Neutron Scattering

After all ttrose constraints on the detected neutrons it might astonish that there remains sufficient
intensity for measurements . We had learned about the cost of intensity for optimizing the
resolution . In order to aehieve a useful signal/noise ratio here, one has to relax the resolution
in the momentum transfer . Taking the width of 45 cm for an analyzer plate being positioned
at a distance of 150 cm to the sample, one gets an angular resolution of about 9° . For an average
Q value, given by Q=4Y slnO s = 1 .41 - 10 10 m7l for O s = 90' and a wavelength  _
6 .3 - 10 -10 m, ttris means a resolution of f 0 .1 - 10 10 m-1 . For comparison : at the triple axis
spectrometer one has a resolution in Q of about 0 .01 - 10 10 m-1 . On the other hand, most
problems investigated on a backscattering spectrometer exhibit smooth functions on ~Qj, only,
which allow for such a relaxed Q -resolution. The isotropie scattering also permits the simultaneous
recording of several momentum transfers by arranging many counters and associated
analyzer plates around the sample. In ttris respect the efficiency of a backscattering instrument
is higher than that of a triple axis spectrometer which uses on detector, only . .
Fig. 18)
Rotational tunneling of
the methyl group in
Paraoetamol .
energy transfer / geV
Finally, as an example for a measurement on the backscattering instrument in Ellich, the temperature
dependence of the spectrum of Paracetamol is shown in Fig .18 . In this case, one is interested
in the rotational or more exactly - permutational - tunneling of the methyl group of
the molecule . Eigenvalues and eigenvectors of the associated hamiltionian result from the
Mathieu equation for threefold symmetry . The goal is to determine those eigenvalues (here
about 3~teV for the AE transition, A = totally synznzetric, E = doubly degenerate) and thus
to obtain rather precise information on the intea- and inter-molecular interactions . A remarkable
observation thereby is that the excitation energies are much smaller than the thermal energy
of say 10 K of the sample (1 lteV z 1/100 K) . This may be understood by considering
thé basically différent coupling of phonon (spin = 0) and neutron (spin ='/z) to thé eigenstates
with différent symmetries (see lecture on Translation and Rotation) .
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