Incoherent Inelastic Scattering
The most interesting component of thermal scattering is called
"incoherent inelastic" because the neutron exchanges energy with
the target molecule or crystalline lattice and all the
scattered waves are assumed to combine incoherently without
interference effects. This component is described in terms
of a scattering function called "S of alpha and beta," where
alpha and beta are reduced values for momentum transfer and
energy transfer, respectively:
Here σb is the bound scattering cross section, σf is the free scattering cross section, E and E' are initial and final neutron energies, μ is the scattering cosine, and A is the ratio of the target mass to the neutron mass.
The scattering function for a gas of particles with no internal structure (free gas) is given by
A bound scattering function is considerably more complex, as shown by the following two figures for hydrogen bound in water:
The sharp features in the first figure are due to the discrete molecular vibrations at .205 and .408 eV. The peak that develops at small alpha and beta is a pseudo-elastic peak resulting from diffusion. For more information on the physics going on in these figures, see the LEAPR write up.
THERMR processes the scattering function into an incoherent-inelastic cross section vs energy and a normalized energy-angle distribution. An example of such a distribution is shown below for beryllium. A number of "up-scatter" peaks corresponding to the deexitation of lattice vibrations are seen for low incident energies.
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