The Mössbauer effect is a physical phenomenon discovered by the German physicist Rudolf Mößbauer in 1957. It involves the resonant and recoilfree emission and absorption of gamma ray photons by atoms bound in a solid form and forms the basis of Mössbauer spectroscopy.
Contents
History
The emission and absorption of xrays by gases had been observed previously, and it was expected that a similar phenomenon would be found for gamma rays, which are created by nuclear transitions (as opposed to xrays, which are typically produced by electronic transitions). However, attempts to observe gammaray resonance in gases failed due to energy being lost to recoil, preventing resonance (the Doppler effect also broadens the gammaray spectrum). Mössbauer was able to observe resonance in solid iridium, which raised the question of why gammaray 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 recoilfree fraction of nuclear events. This discovery was rewarded with the Nobel Prize in Physics in 1961 together with Robert Hofstadter's research of electron scattering in atomic nuclei.
Description
In general, gamma rays are produced by nuclear transitions from an unstable highenergy state, to a stable lowenergy 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 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 energy in the recoiling body (E_{R}) can be found from momentum conservation:
where P_{R} is the momentum of the recoiling matter, and P_{γ} the momentum of the gamma ray. Substituting energy into the equation gives:
where E_{R} (=0.002 eV for ^{57}Fe) is the energy lost as recoil, E_{γ} is the energy of the gamma ray (=14.4 keV for ^{57}Fe), M (=56.9354 u for ^{57}Fe) is the mass of the emitting or absorbing body, and c is the speed of light.^{[1]} 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 xrays, but the photon energy is much less, resulting in a lower energy loss, which is why gasphase resonance could be observed with xrays.)
In a solid, the nuclei are bound to the lattice and do not recoil in the same way as in a gas. The lattice as a whole recoils but the recoil energy is negligible because the M in the above equation is the mass of the whole 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 phonons. The Mössbauer effect occurs because there is a finite probability of a decay occurring involving no phonons. Thus in a fraction of the nuclear events (the recoilfree fraction, given by the LambMössbauer factor), the entire crystal acts as the recoiling body, and these events are essentially recoilfree. In these cases, since the recoil energy is negligible, the emitted gamma rays have the appropriate energy and resonance can occur.
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