We report a simple analytic form for the convolution integral in transmission Mossbauer spectroscopy allowing accurate representation of the line shape even for very thick absorbers {t=10), and permitting easy fitting to the true line-shape function. This representation permits the accurate determination of all Mossbauer-effect (ME} parameters, including position, width, cross section, and interference. This analytic method can be applied to deconvolute accurately information contained in either source or absorber, and an explicit analytic form for the emission and absorption Fourier transforms is given. We show that from the asymptotics of the line shape, it is possible to determine all line-shape parameters, and that line-shape asymptotics can circumvent short-ranged hyperfine or instrumental broadening contributions to the observed spectrum. A formula for the correction to the line shape caused by source self-absorption is given, and it is shown that when there is significant source resonance self-absorption a "good" fit to data, judged by a chi-squared analysis, can yield completely wrong ME line-shape parameters. We find an equation for the dependence of the area under the absorption curve and the resonance peak height, and give its explicit dependence on the interference parameter and source broadening parameters. Although these effects have been neglected in earlier work, their contribution may be of order 10% in many cases of interest.

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Using very-high-intensity (ϳ70 Ci͒ 183 Ta Mössbauer sources, we have measured the Debye-Waller factors ͑DWF's͒ of sodium chloride, potassium chloride, and potassium bromide single crystals for several of the (h00) and (nnn) Bragg reflections. We have used an approach which properly accounts for thermal expansion over the temperature range of our experiment, from 90 K to 900 K, about 100 K below the melting point of our crystals. We have found that a procedure used to analyze data by earlier workers leads to incorrect parameters in the Debye-Waller factor exponent, and our procedure does not require empirical parameters to account for the effects of thermal expansion. Additionally, we find three items of significance. Contrary to earlier results, we observe that the cations and the anions have identical DWF's in NaCl and also in KBr. We observe terms in the expansion of the DWF exponential which are quartic in the scattering wave vector Q ជ in NaCl and KCl, with some evidence for a Q 4 term in KBr. The size of the Q 4 contribution is reported and varies with the direction of momentum transfer. We also observe that the Debye temperature and the coefficient of the anharmonic Q 2 term also vary with the direction of momentum transfer. We believe our data are the definitive evidence for a nonspherical thermal cloud in a cubic crystal; the ions have a larger amplitude of oscillation in the ͓h00͔ direction than in the ͓nnn͔ direction, contrary to the commonly held view of crystallographers that the most general form of the mean-square thermal motion is of an ellipsoid shape.

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