The coherent and incoherent scattering strengths

The concepts of coherence and incoherence are related to the way in which the neutron, both as a wave and as a particle, interacts with the scattering sample. Wave-like representations of the neutron view its interaction with solids as occurring simultaneously at several atomic centres these atoms become the sources of new wavefronts. Since the scattering occurs simultaneously from all of these atoms the new wavefronts will spread out spherically from each new source and remain in phase. Provided the lattice is ordered, the coherence of the incident wave has been conserved. Constmctive interference between the new wavefronts leads to the generation of distinctive diffraction patterns with well-defined beams, or reflections, appearing only in certain directions in space and no intensity in other directions. 

Diffraction patterns are a defining characteristic of coherent scattering. The number of reflections is limited and each is therefore intense. Since the incident neutron wave interacted with many atoms the momentum transferred ( 2.3) to the sample was not absorbed by any single atom but, in the limit, by the whole crystal with its network of bonds. 

To an incident beam of neutrons the atoms of chorine are a random mixture of Cl and Cl. We calculate the proportions of neutrons scattered coherently and incoherently from chlorine (75% Cl, 25% Cl) with coherent scattering lengths, icoh (m) from Appendix 1. The average scattering length, which provides the coherent signal, is 

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