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 $^{12}\mathrm{C(e,e}'\mathrm{p)}^{11}\hbox{\rm B}^*$ 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 $10 \div 20 \%$, 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.