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Some remarks on the calculation of Born partial wave integrals

Published online by Cambridge University Press:  24 October 2008

B. Piraux  and
Colm T. Whelan
B. Piraux
Affiliation:
Blackett Laboratory, Imperial College of Science and Technology, University of London
Colm T. Whelan
Affiliation:
Department of Mathematics, Royal Holloway and Bedford New College, University of London
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Extract

The Born partial wave integrals of Seaton [3] are considered. It is shown that the treatment of Whelan [5] may be further simplified and that these integrals may be expressed as a finite sum of associated Legendre polynomials of the second kind. This provides a convenient method for their numerical evaluation and allows the relationship between the Born and Bethe reactance matrices to be given in explicit analytic form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 375 - 381
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Copson, E. T.. Theory of Functions of a Complex Variable (Oxford University Press, 1935).Google Scholar
[2]Whelan, C. T. and Piraux, B.. (In preparation.)Google Scholar
[3]Seaton, M. J.. The evaluation of partial wave integrals in the Born approximation. Proc. Phys. Soc. 77 (1961), 184.CrossRefGoogle Scholar
[4]Watson, G. N.. Theory of Bessel Functions (Cambridge University Press, 1944).Google Scholar
[5]Whelan, C. T.. On the calculation of cross-sections for electron neutral atom collisions in the Born approximation to the reactance matrix. Math. Proc. Cambridge Philos. Soc. 95 (1984), 179.CrossRefGoogle Scholar
[6]Whelan, C. T.. Ph.D. dissertation, University of Cambridge (1984).Google Scholar
[7]Whelan, C. T.. Cross-sections for electron-hydrogen collisions in the Born approximation to the Reactance matrix. J. Phys. B19 (1986), 2355.Google Scholar
[8]Whelan, C. T.. On the Bethe approximation to the Reactance matrix. J. Phys. B19 (1986), 2343.Google Scholar
[9]Whelan, C. T.. McDowell, M.R.C. and Edmunds, P. W.. J. Phys. B, in the Press.Google Scholar