Double ionization of helium by fast electrons with the Generalized Sturmian Functions method

The double ionization of helium by high energy electron impact is studied. The corresponding four-body Schrodinger equation is transformed into a set of driven equations containing successive orders in the projectile-target interaction. The first order driven equation is solved with a generalized Sturmian functions approach. The transition amplitude, extracted from the asymptotic limit of the first order solution, is equivalent to the familiar first Born approximation. Fivefold differential cross sections are calculated for (e, 3e) processes within the high incident energy and small momentum transfer regimes. The results are compared with other numerical methods, and with the only absolute experimental data available. Our cross sections agree in shape and magnitude with those of the convergent close coupling method for the (10+10) eV and (4+4) eV emission energies. To date this had not been achieved by any two different numerical schemes when solving the three-body continuum problem for the fast projectile (e, 3e) process. Though agreement with the experimental data, in particular with respect to the magnitude, is not achieved, our findings partly clarify a long standing puzzle.