Plane-wave asymptotic form in the electron-atom ionisation problem

The plane-wave asymptotic expansion of the wavefunction for two electrons in a Coulomb field has been investigated in the case when the total orbital momentum, L, is equal to zero. Analytic solutions are obtained for the first term of the asymptotic expansion. The second term is found by numerical integration along classical trajectories. Analytic solutions are obtained for the the Altick (1982-3) asymptotic equations. It is shown that the Altick asymptotic form represents the asymptotic expression of the authors' asymptotic form. The branch point of the later Altick asymptotic form has been discussed and the conclusion is made that this asymptotic form cannot be applied.