Double excitation of helium by ion impact. I. Theory

We study the double excitation of helium by ion impact above 100 keV amu -1 . More precisely, we determine the Shore parameters of the resonance profile observed in the doubly differential ionization cross sections when resonance effects due to doubly excited states show up. We generalize the Fano theory for the present time-dependent situation which allows us to express the impact-parameter-dependent transition amplitude in terms of amplitudes that vary slowly in the vicinity of a resonance. Consequently, we can perform a close-coupling calculation using correlated two-electron states and a 'coarse-grain' discretization of the continuum. For the first time, agreement is obtained between the theoretical and experimental Shore parameters and for energies down to 100 keV for proton impact. We also show that the two-centre effect on the ionization cross section is accurately represented in our one-centre close-coupling calculations.