Proton knockout from 16O and relativistic recoil effects in the Dirac impulse approximation

Abstract

Recoil effects in exclusive nucleon knockout reactions, such as the p2p reaction, are examined within a relativisitic distorted-wave impulse approximation based on the Dirac equation. Starting from a tree-level Feynman diagram in which the Bethe-Salpeter propagator is replaced by the three-dimensional “smooth” propagator, a prescription is developed which preserves the Dirac equation and which reduces to the correct results in the non-relativistic and infinite target-mass limits. Distortions are incorporated in the scheme in a manner consistent with the plane-wave result. Within the scheme, the wave functions of the single-particle bound state and the various distorted waves are evaluated in different two-body and three-body centre-of-momentum frames, which are then boosted, in principle, to a common reference frame. It is found that this feature of the recoil prescription, i.e., the evaluation of the various wave functions in the appropriate centre-of-momentum frames, in conjunction with energy-momentum conservation, is the single most important feature of the recoil prescription. When recoil effects are neglected, the various centre-of-momentum frames coincide with one another, and the imposition of energy-momentum conservation then causes the momentum dependence of the bound-state wave function to be incorrectly folded into the p2p matrix element. Other recoil effects, mainly relativistic in nature, are found to be numerically less important. The scheme is applied to an analysis of the p2p reaction on 16O at 200 MeV incident energy. Overall, the results give a reasonably good account of the existing TRIUMF data, although at certain angle pairs, the calculated cross sections are somewhat too low. The cross sections exhibit a dependence on the bound-state momentum distribution similar to that observed in earlier calculations for a 40Ca target. Unlike the 40Ca results, however, the oxygen results also show a significant dependence on the elastic distorting potentials used, indicating that the elastic data for oxygen does not sufficiently constrain the oxygen optical potential to fix its role in the p2p reaction.