Programs in Physics & Physical Chemistry
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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|
|Keywords: R-matrix, Scattering, Low-energy, Atom-electron, Ion-electron, Electron-molecule, Atom-molecule, Asymptotic solution, Differential equation, General purpose, Hamiltonian matrix.|
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.
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.
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.
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.
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