Lamb-Mossbauer Factor Recoil-Free Fraction

3 Lamb—Mossbauer Factor (Recoil-Free Fraction) 

In Sect. 4.2.1, we have studied that nuclear resonance absorption of y-rays does not occur between nuclei of isolated atoms or molecules (in gaseous or liquid state) because of the large energy loss of the transition energy Eq due to recoil effects. 

If nucleus is moving at velocity vn in the direction of y-ray propagation, the y-photon of energy Ey receives a Doppler energy 1 d(= vn Ey/c). Therefore Ey = Eo — Er) + Ejy 

In solid state, Mossbauer atom is rightly bound to the lattice therefore 

E tr = translational energy transferred through linear momentum to the crystallite as a whole and is very small hence neglected E vib = lattice vibrational energy 

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If the Mossbauer atom is bound in a solid, the recoil energy may be taken up by the matrix via excitation of lattice vibrations. The recoil energy is then reduced by a factor given by the atom and the solid mass ratio. If the phonon energy is low enough, there will be a finite probability, f, that the emission (absorption) will take place with no creation or annihilation of phonon in the lattice, that is, with no recoil energy loss, and this is the Mossbauer effect. The / factor (recoil-free fraction, Debye-Waller factor, Lamb-Mossbauer factor) is given by... 

Mossbauer spectroscopy is a powerful technique that may give information on the occurrence of tin and organotin polymeric structures. This is made possible through the investigation of molecular dynamics of " Sn nuclei embedded in molecular fragments and in particular through the well established correlation between the recoil free fraction of yrays (Debye-Waller-Mossbauer or Lamb-Mossbauer factor) and the mean square displacement of the nuclei (or of the masses bound to the Mossbauer nuclei). This correlation appears to be a linear dependence of the logarithm of the resonant peaks area, InA (proportional to Lamb Mossbauer factor,/ ) and the absolute temperature, T. 

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