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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. 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 rather than the electronic transitions that produce x-rays. However, early attempts to observe this phenomenon in gases failed. The effect is able to be recoil-free because the atom is part of a lattice of other atoms. The emission or absorption of the gamma ray does not change the atomic number or mass of the nucleus.

In general gamma rays are produced by nuclear transitions from an unstable high-energy state to a 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 another atom of the same type as the first. Such 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 corrseponding 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 velocity 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, called the recoil-free fraction, occur such that the entire crystal, rather than just the atom acts as the recoiling body. 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.

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