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How does gamma-ray energy change when a nucleus recoils?

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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.

When an atomic nucleus emits or absorbs a gamma ray, it experiences a recoil due to the conservation of momentum, similar to a rifle kicking back when fired.12

Because the recoiling nucleus carries away a portion of the energy as kinetic recoil energy ( $E_{R}$ ), the energy of the emitted gamma-ray photon is reduced by that amount. Conversely, when a nucleus absorbs a gamma ray, it must also account for this recoil energy, meaning the incoming photon must supply both the transition energy and the additional $E_{R}$ . Consequently, the energy of a gamma ray emitted by a free nucleus is slightly less than the energy difference between the nuclear states, preventing resonance absorption between free nuclei.12

The Mössbauer effect overcomes this by embedding nuclei within a solid crystal lattice. In this configuration, the recoil momentum is absorbed by the entire lattice rather than a single nucleus, making the recoil energy negligible and allowing for recoil-free, resonant emission and absorption of gamma rays.1342