A program for ion-atom collisions involving one electron

Abstract

A program to compute transition amplitudes in the rectilinear-path impact-parameter formulation, for collision processes in which one of the colliding systems is a hydrogen atom or a hydrogenic ion and the other is a bare nucleus, is described. The time-dependent wave function is expressed in orthogonal polynomials in coordinates that, for any given value of the time, are linear functions of the distances of the electron from the two nuclei. Two different methods are used for obtaining approximate solutions of the time-dependent Schrödinger equation, ( H -i∂/∂ t) Ψ = 0: for large internuclear distances the method is variational, aiming to make the normalization integral of ( H -i∂/∂ t)Ψ as small as possible; for smaller internuclear distances the coupled differential equations for the time-dependent coefficients in the expansion of the wave function, arising from the requirement that ( H - i∂/∂ t)Ψ be orthogonal to all the basis functions in which the wave function is expanded, are solved by a Runge-Kutta process. The program is believed to be useful mainly if the incident speed of the collision is roughly comparable with the orbital speed of the electron; at much smaller or much larger incident speeds other (e.g. perturbation, continuum-distorted-wave, etc.) methods may be more efficient. The accuracy achieved depends entirely on the computer resources that one is prepared to spend.