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Manuscript Title: A program for ion-atom collisions involving one electron.
Authors: H.G. Morrison, U. Opik
Program title: PHCOLL
Catalogue identifier: ACPG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 77(1993)403
Programming language: Fortran.
Computer: DIGITAL VAX 9210.
Operating system: VMS.
Keywords: Molecular physics, Ion-atom collisions, Heavy-particle collision, Charge transfer, Electron capture, Excitation collisional, Impact parameter, Transition amplitude, Time-dependent Schrodinger equation, Variational method, Coupled differential Equations, Runge-kutta method, Orthogonal polynomials, Gaussian-type quadrature.
Classification: 16.8.

Nature of problem:
Computation of transition amplitudes for ion-atom collisions in the impact-parameter formulation [2].

Solution method:
The time-dependent wave function is expanded in orthogonal polynomials in coordinates that are linear functions of the distances of the electron from the two nuclei. A variational method is used for large internuclear distances, and coupled differential equations are integrated step by step for smaller internuclear distances [2].

Restrictions:
The total physical system may consist of only two nuclei and one electron. However, it should be fairly easy to adapt the program so that it will handle a system consisting of two ionic cores and one active electron.

Unusual features:
Most large arrays are defined in three so-called sub-master programs (subroutines) as non-common arrays, so that the user can easily change their dimensions by altering a few PARAMETER statements. The naming of variables and arrays follows the recommendations of Roberts [3].

Running time:
Propagation of a wave function from time t=-infinity to a value t=t1 from which the computation could be continued by step-by-step integration, in a typical test, took 5.6 seconds. Step-by-step integration with 112 basis functions took 0.30 seconds per step; between 100 and 160 steps are usually needed. With 365 basis functions, step-by -step integration took 3.0 seconds per step. In the latter computation the step length was one-half of that in the former, so the effective increase in time expenditure was by a factor of 20. 112 basis functions seemed to give sufficient accuracy. Computation of a transition amplitude takes of the order of 10 seconds if the time integral terms in eq. (5.1) of the Long Write-up are present, and a negligible amount of time without these.

References:
[1] A. Balfour and D.H. Marwick, Programming in Standard FORTRAN 77 (Heinemann, London, 1979).
[2] H.G Morrison and U. Opik, J. Phys. B 11 (1978) 473.
[3] K.V. Roberts, Comput. Phys. Commun. 1 (1969) 1.