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There's something I don't understand about the Mossbauer effect. I understand that the Mossbauer effect has a mechanism for eliminating the energy shift due to the recoil of the nucleus, since the inertia can be the inertia of the lattice over-all, rather than the inertia of the individual nucleus. What I don't understand is what happens to the Doppler broadening that I would expect due to the thermal motion of the nucleus. In the Pound-Rebka experiment, for instance, the natural line width gives $\Delta E/E \sim 10^{-12}$, and the general-relativistic effect they were measuring was a shift of about 10-14. On the other hand, the typical thermal velocity of an iron nucleus at room temperature is going to be about 100 m/s, which will give a random Doppler shift of about 10-6. Can anyone explain what I'm missing? It seems as though the random thermal Doppler shifts would be many orders of magnitude bigger than all the other effects involved.
TIA!
-Ben
P.S. I'm new here. When posting math, is the idea to insert it between dollar signs in LaTeX format?
TIA!
-Ben
P.S. I'm new here. When posting math, is the idea to insert it between dollar signs in LaTeX format?