Environmental Engineering Reference
In-Depth Information
Fig. 4.1. The principle of a neutron-scattering experiment, carried out
on a triple-axis spectrometer . An incident beam of neutrons, with well-
defined momenta, is selected from the continuous reactor spectrum by the
monochromator crystal, and scattered from the sample. The intensity of
the scattered beam of neutrons, with generally different momenta defined
by the analyser crystal, is measured by the detector. The scattered in-
tensity, proportional to the scattering cross-section, is thus determined
as a function of the energy transfer and the momentum transfer h
κ
κ
to the sample, whose orientation relative to
can be varied by rotating
the sample table.
H int is the Hamiltonian describing the interaction between the neutrons
and the sample, and the sum extends over all possible scattering pro-
cesses. It comprises a summation over all possible final states
|
f> of
the sample, and an average over all initial states
i> , which occur with
the probability P i . Energy conservation requires that the energy differ-
ence between the final and initial states of the sample, E f
|
E i ,must
be equal to the energy transferred from the neutron to it:
= ( hk ) 2
( hk ) 2
2 M
2 M
.
(4 . 1 . 2)
h k ,where
The linear momentum transferred to the sample is h
κ
= h k
κ
is the scattering vector ,
= k k .
κ
(4 . 1 . 3)
The information about the sample is obtained by measuring the scat-
tered intensity as a function of the natural variables of the experiment,
the energy transfer and the momentum transfer h
.
The scattered neutrons with momenta lying in a narrow range
around h k are counted by placing a detector in a direction along k ,
subtending a small element of solid angle d Ω. The value of k , or the final
κ
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