Theory of Slow Neutron Scattering by Liquids. I
- 1 May 1962
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 126 (3) , 986-996
- https://doi.org/10.1103/physrev.126.986
Abstract
Based on Van Hove's formalism, a general discussion of scattering in liquids has been given. The scattering cross section has been expressed in terms of velocity correlation functions; in particular, for the incoherent scattering cross section it is shown that in the Gaussian approximation for Van Hove's function, only a knowledge of the velocity autocorrelation function is necessary. The departure from the Gaussian approximation is expressed in terms of higher order velocity correlation functions. A derivation of an approximate formula for the width function of the Gaussian , suggested earlier by the authors, has been given. The frequency spectrum of the velocity autocorrelation function has been introduced, and it has been shown that, as a consequence of the fluctuation-dissipation relations, the spectral representation of the width function is formally identical with that obtained earlier for a harmonic solid. The first few moments of the energy transfer have been discussed. Some of these moments have been shown to satisfy certain relations which involve only experimentally observable quantities; and hence, these relations can be used as a check on the internal consistency of the experimental data.
Keywords
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