A Test of the Eikonal Approximation in High–energy (e,e ′ P) Scattering

The Glauber method is extensively used to describe the motion of a hadronic projectile in interaction with the surrounding nuclear medium. One of the main approximations consists in the linearization of the wave equation for the interacting particle. We have studied the consequences of such an assumption in the case of the 12 C(e, e ′ p) 11 B * reaction at high proton momenta by comparing the results with the predictions obtained when all the ingredients of the calculation are unchanged but the second-order differential equation for the scattered wave, which is solved exactly for each partial wave up to a maximum of 120 spherical harmonics. We find that the Glauber cross section is always larger by a factor 10 ÷ 20%, even at vanishing missing momenta. We give a quantum-mechanical explanation of this discrepancy. Nevertheless, a good correlation is found between the two predictions as functions of the missing momentum, especially in parallel kinematics. The problem of the validity of the Glauber approximation [1] in (e,e ′ p) scattering from finite nuclei is receiving more and more interest in relation with the experiments planned at CEBAF, where the proton momentum can be larger than 1 ÷ 2 GeV/c. At large missing momenta of the recoil the details of the short-range nucleon-nucleon interaction are expected to show up [2], but the few experimental data available [3] still prevent from putting stringent constraints on the theoretical models. On the other side, at moderate missing momenta an accuracy within 10% is required to unambigously identify exotic effects like Colour Transparency, if any [4]. The recent NE18 experiment [5] has shown that calculations based on the standard Glauber approximation overestimate the cross section even at vanishing missing momenta, unless some phenomenological corrections are introduced. Various suggestions have been made both on the way of analyzing the NE18 data [6, 7] and on how to improve the Glauber method [8]. Starting from a different point of view, we show that the latter is affected by an intrinsic systematical error, which can be relevant at the kinematics 1