Transmission integral

The expression is known as the transmission integral in the actual formulation, which is valid for ideal thin sources without self-absorption and homogeneous absorbers assuming equal widths F for source and absorber [9]. The transmission integral describes the experimental Mossbauer spectrum as a convolution of the source emission Une N(E,o) and the absorber response exp —cr( )/abs M - The substitution of N E,d) and cr( ) from (2.19) and (2.20) yields in detail ... 

For thin absorbers with t exponential function in the transmission integral can be developed in a series, the first two terms of which can be solved yielding the following expression for the count rate in the detector ... 

Exact analyses of experimental spectra from thick absorbers, however, have to be based on the transmission integral (2.26). This can be numerically evaluated following the procedures described by Cranshaw [10], Shenoy et al. [11] and others. 

Analysis of Au MES measurements as a function of temperature between 1.25 K and 60 K on the AU55 system, employing the transmission integral... 

Fig. 3. Mossbauer spectra of AU55 at several temperatures between 1.25 K and 30 K, with transmission integral fit [24], The subspectra at 4.2 K are loren-ztian simulations to indicate the singlet and the three doublets, and are only meant as a guide to the eye.

The transmission throngh an absorber of thickness teff as a ftmction of the relative velocity V between source and absorber is given by the evalnation of the transmission integral discussed, for example, in Ref 2. In case of Fe Mdssbaner spectroscopy for almost all samples which are not enriched in the Mossbauer isotope Fe (the natural abundance of Fe is 2%), the evaluation of the transmission integral leads to Lorentzian line shape with a minimum linewidth of 0.19mms , which is twice the natural linewidth of the Fe Mossbauer transition. The absorption cross section as a ftmction of source velocity is then given as (with... 

In the case of an infinitely thin source - when the radioactive parent forms a monatomic layer on the front of the source at x = 0, and therefore p(x) = 5(x), where 5 is the Dirac function - lines 1 and 3 inO Eq. (25.29) are equal to (1 — fs) and 1, respectively. Therefore, one obtains the following formula, generally called the transmission integral ... 

The Mdssbauer—Lamb factors fs (for the source) and /a (for the absorber) show up as coefficients to determine the Mdssbauer peak intensity (seeO Eq. (25.31) for the transmission integral). Unfortunately, it is difficult to determine the absolute values of fs and from the absorption intensity without tedious and difficult experimentation. 

The most precise way of fitting is based on the computation of the transmission integral given by Eq. (25.31). 

In general, the transmission integral (O Eq. (25.31)) can be used to evaluate the peak area that depends nonlinearly on the effective thickness, which, in turn, is proportional to the concentration of the resonant atoms. 

The internal conversion coefficient for Fe has been accurately determined from the transmission integral (seeO Eqs. (25.11), (O 25.30), and (O 25.31)) by using a series of iron absorbers all having the same thickness of iron atoms but the enrichment in Fe varied by a factor of as much as 37 (Hanna and Preston 1965). 

The subject of the recoil-free fraction was initially discussed in Mossbauer s original paper (Mossbauer, 1958). Since then, many books and review articles (e.g. Nussbaum, 1966) have been devoted to describing experimental measurements and theoretical calculations of the recoil-free fraction f Hence this discussion will be limited to some of the major aspects of the information obtainable from /-factor measurements. The measurement itself is relatively easy, since for thin absorbers the Mossbauer spectral area is proportional to /, and thus the relative change in / with temperature is readily obtainable. With thick absorbers one can still obtain accurate values, although the analysis requires transmission integrals (Shenoy, 1973). 

So far, we did not take into account any thickness effects. The aforementioned formulas are only valid in the case of small thicknesses, because only in that case the transmission integral function, which mathematically describes the spectrum, can be replaced by a sum of Lorentzian fines. The latter profile can be considered... 

Chapter no. Sensors/actuators Signal transmission. Integrated processing processes and control and products Bio-processes and products... 

Figure 6.15. Comparison of IR mapping and IR imaging of a thin tissue section measured in transmission. Integrated intensities of a band typical of sugar polymers in tissues (at 1,155 cm ) are plotted at the top and those for methylene (at 2,850cm ) at the bottom. Mapping with 12 ttm aperture and lO/tm stepping is shown on the left (32 x 32) IR imaging (64 x 64) on the right. Images are 250/im square. (From Schultz [307] reproduced with permission.)...

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