Eikonal Exchange Amplitude in Coulomb Break-Up Processes

The first evaluation of the ionization cross section of the hydrogen atom by electron impact is made in the cikonal approximation with electron exchange. The result obtained for the integrated cross section turns out to be in excellent agreement with experimental results in the intermediate energy region as well as in the high energy region. In the eikonal approximation the direct amplitude of the most fundamental break­ up process in the hydrogen atom by electron impact was first evaluated with reduction to an integral representation including the Coulomb wave function.u A little later, another evaluation of the ionization cross section with the electron exchange was proposed. 2 l However only symmetry consideration was introduced and no exchange amplitude was explicitly evaluated. In connection with the reli­ ability of the eikonal appoximation a com­ plete evaluation of the exchange ampli­ tude might be desired especially in the intermediate energy region. Recently the eikonal exchange amplitude for electron-hydrogen elastic scattering was evaluated by reducing to a two­ dimensional integral form, where the assumption of the forward scattering was removed. 3l Following the same line of approach, the eikonal exchange scattering amplitude of the present break-up process is given in atomic units as follovvs: