A PROGRAM FOR ION-ATOM COLLISIONS INVOLVING ONE-ELECTRON

A program to compute transition amplitudes in the rectilinear-path imp act-parameter formulation, for collision processes in which one of the colliding systems is a hydrogen atom or a hydrogenic ion and the othe r is a bare nucleus, is described. The time-dependent wave function is expressed in orthogonal polynomials in coordinates that, for any give n value of the time, are linear functions of the distances of the elec tron from the two nuclei. Two different methods are used for obtaining approximate solutions of the time-dependent Schrodinger equation, (K - i partial derivative/partial derivative t)PSI = 0: for large internu clear distances the method is variational, aiming to make the normaliz ation integral of (K - i partial derivative/partial derivative t)PSI a s small as possible; for smaller internuclear distances the coupled di fferential equations for the time-dependent coefficients in the expans ion of the wave function, arising from the requirement that (K - i par tial derivative/partial derivative t)PSI be orthogonal to all the basi s functions in which the wave function is expanded, are solved by a Ru nge-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 comp uter resources that one is prepared to spend.