The Line Shape for Thin Absorbers

For thin absorbers with t C 1, the 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  

Since the resonance absorption vanishes for d oo, the count rate off resonance is given entirely by mass absorption 

the experimental Mossbauer spectmm of a thin single-line absorber is a Lorentzian line, with full-width at half maximum twice the natural Une width of the separate emission and absorption lines Texp = 2E. 

Although Lorentzian line shapes should be strictly expected only for Mossbauer spectra of thin absorbers with effective thickness t small compared to unity, Margulies and Ehrman have shown [9] that the approximation holds reasonably well for moderately thick absorbers also, albeit the line widths are increased, depending on the value of t (Fig. 2.7). The line broadening is approximately 

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. 

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