The interaction between the neutron and the spin is of
the form - B were
is the moment
of the neutron
and B
is the magnetic field created by the spins in the sample.
Write an expression for the scattering cross section for scattering from
an initial state to a final state
or
in the Born Approximation. This is just a review
of undergraduate quantum mechanics.
Now consider a regular array of spins occupying a
lattice with positions
Express the measured scattering cross section in terms of the spin spin auto correlation function.
a) If the incoming neutrons are all polarized in the Z interaction (with spin up) and the detectors only count neurtons with spin down in the Z direction.
b) What if the initial beam is unpolarized and the the detector does not care about polarization.
c) Assume the spins are ordered,when do you expect a large scattering cross section for elastic scattering?