Neutron Scattering

(A(0)A(T»
Figure 5 .9 : Simulated result of a dynamic light scattering experiment . The circular
dots show the output of the correlator electronics . The continuons curve is the expected
exponential decay (5 .25) . The dashed line shows the underlying fluctuating intensity .
5 .3 .2 The Van Hove Correlation F unction
In order to consider inelastic scattering the differential cross section d6/dÇZ is generalized
with respect to its dependence on the energy transfer hrw . This leads to the double
differential cross section in quantum mechanical notation :
020, k'
- -E PaPl
~ (A', 6 I b i exp(iQ - ri ) IA, 6 Î
2
S (hw + EA - Ey) . (5 .27)
Here, A and a describe the relevant space and spin quantum number respectively in the
initial state and A' and Q' those in the final state. PA and PQ are the respective probabilities
for the initial states A and a . The inner sum refers to all particles with scattering lengths bi
and single-particle coordinate operators r i . k and k' are the wave vectors of the incident
and scattered neutrons . The delta function expresses energy conservation : the energy
transfer of the neutron hw is exactly compensated by the energy change of the quantum
state ofthe scattering system Ey-E A . In the following we will neglect the spin coordinates
for the sake of simplicity.
5- 13