Neutron Scattering

is obtained, all constant factors are omitted and lumped into a still undetermined proportionality
factor 6 . Note the factor t- ' between S and I which causes a significant
intensity enhancement for the early arriving time channels, however intimately connected
with a corresponding loss of energy resolution . Application of the transforms Eqns . 10 .5
and 10 .11 allows a display of the spectra in terms of S(20, cw) . Figure 10 .6 shows a
corresponding S(20, cw) derived frein the water data (medium angle data in fig . 10 .5) .
1 .5-
1 .5-
0 .5-
0 .5-
0
-4 -2 0 2 -40 -20
AE/meV
AE/meV
Figure 10 .6 : TOF spectrum from liquid water (see fig . 10 .5) converted to S(2(9, w)
displayed over two different energy ranges .
The diffusion is easily recognizable but the structure due to (internal) vibrations is lest in
this type of representation. As soon as a model for S(Q, cw) is available, it is in most cases
more advantageous to apply the inverse transform to that model to compute I(28, K)
and to compare this result with the raw TOF data . This procedures also allows for a
simpler more direct application of resolution corrections .
Remark : application of a coordinate transform (here (Q, w) - (20, K) resp . (Q, w)
(20, K)) requires -besicles the observation of the (nonlinear) coordinate dependence- the
application of a Jacobian determinant as factor to preserve "volume" . For the timefrequency
part this is also donc here (t-4 -factor) . The transform 20 ----> Q, however
'Fer practical purposes the proportionality factor is determined by an absolute calibration using a
standard sample, e .g . vanadium which is a purely incoherent elastic scatterer .
10-10