Neutron Scattering

allow a good determination of the EISF in the accessible Q range . Thus precise conclusions
on the possible rotations can be drawn .
Rotational jumps are thermally activated and obey the Arrhenius law (17 .23) . Po = o is
called attempt frequency. Its inverse is about the time requiredby the atom at roomtemperature
to pass the jump distance . For a methyl group P o - 10 13 .sec 1 . The exponential factor represents
the succes rate : the larger the barrier E o , the rarer a crossing . If the shape of a potential
is given one gets the potential from the activation energy E a . It is assumed that the potential
does not change with temperature .
In general a large Q range is required at good energy resolution to get conclusive answers
. Adamantan (fig . 17 .6) is an exceptionally good example . Best suited are backscattering
instruments . Time-of-flight spectrometers suffer from a small Q-range . More complex 3-
dimensionaljump models involve jump matrices of higher dimensions [6] .
Possible reasons for wrong conclusions may be the occurrence of multiple jumps .
neutron distinghuishes only the starting and the final orientation . Double jumps about an easy
axis may look as a single jump about a high barrier [7] . The scattering function is calculated on
the assumption of single jumps, however . Monte Carlo simulations eau clarify discrepancies .
The
17 .3 .2 Rotational tunnelling : single particle model
Stochastic motions take their energy from a thermal bath . At low temperature they die out
and a classical description fails . A quantummechanical theory is needed . In quantum mechanics
the indistinghuishable protons of a molecule are connected by a common wave function .
This introduces coherence effects . Eigenenergies of rotation are the so-called librations in the
meV regime - similar te , harmonie oscillations - and the new low energy tunnelling modes in
the peV regime. A "pocket states" formalisme - described in more detail below for methyl
groups - gives a qualitative picture . The molecule can exist in three possible orientations
123 >, 1231 > and 1312 > . If the barrier between these orientations is large, the orientational
subgroups are decoupled and molecules can perform almost harmonie oscillations only
(threefold degenerate) . For lower barrier the orientational substates are coupled. In quantum
mechanical language : the wave funetions overlap and the librational states split by tunnelling .
Thus rotational tunnelling is not a dynamical event. Only if one could prepare a system in a
Gedanken experiment in a single orientation it would move into a new orientation within a
time t - ~t
. Tunnelling energies h~ are of the order of peV. Monographs are [4, 8, 9] .
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