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Manuscript Title: Analytic first Born atomic scattering: a computer algebra solution using Maple V.
Authors: A.J. Blackett, A.T. Stelbovics
Program title: BORN
Catalogue identifier: ADJW_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 116(1999)78
Programming language: Maple.
Computer: Pentium 100MHz.
Operating system: MS Windows 95, Windows NT v 4.0, Unix.
RAM: 32M words
Keywords: Computer algebra, Born approximation, Atomic scattering, Symbolic computing.
Classification: 5.

Nature of problem:
Computation of analytic expressions in atomic scattering for scattering amplitudes, differential cross-sections and total cross-sections for electron scattering from hydrogenic ions in the first Born approximation [2,3].

Solution method:
Symbolic algebra using Maple V R4 [1]algebraic computing software.

The complexity of calculating scattering amplitudes, differential and total cross-sections increases rapidly with increasing n in the target states.

Running time:
Running times vary depending on the calculation and the initial and final states of the target. Scattering amplitudes take the least time to compute, while total cross-sections take the longest. Selecting the no simplification option improves the speed of calculating differential and total cross-sections, but the resulting expression is often extremely large. On a Pentium 100MHz machine, results for typical scattering amplitudes can be returned within a few seconds. Total cross-section calculations can take 300 seconds or longer.

[1] B.W. Char, K.O. Geddes, G.H. Gonnet, B.L. Leong, M.B. Monagan and S.M. Watt, Maple V Library Reference Manual (Springer-Verlag, New York, 1991).
[2] L.I. Schiff, Quantum mechanics (3rd ed.) (McGraw-Hill Book Company, New York, 1968).
[3] L.D. Landau and E.M. Lifshitz, Quantum mechanics (non-relativistic theory) (3rd rev. ed.) (J.B. Sykes and J.S. Bell, Trans.) (Pergamon Press, Oxford, 1987).