Recoil Energy, Resonance, and Doppler Effect

Consider a gas-phase experiment in which quanta emitted by excited atoms of an element are used to excite atoms of the same element in their ground state. For the sake of simplicity, only a single transition with energy q and average lifetime r will be assumed to be involved. 

A collection of gas particles, however, exhibits a statistical distribution of velocities, a phenomenon that will give rise to a broadening in the emission and absorption energies. The characteristic width of this so-called Doppler broadening may be shown to be given by D = 2(6/ A r), where k is the Boltzmann constant. It follows that the resonance probability will be determined by the relative values of F/6r and F/D. 

The following sections will provide a brief introduction to some of the principles upon which Mbssbauer spectroscopy is based. The discussion will be restricted to Fe and Sn as to date only these nuclides have been the subject of in situ investigations involving electrochemical systems. More extensive treatments of theoretical and experimental aspects of Mbssbauer spectroscopy may be found in a number of excellent specialized books and monographs.  

An explicit expression for the fraction of such recoilless or zero-phonon processes, commonly denoted as /, can be derived from the specific model used to represent the solid. The Debye model, for instance, predicts an increase 

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