Mdssbauer: recoil free fraction

X-ray scattering has good momentum transfer resolution, but very poor energy resolution and thus does not yield information on the dynamical behaviour of atoms. Only the static Debye-Waller factor, with its dependence on momentum transfer, is obtained. Because of its coherent nature. X-ray scattering contains in its cross-section (Debye-Waller factor) contributions from both dynamical displacements and displacements due to static disorder, whereas static disorder does not influence the Mdssbauer recoil-free fraction. Thus comparison of the results of the two techniques is valuable in separating the two contributions to the mean-square displacements. 

However, in contrast, the resonance effect increased by cooling both the source and the absorber. Mdssbauer not only observed this striking experimental effect that was not consistent with the prediction, but also presented an explanation that is based on zero-phonon processes associated with emission and absorption of y-rays in solids. Such events occur with a certain probability/, the recoil-free fraction of the nuclear transition (Sect. 2.4). Thus, the factor/is a measure of the recoilless nuclear absorption of y-radiation - the Mdssbauer effect. 

Equation (1.10) indicates that the probability of zero-phonon emission decreases exponentially with the square of the y-ray energy. This places an upper limit on the usable values of Ey, and the highest transition energy for which a measurable Mdssbauer effect has been reported is 155 keV for Os. Equation 1.10 also shows that/increases exponentially with decrease in which in turn depends on the firmness of binding and on the temperature. The displacement of the nucleus must be small compared to the wavelength X of the y-ray. This is why the Mossbauer effect is not detectable in gases and non-viscous liquids. Clearly, however, a study of the temperature dependence of the recoil-free fraction affords a valuable means of studying the lattice dynamics of crystals. 

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