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Manuscript Title: ASYPCK: a program for calculating asymptotic solutions of the coupled equations of electron collision theory.
Authors: M.A. Crees
Program title: ASYPCK
Catalogue identifier: AAJA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 19(1980)103
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE 2.1.4.
RAM: 27K words
Word size: 60
Peripherals: disc.
Keywords: Atomic physics, Asymptotic, Solutions, Electron-ion, Electron-atom, Electron-molecule, Scattering, Expansion methods, Fox-goodwin integration.
Classification: 2.4.

Subprograms used:
Cat Id Title Reference
AAJB_v1_0 ASYPRO CPC 19(1980)103

Nature of problem:
The program ASYPCK obtains solutions, at large radial distances, of the second-order differential equations of the type encountered in electron-ion and electron-atom scattering problems. ASYPCK can obtain either solutions at two radial points or solutions and their first derivatives at one point. Such solutions can be used as boundary solutions for a complete solution of a full set of close-coupling integro-differential equations encountered in electron collision problems (for example in the programs IMPACT and RMATRX). ASYPCK can also obtain sets of wave functions at a discrete mesh of radial points. These sets of functions can be used, for example, to obtain photo-ionization cross-sections and oscillator strengths.

Solution method:
For each reaction channel and associated boundary condition, the program obtains solutions at a point rf using an asymptotic expansion method either the Burke and Schey expansion method or the iterative WBK method of Norcross and Seaton. These solutions are then inwardly integrated to obtain solutions at the desired radial distance. To overcome difficulties which can arise in the inward integrations, the Fox-Goodwin integration technique, decribed by Norcross and Seaton, has been included as an option.

The program ASYPCK is provided in a form which must be pre-processed by a program ASYPRO, which inserts dimensions and activates/deactivates machine dependent FORTRAN statements. The program ASYPCK is designed to work for both neutral atoms and ions and for both the cases of some channels open and all channels closed. Restrictions on the range of energies that can be handled are confined to a small range just below a threshold for neutrals and ions and also at a threshold for neutrals. The program can encounter difficulties in the cases where the channel energies are nearly degenerate or are very close to and above a threshold.

Running time:
The running time depends on the problem being solved. The time increases approximately as (NCHF)**2 where NCHF is the number of free channels. The time also increases in cases where channel energies are nearly degenerate or close to a threshold. The time taken for the test run on the CDC 7600 at the University of London Computer Centre was 0.22 s.