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Quasielastic Neutron Scattering and Solid State Diffusion$
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Rolf Hempelmann

Print publication date: 2000

Print ISBN-13: 9780198517436

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198517436.001.0001

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The basic theory of neutron scattering

The basic theory of neutron scattering

Chapter:
(p.26) 3 The basic theory of neutron scattering
Source:
Quasielastic Neutron Scattering and Solid State Diffusion
Author(s):

Rolf Hempelmann

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198517436.003.0003

This chapter discusses ways to describe theoretically neutron scattering as a probe for condensed matter, first the scattering on a rigidly bound and isolated nucleus by the neutron-nucleus interaction as well as coherent and incoherent neutron scattering. Then the corresponding matrix element, in terms of perturbation theory of quantum mechanics, is derived which yields the double differential scattering cross-section of the sample as a function of momentum and energy transfer of the scattered neutrons. With the concept of the van Hove correlation functions, this matrix formulation is finally transformed into classical correlation functions, which are convenient if the particle motion can be described by classical dynamical models. In this way, the coherent scattering function S(Q, ω) is the double Fourier transform of the correlation function G(r,t), whereas the incoherent scattering function Si(Q, ω) is the double Fourier transform of the self-correlation function Gs(r,t). The convolution approximation relates S(Q, ω) to Si(Q, ω). The scattering intensity decreases with increasing Q due to the Debye–Waller factor which is directly connected to lattice vibrations.

Keywords:   coherent neutron scattering, incoherent neutron scattering, quantum mechanics, van Hove correlation function, Debye–Waller factor

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