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Manuscript Title: A generalized R-matrix propagation program for solving coupled second- order differential equations.
Authors: L.A. Morgan
Program title: RPROP2
Catalogue identifier: AAJK_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 31(1984)419
Programming language: Fortran.
Computer: VAX 11/780.
Operating system: VMS, COS.
Word size: 32
Peripherals: disc.
Keywords: R-matrix, Scattering, Low-energy, Atom-electron, Ion-electron, Electron-molecule, Atom-molecule, Asymptotic solution, Differential equation, General purpose, Hamiltonian matrix.
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 sub-ranges and the Hamiltonian is diagonalized in each sub-range 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 restrictions imposed in a previous version of the program on the form of the potential interaction is removed. Instead, the user must provide a subroutine which generates the potential matrix at the abscissae of the quadrature scheme.

Running time:
The program is most efficient if calculations are carried out for many energy points within a fairly small range of energies. The time taken for the test run, at a single energy on a VAX11/780 was 13 seconds. A much larger run which solves 60 coupled equations at 100 energy points took 75 seconds per subrange on the Cray.