# Phonon neutron scattering

#### gheremond

Consider a monoatomic 1-D chain of atoms (only acoustic branch). What happens with the inference of the dispersion curve through neutron scattering? In one dimension, conservation of momentum dictates $$k'=k+K_s$$, if k_s is the phonon momentum vector and we only consider processes where a phonon is absorbed by the neutron. The corresponding omega you get from conservation of energy is thus $$\omega = \frac{\hbar}{2 m_n} (2 k K_s+K^2_s)$$, at odds with the usual dispersion relation for the acoustic branch. What went wrong?

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#### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

#### Henryk

Gold Member
How exactly did you get this formula?
ω=ℏ2mn(2kKs+K2s)
Scattering process involves conservation of both: energy and momentum.
Neutron diffraction studies of phonons use triple axis spectrometer where you can scan the momentum and energy change of the neutrons independently.

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