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I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy conservation law.

Is it the same as how a beam of light is diffracted from the Bragg lattice? In that case, the atoms in the crystal are not moving, so there is no phonon. Now we further assume that the light beam does not excite any mechanical vibration in the crystal so that no phonons are created. Then the change of the momentum of the light can be an integer multiple of the three inverse lattice vector.

How can this be generalize when there are crystal vibrations (e.g. phonons with certain momenta.)? Can anyone give me an explanation of the origin of the generalized momentum conservation law?

Thanks.

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