NNR IN RAPIDLY ROTATED METALS By - Nottingham eTheses ...

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3.7 THE EFFECT OF ROTATION ON THE NUCLEAR LINESHAPE
We have shown that sample rotation at the magic angle averages
out internal line-broadening interactions, although this result does
presuppose a sufficiently rapid rotation rate. We now consider
the form of the resulting spectrum.
written as
where p
The Hamiltonian describing the nuclear spin system may be
_+ae jr
Zpm
+jP
is the sum of the secular perturbations and. *' is the mot-
Tonal Hamiltonian representing the kinetic energy. From equation
(2.18) the second moment of the nuclear lineshape about the centre
frequency is given by
M2
In the absence of p,
Tr kp + ý, i 12
3i2 Tr
[Ixi 2
the orientation of the nuclear spins in the
external magnetic field is independent of position or any relative
motion between spins. Consequently m commutes with IX. The
second moment of any resonance spectrum is therefore unaffected by
any sort of motion. However, as does not commute with p,
can be shown(40) that the fourth moment is increased and the line-
shape altered in such a way as to narrow the central component and
enhance the wings.
Detailed calculations for the cases of both uniformly rotating
and randomly reorientating nuclear pairs confirm the above argu-
ments(41,42), In liquids rapid random reorientation can be thought
it