Asymptotic form of the electron-hydrogen scattered wave

A relationship between the total wave function describing electron-impact ionization of hydrogen and the one representing scattering of two electrons and a proton in the continuum is revealed. On the basis of this relationship, forms of the scattered wave for the ionization process valid in all asymptotic domains are obtained. When all interparticle distances become large, the new wave functions reduce to the well-known Peterkop asymptotic wave function obtained in the hyperspherical approach. In particular, the Peterkop wave function is obtained by direct application of the present approach. This allows one to resolve the long-standing amplitude-phase ambiguity problem, which is an artifact of the hyperspherical approach to the ionization process. The Peterkop wave function is invalid when the two electrons are close to each other. This causes problems in practical calculations even in the domain where all particles are far apart. Our formulation provides a solution to this problem.