Off shell pi N amplitude and the p p->p p pi0 reaction

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.