Hartree-Fock treatment of exchange in (e, 2e) collisions

The distorted-wave Born approximation has been very successful for treating electron-impact ionization (e, 2e) of heavy atoms for high-energy incident electrons. However, as the energy of the incident electrons approaches thr eshold, significant differences between experiment and theory are observed. In these calculations, the continuum projectile electron wavefunction is t ypically calculated using the static field of the atom plus a local approxi mation for electron exchange. While this approximation is believed to be re asonable for higher energies, it is likely to become unreliable for energie s near threshold. Here we report a proper treatment of electron exchange in which a full Hartree-Fock calculation is performed for both the atomic and projectile electrons. For the initial stare, the projectile orbitals are c alculated in the Hartree-Fock approximation with full exchange with the tar get electrons and for the final state, the Hartree-Fock continuum orbitals are computed for an ion. It is found that the static-exchange approximation is not valid for lower incident energy projectiles.