Neutron Scattering

Figurel Schematical drawing of a general scattering experiment .
G dA'I f d'r- exp(ilk' - r)V(r)exp(ik - r) > ~2
*s(w+E'-E)
T'he cross section in equation (13 .1) is given by the sum of the transition matrix
elements between initial states aiAi and the final states (T'A' weighted by the probabilities
of the initial states .
In order to calculate the cross section and the observable intensity
distribution, one needs the interaction potential Ù (r) and detailed knowledge of the states
in the sample ~i .
In the inverse way one may use a measured intensity distribution in
order to characterize the sample states, for example the phonons .
This is the usual way of
the interpretation of any scattering experiment .
The sample states may be characterized
by specific parameters, for example the frequencies and the polarization patterns in case
of phonons, which with the aid of equation (13 .1) will be deduced from the experimental
intensity distribution .
13 .1 .2 Nuclear interaction - phonons
The nuclear interaction between the neutron and the core of the atoms is characterized
by an extension of 10 -'À, which is extremely small in comparison to the wavelength of
thermal neutrons . Therefore, the scattering is isotrope and may be described by only one
parameter, the scattering length .
The interaction with the hole crystal is given by the
sum over the atoms
(13 tir (r) = 21 bjb(r - Rj )
.2),
where bj and Rj are the scattering length and the position of the j-th atom . 'The
mixing of different isotopes at the same atom site in the crystallographic lattice yields a
further complication, rince different isotopes have different scattering lengths .
This means
13-2