# How is Mössbauer spectroscopy so resistant to thermal motion?

Mössbauer spectroscopy detects tiny shifts (on the order of $\rm{\mu eV}$ or $\rm{meV}$) in a gamma ray's energy due to the chemical environment of the nucleus.

The scan consists of moving a source of excited nuclei and measuring how much is absorbed by the corresponding ground-state isotope in the sample. The velocity, on the order of $\rm{mm/s}$, Doppler-shifts the source's gamma rays to produce tiny differences in energy. The gamma ray's extremely narrow line-width allows such an exquisite selectivity.

Why don't thermal motions (lattice phonons, etc), which are on the order of $100\,\rm m/s$ (in the form of phonons at various frequencies) swamp such a sensitive measurement?

• I'm presuming you did not read the 'Basic Principle' paragraph in your linked article, and did not follow the link to the Lamb-Mossbauer factor? Now, at first take, your objection is exactly that of about everyone else at the time. However, enough gammas on the zero-phonon line are emitted for it to be practical. – Jon Custer Apr 25 '16 at 16:59
• The natural line width of these gamma transitions is extremely small, which means that the effective interaction time (per time/energy uncertainty) is long, which also means that the system averages out over many lattice oscillations. This may seem counterintuitive because of the (fundamentally flawed) photon-is-a-hard-billiard-ball-and-photon-emission-is-an-instantaneous-process model that we are used to. Nothing could be further from the truth. This experiment is much closer to the resonant coupling of two very high Q harmonic oscillators than to a scattering experiment. – CuriousOne Apr 25 '16 at 18:54
• @Jon Custer The thermal motions are going to populate too many phonons to ever get stillness on the mm/s scale regardless of recoil. The odds that ~cm/s small-scale-collective motions all the way to ~100 m/s single-atom motions will lay dormant are very rare, yet we see ~mm/s sharp peaks. – Kevin Kostlan Apr 25 '16 at 21:19
• @CuriousOne: So you average the motion over about one half-life to estimate how much thermal effects smear things? Also it would be far-field (one-way) resonant coupling? – Kevin Kostlan Apr 25 '16 at 21:19
• That would by my (classical) mental picture, but remember that the volume of the light cone of a half life is much larger than the volume of the crystal, so the limit is not the half life but the crystal volume. You still have to do the quantum mechanical calculation, of course, to get a quantitative result. – CuriousOne Apr 25 '16 at 21:32