Neutron Scattering

With this example we can also demonstrate that neglecting the operator character of the
position vectors leads to a wrong result .
classical expression (5 .60)
If we write the scattering function using the
S cl (Q' w) - 27r t
dtexp(-iwt) Cexp (-iQ - (r(t) - r(0») > (5 .86)
is obtained . For a free atour we have r(t) = r(0) + tp/msc . Inserting this expression
into (5 .86) and averaging leads to :
1 _ W2msc l
Sc'MW)
2kBTQ2l - 47rErkBT exp (
.
Comparison with (5 .73) shows that this result is wrong by neglecting the recoil energy
term . Instead of being centred at Er the expression (5 .87) is symmetric with respect to
W = 0 .
(5 .87)
References
[1] G . E . Bacon : "Neutron Diffraction" (Clarendon Press, Oxford, 1975) .
[2] G . E . Bacon (ed .) : "Fifty Years of Neutron Diffraction : The Advent Of Neutron
Scattering" (Adam Hilger, Bristol, 1986) .
[3] S . W . Lovesey : "Theory of Neutron Scattering from Condensed Matter" (Clarendon
Press, Oxford, 1984)-
[4] G . L . Squires : "Introduction to the theory of thermal neutron scattering" (Cambridge
University Press, Cambridge, 1978) .
[5] M . Bée : "Quasielastic neutron scattering" (Adam Hilger, Bristol, 1988) .
[6] G . Placzek, Phys . Rev . 86 377 (1952) .
[7] J . L . Yarnell, M . J . Katz, R . G . Wenzel, S . H . Koenig, Phys . Rev . A 7 2130 (1973) .
[8] G . D . Wignall, D . G . H . Ballard, J . Schelten, Eur . Polym . J . 10 861 (l973) .
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