Rudolf Mossbauer won his nobel prize for discovering the effect which has his name. The nuclear recoiless resonance of gamma rays is the phenomenon which was registered in a iridium Crystal when this was close to absolute zero. The recoiless resonance absorption is said to occur because the Crystal reacts as a Whole. In his nobel laureate lecture it is also reported that the kinetic energy of the Crystal was "negligibly small" when the gamma is emitted from the nucleus. According to my opinion behind this process there is something that so far nobody has fully understood.
Because at near zero temperature the atoms are rigidly bound in the crystal lattice. There are then no vibrations in the crystal. Vibrations correspond to temperature.
The atomic bindings between electrons and nuclei are not strong enough to guarantee that the nucleus doesn't recoil under the emission of a gamma ray. The force exerted should to be significantly higher, between the nucleus and the electrons and the Crystal has to react as a Whole. A very fascinating hypothesys was made by Giuliano Preparata and the russian physicists Skorobogatov e Dzevitskii, who explain such phenomenon with the collective response of the nuclei of the Crystal.
When considering the emission of a photon from a nucleus, one can contrast two cases: (i) when the nucleus is free; and (ii) when it is embedded in a crystal. The analytic tool in both cases is conservation of linear momentum (rather like a bullet fired from a gun). In case (i), the nucleus recoils to conserve the linear momentum. In case (ii), however, the mass which enters the conservation-of-momentum equation is that of the crystal as a whole, which is much more massive than a single nucleus. Thus, the recoil is in effect zero. This is Mossbauer's explanation which, to my knowledge, has been adopted by all physicists.
Incidentally, vibrations in the crystal exist even at absolute zero, thanks to Heisenberg's uncertainty principle. To a first approximarion, one can then take the wave function of the crystal as a product of simple-harmonic wave functions. The development of this idea further is carried out lucidly by Feynman is his famous book on statistical mechanics.
@Humam
We only consider the second case when it is embedded in the Crystal.
"Thus, the recoil is in effect zero. This is Mossbauer's explanation which, to my knowledge, has been adopted by all physicists.". In his nobel lecture Mossbauer talks about of being "negligibly small " the momentum because the Crystal is much bigger that a single nucleus. This is not satisfactory at all, negligibly small respect to what???
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