Effective Thickness, Lamb-Mossbauer Factor

NES is an elastic and coherent scattering process, i.e., it takes place without energy transfer to electronic or vibronic states and is delocalized over many nuclei. Owing to the temporal and spatial coherence of the radiation field in the sample. 

9 Nuclear Resonance Scattering Using Synchrotron Radiation 

AEy is the bandwidth of the incoming radiation and Cei is the electronic absorption cross section. The exponential decay is modulated by the square of a Bessel function of the first order (/j), giving rise to the aforementioned dynamical beats. The positions of their minima and maxima (i.e., the slope of the envelope of the time-dependent intensity) can be determined with high accuracy and thus give precise information about the effective thickness of the sample. 

The mathematical description of the time-differential NFS intensity is, in many cases (e.g., in cases when frozen solutions are investigated), not as straightforward as it may appear in (9.2). The reason is that couplings between the various components of the delocalized radiation field in the sample have to be taken into account by an integration over all frequencies. This problem has been solved in different ways in a series of program packages, the most prominent of which are called CONUSS [9, 10], MOTIF [11, 12] and SYNFOS [13, 14]. 

This situation illustrates that special care has to be taken when analyzing NFS data. Nevertheless, high expectations rest on MS in the time domain especially for biological applications because it promises to be more sensitive to hyperfine parameters when the measurements are performed at high delay times and because of its applicability to samples of much smaller size. 

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By inspecting Eqs. (I2.I)-(I2.3), one can find that NFS intensity is proportional to the square of the number of resonant nuclei in the sample and Lamb-Mossbauer factor f due to the effective thickness of the absorber. Furthermore, in the absence of hyperfine interactions (the sublevels of the ground and excited nuclear states are degenerate), the NFS intensity reduces to a natural nuclear decay (Fig. 12.2). 

Absolute/ values,// , may be calculated according to the following procedure. The Lamb-Mbssbauer factor of the source, /, may be calculated from the area of Mossbauer spectra, A, at liquid nitrogen temperature, of 0.1mm thin 3-tin, whose effective thickness, t., is... 

Dependence of the peak area A, peak height H, and peak width Won the effective thickness of the absorber (ta). F is the natural line width and fs is the Mossbauer-Lamb factor of the source... 

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