Editing Mössbauer effect (section)

== Description ==
[[File:MössbauerSpectrum57Fe.svg|thumb|right|250px|Mössbauer absorption spectrum of <sup>57</sup>Fe]]
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. This emission and subsequent absorption is called [[resonant fluorescence]]. 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 energy in the recoiling body ({{math|''E''<small>{{sub|R}}</small>}}) can be found from momentum conservation:
: <math>|P_\mathrm{R}|=|P_\mathrm{\gamma} |\,</math>

where {{math|''P''<small>{{sub|R}}</small>}} is the momentum of the recoiling matter, and {{math|''P''{{sub|γ}}}} the momentum of the gamma ray. Substituting energy into the equation gives:
: <math>E_\mathrm{R}=\frac{E_\mathrm{\gamma}^2}{2Mc^2}</math>

where {{math|''E''<small>{{sub|R}}</small>}} ({{val|0.002|ul=eV}} for {{SimpleNuclide|Fe|57}}) is the energy lost as recoil, {{math|''E''{{sub|γ}}}} is the energy of the gamma ray ({{val|14.4|ul=keV}} for {{SimpleNuclide|Fe|57}}), {{math|''M''}} ({{val|56.9354|ul=u}} for {{SimpleNuclide|Fe|57}}) is the mass of the emitting or absorbing body, and ''c'' is the [[speed of light]].<ref>
{{cite web
|last=Nave |first=C.R.
|year=2005
|title=Mössbauer Effect in Iron-57
|work=[[HyperPhysics]]
|publisher=[[Georgia State University]]
|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/mossfe.html
|access-date=7 June 2010
}}</ref> In the case of a gas, the emitting and absorbing bodies are atoms, so the mass is relatively small, resulting in a large recoil energy, which prevents resonance. (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.)

In a solid, the nuclei are bound to the lattice and do not recoil as in a gas. The lattice as a whole recoils, but the recoil energy is negligible because the {{math|''M''}} in the above equation is the mass of the entire lattice. However, the energy in a decay can be taken up or supplied by lattice vibrations. The energy of these vibrations is quantised in units known as [[phonon]]s. The Mössbauer effect occurs because there is a finite probability of a decay involving no phonons. Thus in a fraction of the nuclear events (the '''recoil-free fraction''', given by the [[Lamb–Mössbauer factor]]), the entire crystal acts as the recoiling body, and 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 (depending on the half-life of the decay), gamma rays have very narrow line widths. 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 Mössbauer spectroscopy, which combines the Mössbauer effect with the [[Doppler effect]] to monitor such interactions.

[[Zero-phonon line and phonon sideband|Zero-phonon optical transitions]], a process closely analogous to the Mössbauer effect, can be observed in lattice-bound [[chromophore]]s at low temperatures.