Off-Shell Effects in Knockout Reactions

The amplitude for a knockout reaction in the plane-wave impulse approximation is derived from the Faddeev equations. It factorizes into the product of an off-shell two-body $t$ matrix times the bound-state wave function in momentum space. In this paper results are derived for the ($p,2p$) experiment from a realistic potential and compared with those arising from some current approximations. Distortion effects are ignored in order to isolate the off-shell effects. We find that for incident protons with lab energy below 200 MeV using an off-shell amplitude can change the cross section significantly as compared with the on-shell approximations in current use. The effect increases with the binding energy of the struck proton and with the recoil momentum. This indicates that ($p,2p$) reactions below 200 MeV are sensitive to the off-shell behavior of the two-body amplitude and that they should not be used to obtain nuclear information using on-shell approximations.