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In solid state physics, inelastic neutron scattering is a commonly-used experimental technique for probing the energy spectrum of phonon and magnon excitations. This technique relies on the interaction between neutrons and the excitations.

What is the origin of the interaction in these cases? Is there a similar interaction that would allow the determination of electronic band structures using the technique?

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As I recall (it was thirty years ago!) the main interaction is between neutrons and atomic nuclei, which is presumably a strong force interaction. The neutrons have no significant direct coupling to electrons, but the nuclei are charged so displacing a nucleus interacts with the electrons and can transfer energy to them.

Neutrons have a non-zero magnetic moment, and I think there are special cases e.g. with ferromagnetic materials, where this is significant. However I have to confess I know little of this area.

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It is true what you say. Inelastic neutron scattering happends due to neutron - nucleon interactions and is therefore fit to examine the lattice structure of a material rather than its electronic structure, which you can do reasonably well with different kinds of electron scattering experiments. You can, on the other hand, use a spin-polarized neutron beam to test the magnetic structure and its excitations of a given solid. – Neuneck May 16 '13 at 10:27

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