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Manuscript Title: FARM: a flexible asymptotic R-matrix package.
Authors: V.M. Burke, C.J. Noble
Program title: FARM
Catalogue identifier: ADAZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 85(1995)471
Programming language: Fortran.
Computer: Cray Y-MP8.
Operating system: UNICOS, UNIX, AIX.
RAM: 1.5M words
Word size: 64
Peripherals: disc.
Keywords: Atomic physics, Electron-atom, Scattering, Electron-ion scattering, R-matrix, Propagator, Gailitis, Asymptotic expansion, K-matrix, T-matrix, Collision strength, Cross-section, Eigenphase, Asymptotic Distorted wave.
Classification: 2.4.

Nature of problem:
The program solves the scattering problem in the asymptotic region of R-matrix theory where exchange is negligible.

Solution method:
A radius is determined at which the wave function, calculated as a Gailitis expansion [1] with accelerated summing [2] over terms, converges. The R-matrix is propagated from the boundary of the internal region to this radius and the K-matrix calculated. Collision strengths or cross sections may be calculated and summed over partial waves.

The code requires as input a file, H, output from an internal region R-matrix program [3], [4] defining the potential in the external region and the R-matrix on the boundary. The code can be used for scattering by ions as well as by atoms but averaging over Rydberg resonances is not included in the current version. The code can be easily modified by replacing the routines which read the file H to interface with other internal region R-matrix codes including those for molecular scattering problems.

Unusual features:
Mathematical routines from the LAPACK and BLAS libraries are included in both single and double precision to facilitate running the code on different machines. The namelist facility is used for data input and core is dynamically allocated using the "big vector" technique. The memory required for the test run can be reduced by decreasing the dimension of the big vector. There is a choice of R-matrix propagators. The Baluja-Burke-Morgan [5] can be used at small radii and the Light- Walker [6] at larger radii where the potential is more slowly varying. Tightly bound channels can be systematically dropped during propagation. Higher multipoles can be included without loss of efficiency. It can calculate at scattering energies close to threshold and can cope with nearly degenerate channels. At high partial waves, the asymptotic distorted wave method [7] can be used to avoid the diagonalisation of the Hamiltonian in the internal region. The code can output cross- sections summed over partial waves or, for higher waves, as a sections of total angular momentum ready to be extrapolated by a top-up procedure.

Running time:
The time-consuming part of the propagation is independent of energy so the code is more efficient for several energies. The time also depends on the number of channels but where possible the code is vectorised with respect to channels. The time will be greater for energies close to a threshold and if target states are nearly degenerate. The test runs each took less than 1 second on the Cray Y-MP8.

[1] M. Gailitis, J. Phys. B 9(1976)843.
[2] C.J. Noble and R.K. Nesbet, Comput. Phys. Commun. 33(1984)399.
[3] V.M. Burke, P.G. Burke and N.S. Scott, Comput. Phys. Commun. 69(1992)76.
[4] K.A. Berrington, W. Eissner, P. Norrington, Comput. Phys. Commun. to be submitted.
[5] K.L. Baluja, P.G. Burke and L.A. Morgan, Comput. Phys. Commun. 27(1982)299.
[6] J.C. Light and R.B. Walker, J. Chem. Phys. 65(1976)4272.
[7] R.K. Nesbet, J. Phys. B: At. Mol. Phys. 17(1984)L897.