Abstract
According to Eq.(2.127) the ratio of the scattering cross section of a uniform sphere to its geometrical cross section depends upon three independent parameters
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Notes and References
The cross section for x « 1 was first derived by Lord Rayleigh (1871); see also Lord Rayleigh (1899); and for recent work, A. Ramm (1980a).
The name Rayleigh-Gans is based on the following papers: Lord Rayleigh (1881); R. Gans (1925); for more recent work, see, for example, M. Kerker et al. (1963); and for Rayleigh-Gans scattering by nonspherical particles, see Barber and Wang (1979).
The original work on resonances scattering is that by P. Debye (1909a).
For more details, see H. C. van de Hulst (1957), chap. 11. See also L. I. Schiff (1956b).
The method of obtaining the geometrical-optics limit from physical optics goes back to P. Debye (1909a).
The outline given follows essentially H. C. van de Hulst (1957).
and
The poetic description of the rainbow is from Ode to Sir Isaac Newton by James Thomson.
The second poem is The Rainbow, by D. H. Lawrence. I am indebted to Prof. John Hollander of Yale University for these references.
For more details on the rainbow, see T. Ljunggrén (1948); H. C. van de Hulst (1957). Relevant numerical tables can be found in J. C. P. Miller (1946); Integrals (1958). For recent work see H. M. Nussenzveig (1969b); and Khare and Nussenzveig (1974).
The single fact which is perhaps most notable about the glory from the point of view of the history of physics is that in the attempt to study it experimentally C. T. R. Wilson discovered the cloud chamber. See the quotation on pp. 14 and 15 of C. N. Yang (1961).
The procedure on which the Watson method is based is due to Poincaré and Nicholson. It was first used in the context of electromagnetic theory by G. N. Watson (1918). See also E. P. White (1922); O. Laporte (1923); Van der Pol and Bremmer (1937); A. Sommerfeld (1949), pp. 282ff.
The split-up into the geometrical-optics part and the creep-wave part is due to W. Franz (1954).
The zeros of Hankel functions and of their derivatives, in the complex λ plane, are studied by J. B. Keller et al. (1963), where other references may be found.
Other recent references are Kazarinoff and Ritt (1959); Goodrich and Kazarinoff (1963); Senior and Goodrich (1964); H. M. Nussenzveig (1965 and 1970).
The method of saddle-point integration goes back to F. Debye (1909b and 1910). For examples of more recent discussions see A. Sommerfeld (1949), pp. 98ff. and 116ff.; B. L. van der Waerden (1951); Morse and Feshbach (1953), vol. 1, pp. 434ff; A. Erdelyi (1955).
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© 1982 Springer Science+Business Media New York
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Newton, R.G. (1982). Limiting Cases and Approximations. In: Scattering Theory of Waves and Particles. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88128-2_3
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