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Appendix: Quantum Mechanical Approach of Born and Distorted-Wave Born Approximations

: Baumbach, T.; Mikulik, P.

Daillant, J.; Gibaud, A.:
X-Ray and Neutron Reflectivity: Principles and Applications
Berlin: Springer, 1999 (Lecture Notes in Physics M 58)
ISBN: 3-540-66195-6
Aufsatz in Buch
Fraunhofer IZFP ()
multilayer; Random; fluctuation

In this appendix we treat the formal quantum-mechanical approach to scattering by mulitlayers with random fluctuations. That can be interface roughness, but also porosity or density fluctuations. In particular we develop the differential scattering cross section in the kinematical approximation(first Born approximation) and in the distorted wave Born approximation in terms of the structure amplitueds of the individual layers an of their disturbances.This approach is wirtten in a general way. In Chap. 8 it will be applied to the reflection and to diffraction under conditions of specular reflection under grazing incidence by rough multilayers and multilsayered gratings. We would like to notice that we adopted her the phase-sign notation of this book, with plane waves e(-ikr) and Fourier transforms e(+iqr), which is contrary to that used in most publications using this formalism.