 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2011/paper-1/section-c/c10/b/solution

(q, ω)

E_{f} = E_{i} + ℏ ω, k_{f} = k_{i} + q + G .

For phonon creation,

E_{f} = E_{i} - ℏ ω, k_{f} = k_{i} - q + G .

The signs follow whether the neutron gains or loses the phonon's energy and crystal momentum. These are one-phonon coherent inelastic neutron scattering conditions, with

G

accounting for lattice periodicity.

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