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Manuscript Title: R-matrix propagation program for solving coupled second-order differential equations.
Authors: K.L. Baluja, P.G. Burke, L.A. Morgan
Program title: RPROP
Catalogue identifier: AAJK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)299
Programming language: Fortran.
Computer: NAS AS7000.
Operating system: MVT.
RAM: 24K words
Word size: 32
Peripherals: disc.
Keywords: R-matrix, Electron-ion, Electron-atom, Electron-molecule, Atom-molecule, Asymptotic solution, Differential equation, General purpose, Hamiltonian matrix, Scattering.
Classification: 4.3.

Nature of problem:
Coupled second-order differential equations which arise in electron collision with atoms, ions and molecules are solved over a given range of the independent variable. The R-matrix at one end of the range is calculated given the R-matrix at the other end of the range.

Solution method:
The range is divided into a number of subranges and the Hamiltonian is diagonalized in such subrange in terms of an expansion in shifted Legendre polynomials. A correction introduced by Bloch is included at each end of each subrange. The integrals are carried out using Gauss- Legendre quadrature.

Restrictions:
The potential interaction is restricted to the long-range multipole potential between an electron and an atom ion or molecule. More general potentials, for example those occuring in atom-molecule scattering, could be treated by a straightforward modification of the program.

Running time:
The program is most efficient if the calculation is required for many energy points in a limited range of energies. The time taken by the test run, which was inefficient since only one energy point was calculated, was 1.3 s.