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Manuscript Title: VPM: a new asymptotic package.
Authors: J.P. Croskery, N.S. Scott, K.L. Bell, K.A. Berrington
Program title: VPM
Catalogue identifier: AAOE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)385
Programming language: Fortran.
Computer: CRAY-1.
Operating system: COS 1.10.
RAM: 0K words
Word size: 64
Peripherals: disc.
Keywords: General purpose, Differential equation, Asymptotic solutions, Electron-atom, Electron-molecule, Scattering, Photodetachment, Free-free, Variable phase, R-matrix, Long-range potential.
Classification: 4.3.

Nature of problem:
This program solves the outer region coupled equations which occur in electron-atom, electron-molecule scattering and obtains the scattering K-matrix together with slowing varying amplitudes from which the wavefunctions and their derivatives may readily be obtained.

Solution method:
The equations are solved using a method which is generally based on the variable phase method discussed by Calogero, but modified to take into account the peculiar features of the first order non-linear ordinary differential equations. The differential equations are solved using the powerful and stable package of Shampine and Gordon.

Restrictions:
The current version cannot treat the case of (i) a Coulombic potential, (ii) all closed channels. A modified version to treat these cases is in preparation. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see listing for details).

Running time:
The running time depends critically upon: the number of channels included; the number of open channels; the convergence radius for the asymptotic analytic expansions employed; energies near thresholds or in resonance regions; and whether one is performing only a K-matrix calculation or a full K-matrix plus wavefunction calculation. Typically a full calculation takes approximately three times longer than a K- matrix only calculation. The test run took 10.5 s on the CR AY-1. CRAY-1.