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Atomic Nuclear Physics

Neutron Scattering by Kurt Sköld and David L. Price (Eds.)

By Kurt Sköld and David L. Price (Eds.)

Sköld e.K., fee D.L. (eds.) Neutron scattering (AP, 1986-1987)(ISBN 0124759653)

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34 DAVID L. PRICE AND KURT SKC)LD FIG. 10. Coherent and incoherent scatteringfunctions for liquid argon. 3. Symmetry and Moment Relations The scattering functions S,(Q, w ) and S , ( Q , w), and by implication the intermediate scattering functions and space-time correlation functions, must satisfy certain general relations regardless of the details of the system under consideration. These relations serve several important functions: They provide a consistency check on experiment data. (2) They provide a necessary constraint on theoretical models.

72a) reduces to (0-0 where we neglect surface effects and assume that all d atoms are equivalent to the one at the origin. 79) Similarly we find that Gf(r, 0) = 6(r). 80) 32 DAVID L. 81) = Idd’(Q, 0), then Eq. 82) For incoherent scattering we note from Eq. 41b) that s-mm SP(Q, E ) d E = I:(Q, 0) = 1. 83) The structure factors Sdd‘(Q)are measured in a total scattering experiment in which the integral of the scattering over energy at constant Q is determined : const. 84) where the second term incorporates the total scattering cross section ad and the first term represents the “distinct” scattering excluding the self term.

The calculations of the inelastic cross section can in principle be carried out to all orders if the force constants of the crystal are known, using the result of Eq. 46)in Eq. For the coherent cross section this is a tedious calculation and it is usual to assume that for the multiphonon terms it is equal to the incoherent cross section (“incoherent approximation”), which is a much simpler calculation. For crystals with only one type of atom, an expression similar to Eq. 70)can be used to give the exponent in Eq.

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