Mechanism of the (e, 2e) reaction with atoms

The ($e, 2e$) reaction is studied under kinematic conditions designed to test different reaction theories. The problem is reduced to a calculation involving distorted waves for the electron-ion interactions and a two-body operator for the electron-electron interaction. The amplitude factorizes into an $\mathrm{ee}$ factor and a distorted-wave factor if the eikonal approximation is made for the distorted waves. The factorization is tested by choosing kinematics so as to keep the distorted-wave factor constant while varying the $\mathrm{ee}$ factor. The value of the average eikonal potential is established in coplanar symmetric kinematics. The target is helium. At incident energies of 400 and 800 eV, the approximation is good for recoil momenta less than about 1 a.u., provided the effective two-body operator is the $t$ matrix. The $v$ matrix is ruled out. There are strong indications that the impulse approximation itself breaks down for small relative momenta between the outgoing electrons.