Theory of Neutron Scatterings

Rigorous derivation of the equations used in small angle neutron scattering is not presented here. The interested reader can find such derivations in the texts by Marshall 

Fundamental neutron scattering theory shows that da/dfl is given by  

Where V(r) is the Fermi pseudo potential describing neutron-nucleus interaction during scattering, M the neutron mass and r the vector separation of neutron and nucleus. Considering one nucleus then the scattering amplitude from that nucleus is  

Two contributions to Eq. (8) can be identified, the first of these is b — b ) and represents the mean square deviation of individual scattering lengths from the average value. As such it is called the incoherent scattering cross section and constitutes a uniform, isotropic background scattering since it retains no information on the phase of the scattered neutrons. Incoherent scattering cross sections are tabulated as values of a. where  

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Lovesey S W 1984 Theory of Neutron Scattering from Condensed Matter vo 1 (Oxford Oxford University Press)... 

From the theory of neutron scattering [62], S JQ, CO) may be written as the Fourier transfonn of a time correlation function, the intermediate scattering function, hJQ, t) ... 

Pearson DS, Fetters LJ,Younghouse CB,Mays JW (1988) Macromolecules 21 478 Lovesey SW (1984) Theory of neutron scattering from condensed matter. Clarendon, Oxford... 

An introduction to the theory of neutron scattering can be found, for instance, in a books by Hansen and Donald (1986) and Higgins and Benoit (1994). The scattering function for a single macromolecule is known for some models of... 

S. W. Lovesey, Theory of Neutron Scattered from Condensed Matter, Vol. I Nuclear Scattering, Clarendon Press, Oxford, 1984. 

To make the most of the INS technique and to avoid pitfalls some knowledge of the physics of neutron scattering is desirable. The theory of neutron scattering can be presented at various levels of sophistication. In the classic texts [14, 15] the formalism and the accompanying symbolism can look formidable indeed. In this book, while the presentation of the necessary theory is accurate and rigorous, our concern is the information content of the equations rather than their derivation. Our aim is to acquaint the reader with the basic concepts of neutron scattering, to make the connection between theory and experiment and to show how useful information can be extracted from the experimental data. 

J. A. Janik A. Kowalska (1965). In Thermal Neutron Scattering, (Ed.) P.A. Egelstaff, Academic Press, London and New York, Chapter 9. The theory of neutron scattering by molecules. 

M. Warner, S.W. Lovesey J. Smith (1983). Z. Phys. B-Condens. Matter, 51, 109-126, The theory of neutron scattering from mixed harmonic solids. 

For a detailed review of the theory of neutron scattering, see Thermal Neutron Scattering, P. A. Egelstaff, ed., Academic Press, New York (1965). 

The theory of neutron scattering (Marshall and Lovesey, 1971) is very closely related to that of light scattering. Neutrons are scattered by the nuclei of atoms and molecules... 

The theory of neutron scattering from vibrating molecules was developed by Zemach and Glauber. Recently, the method was applied to complex biological substances (bovine pancreatic trypsin inhibitor). ... 

Much of the theory of neutron scattering concern the elaboration of expressions (closed formulas) for the partial differential cross section, starting from (model) interaction potentials between the neutron and the nucleus (see, e.g.. Squires 1996 Lovesey 1987). The final result of these calculations for nuclear scattering will be outlined below. 

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