Neutron Scattering

4
0
-5 0 5 10 15 20
ho) [meV]
Figure 5 .3 :
Scattering vectors Q accessed by a diffraction experiment with the detector
at scattering angles 20 = 10 . . .115' vs . the energy transfer hw (incident wavelength
A; = 5 .1 Â) .
For neutrons on the other hand, incident energies are just in the latter range .
the errors which occur due to neglect of inelasticity are still not too large .
Fortunately,
Therefore, it
is possible to derive a correction formula by expanding the true differential cross section
under constant angle into a series in the ratio of the mass of the scattering nucleus and
the neutron mass mn/ms, . In this way one obtains to first order 3 :
al
(dd5~
ze = IbI 2N (S(Q) + .fp(Q» with .fp(Q) = mC (E - CQ~z ) (5 .14)
Here, E is the incident energy and k = 2m~É/1i the respective wave vector .
3 This formula is actually the specification of Placzek's original result [6] to the case of a
detector which is equally sensitive for all neutron energies ("black" detector) .
As pointed
out in [7]
the correction depends strongly on the energy dependence of the sensitivity.
Therefore, except for low Q values, formula (5 .14) is
not the one which is used in practical
applications .
5-6