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# Mossbauer effect

The Mössbauer effect, a physical phenomenon discovered by Rudolf Mössbauer in 1957, refers to the resonant and recoil-free emission and absorption of gamma rays by atoms bound in a solid form. The resonant emission and absorption of x-rays by gases had been observed previously, and it was expected that a similar phenomenon existed for gamma rays, which are created by nuclear transitions (as opposed to x-rays, which are produced by electronic transitions). However, attempts to observe gamma-ray resonance in gases failed due to energy being lost to recoil, preventing resonance. Mössbauer was able to observe resonance in solid iodine, which raised the question of why gamma-ray resonance was possible in solids, but not in gases. Mössbauer proposed that, for the case of atoms bound into a solid, under certain circumstances a fraction of the nuclear events could occur essentially without recoil. He attributed the observed resonance to this recoil-free fraction of nuclear vents.

In general, gamma rays are produced by nuclear transitions: from an unstable high-energy state, to a stable low-energy state. The energy of the emitted gamma ray corresponds to the energy of the nuclear transition, minus an amount of energy that is lost as recoil to the emitting atom. If the lost "recoil energy" is small compared with the energy linewidth of the nuclear transition, then the gamma ray energy still corresponds to the energy of the nuclear transition, and the gamma ray can be absorbed by a second atom of the same type as the first – and, in a solid, such a second atom is immediately available. This emission and subsequent absorption is called resonance. Additional recoil energy is also lost during absorption, so in order for resonance to occur the recoil energy must actually be less than half the linewidth for the corresponding nuclear transition.

The amount of lost energy is described by the equation:

$E_R = \frac{E_\gamma^2}{2Mc^2}$

where ER is the energy lost as recoil, Eγ is the energy of the gamma ray, M is the mass of the emitting or absorbing body, and c is the speed of light. In the case of a gas the emitting and absorbing bodies are atoms, so the mass is quite small, resulting in a large recoil energy, which prevents resonance. (Note that the same equation applies for recoil energy losses in x-rays, but the photon energy is much less, resulting in a lower energy loss, which is why gas-phase resonance could be observed with x-rays.)

Due to the fundamental quantum nature of solids, atoms bound in solids are restricted to a specific set of vibrational energies called phonon energies. If the recoil energy is smaller than the phonon energy, then there is insufficient energy to excite the lattice to the next vibrational state, and a fraction of the nuclear events (the recoil-free fraction), occur such that the entire crystal acts as the recoiling body, rather than just the single atom. Since the mass of the crystal is very large compared to that of a single atom, these events are essentially recoil-free. In these cases, since the recoil energy is negligible, the emitted gamma rays have the appropriate energy and resonance can occur.

In general, gamma rays have very narrow linewidths. This means they are very sensitive to small changes in the energies of nuclear transitions. In fact, gamma rays can be used as a probe to observe the effects of interactions between a nucleus and its electrons and those of its neighbors. This is the basis for Mossbauer spectroscopy, which combines the Mossbauer effect with the Doppler effect to monitor such interactions.