Test of final state approximations using threshold $pp \to pp\pi^0$

The Watson-Migdal approximation scheme to take into account final state interactions is shown to give the actual threshold momentum dependence of the reaction $pp \to pp\pi^0$. However, by an explicit plane wave replacement of the final state wave function it is stressed that not too much physical significance should be given to the proportionality coefficient extracted using this procedure. The plane wave approximation is not physically reliable even after introducing the Watson-Migdal or a more sophisticated final state interaction factor, since direct production (impulse term) is missed. Also with short range interactions there can be discrepancies of a factor two.