  We have used a conventional model for the $pp \rightarrow pp \pi^{0}$
reaction consisting of the Born term plus the $s$-wave rescattering term. As a
novelty we have introduced the off shell dependence of the $\pi N$ $s$-wave
isoscalar amplitude. This amplitude is appreciably enhanced when one moves to
the off shell situations met in the problem and, as a consequence, the $pp
\rightarrow pp \pi^{0}$ cross section becomes considerably larger than with the
use of the $\pi N$ on shell amplitudes. Two different models for the off shell
extrapolation found in the literature have been used and the cross sections
obtained are large enough to account for the experimental data, although
uncertainties remain due to the incomplete knowledge of the off shell
extrapolation.
