Book contents
- Frontmatter
- Contents
- Preface
- 1 Critical effects in semiclassical scattering
- 2 Diffraction and Coronae
- 3 The rainbow
- 4 The glory
- 5 Mie solution and resonances
- 6 Complex angular momentum
- 7 Scattering by an impenetrable sphere
- 8 Diffraction as tunneling
- 9 The Debye expansion
- 10 Theory of the rainbow
- 11 Theory of the glory
- 12 Near-critical scattering
- 13 Average cross sections
- 14 Orbiting and resonances
- 15 Macroscopic applications
- 16 Applications to atomic, nuclear and particle physics
- References
- Index
13 - Average cross sections
Published online by Cambridge University Press: 02 December 2009
- Frontmatter
- Contents
- Preface
- 1 Critical effects in semiclassical scattering
- 2 Diffraction and Coronae
- 3 The rainbow
- 4 The glory
- 5 Mie solution and resonances
- 6 Complex angular momentum
- 7 Scattering by an impenetrable sphere
- 8 Diffraction as tunneling
- 9 The Debye expansion
- 10 Theory of the rainbow
- 11 Theory of the glory
- 12 Near-critical scattering
- 13 Average cross sections
- 14 Orbiting and resonances
- 15 Macroscopic applications
- 16 Applications to atomic, nuclear and particle physics
- References
- Index
Summary
Such averaging is required to wash out the sharp bumps.
(Friedman & Weisskopf 1955)When absorption within the scatterer is taken into account, the incident beam is extinguished both by scattering and by absorption, and one associates a specific cross section with each of these processes. In applications to radiative transfer, it is important to consider the balance not only of energy but also of momentum: this is related with the radiation pressure cross section.
All of these cross sections, for Mie scattering, are plagued by ripple fluctuations similar to those discussed in Sec. 5.2, complicating considerably their numerical evaluation. These fluctuations are irrelevant for most applications, because they are quenched by size dispersion, and one usually deals with a polydisperse population of scatterers.
Thus, one would like to obtain average cross sections, where the average is taken over a size interval just large enough to eliminate the ripple fluctuations, while still allowing slower-scale variations to be resolved. A similar problem occurs in the application of the nuclear optical model to the theory of nuclear reactions (see the above quotation), and one might describe the procedure employed as an ‘optical application of the optical model’.
In special circumstances, one may observe, instead of the irregular ripple fluctuations, smooth oscillations of the cross sections about their averages, arising from forward optical glory effects, predicted and explained by complex angular momentum theory.
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- Information
- Diffraction Effects in Semiclassical Scattering , pp. 164 - 177Publisher: Cambridge University PressPrint publication year: 1992