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Why does the chance of recoil-free gamma-ray emission depend on thermal vibrations?

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Figure 1: Spectrometer utilizing Mössbauer effect concept Effect is usually observed by measuring transmission of gamma rays from radioactive source through absorber containing resonant isotope. — Mössbauer effect Figure 1: *Spectrometer utilizing Mössbauer effect concept* Effect is usually observed by measuring transmission of gamma rays from radioactive source through absorber containing resonant isotope.

The chance of recoil-free gamma-ray emission depends on thermal vibrations because the Mössbauer effect relies on the ability of a crystal lattice to absorb the recoil momentum of a nucleus.12

Under normal conditions, a free nucleus recoils when it emits a gamma-ray photon, causing a loss of energy that prevents resonant absorption. However, when a nucleus is embedded in a solid, there is a finite probability that the recoil momentum is transferred to the entire crystal lattice rather than the individual nucleus. Because the mass of the entire lattice is effectively infinite compared to a single nucleus, the kinetic recoil energy becomes negligible, allowing the emitted gamma ray to retain the full energy of the nuclear transition.321

This process is sensitive to thermal vibrations because the probability of this recoil-free event is linked to the relationship between the free-atom recoil energy and the characteristic lattice vibration energy. If the recoil energy is small compared to these vibrations, the lattice can successfully absorb the momentum. Consequently, the effect is typically observed at low temperatures, where thermal energy is minimized, ensuring the gamma rays are not broadened by thermal motion and remain suitable for resonant reabsorption.13