly enough to describe the data.
