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Why do free atomic nuclei have difficulty absorbing gamma rays emitted by other free nuclei?

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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.

Free atomic nuclei struggle to undergo resonance absorption of gamma rays because of the laws of conservation of momentum and energy. When a nucleus emits a gamma-ray photon, it must recoil to conserve momentum, which causes the photon to lose a portion of its energy as kinetic recoil energy ( $E_{R}$ ).12

Similarly, when a nucleus absorbs a photon, it must also recoil, requiring the incoming photon to provide both the energy difference between the nuclear states and an additional amount of energy to account for that recoil. Consequently, a photon emitted by a free nucleus has less energy than what is required for resonance absorption by another free nucleus—specifically, it is missing an amount equal to $2 E_{R}$ .12

While this effect is negligible for visible light, it is significant for gamma rays because their recoil energy is over 10,000 times greater, and nuclear energy transitions are much more sharply defined. The Mössbauer effect overcomes this by embedding nuclei in a solid lattice, allowing the entire crystal to absorb the recoil momentum, which reduces the recoil energy to nearly zero.21