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Manuscript Title: CFASYM: a program for the calculation of the asymptotic solutions of the coupled equations of electron collision theory.
Authors: C.J. Noble, R.K. Nesbet
Program title: CFASYM
Catalogue identifier: ACCT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 33(1984)399
Programming language: Fortran.
Computer: NAS 7000.
Operating system: MVT.
RAM: 400K words
Word size: 8
Keywords: Atomic physics, Asymptotic solutions, Electron-ion, Electron-atom, Electron-molecule, Scattering, Expansion methods, Continued fraction, Pade approximants.
Classification: 2.4.

Subprograms used:
Cat Id Title Reference
ABNK_v1_0 COULFG CPC 27(1982)147
ACCU_v1_0 COULN CPC 33(1984)413

Nature of problem:
The linearly independent asymptotic solutions of the second-order differential equations encountered in close-coupling formulations of electron-atom, electron-molecule and electron-ion scattering are calculated by analytically continuing the appropriate asymptotic expansions. These solutions provide the boundary conditions necessary to compute the K- or S-matrices for the complete scattering problem.

Solution method:
The asymptotic expansions of the scattering wavefunction for an electron interacting with a target system at large separations via simple multipole potentials suggested by Burke and Schey, Burke et al. and by Gailitis are analytically continued and calculated in the form of a continued fraction using an algorithm devised by Nesbet. The method is equivalent to the use of Pade approximants and allows the radial point at which the asymptotic boundary conditions are used to determine the K- matrix to be considerably reduced compared to previous methods. This results in significant reductions in the computational expense of the overall calculation in the asymptotic region.

Restrictions:
At energies close to thresholds the required accuracy can only be obtained at larger radial distances or by increasing the number of terms used in the asymptotic expansion. The second alternative is eventually limited by numerical round-off or by exponent overflow. Additional core storage is necessary if the number of channels or the number of terms in the asymptotic series is increased. Other limitations can arise from from the Coulomb function routines employed (these could easily be replaced).

Running time:
The running time depends on the number of channels included. The total time for the test run on the NAS 7000 was 24 s (1.4 s for the execution step) and 1.96 s (0.48 s for the execution step) on the CRAY-1S.