Neutron Scattering

G(r, t)
G(r, t) i(Q, t)
r
Q
i(Q, t)
r
0. Q
Figure 5 .10 : Schematic Comparison of the correlation functions G (r, t), G, (r, t) and the
intermediate scattering functions Sc oh(Q, t), S;n,(Q, t) for a simple liquid at different times .
The solid lines denote the coherent case, the dashed lines the self/incoherent .
tering functions decay with respect to the t = 0 value . The decay is faster for higher
Q and (in the coherent case) less pronounced at the structure factor maximum .
The long time limit of the pair correlation function is the average density po while
the self correlation simply vanishes (in a liquid) . In consequence both the coherent
and the incoherent intermediate scattering function decay to zero for long times and
any Q .
5.4 Scattering from an Ideal Gas
We consider a gas ofN atoms in a volume V neglecting the spin coordinates Q and assume
that all scattering lengths are identical b i = 1 . The wave function of a free atom confined
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