Measurement of the Mössbauer Recoilless Fraction inβ-Sn for 1.3 to 370°K

Abstract

Doppler-shift measurements of Mössbauer recoilless fractions $f$ in $\beta$-Sn show discrepancies of the order of 20 to 30% and sometimes bear quoted errors of ±10%. Such discrepancies can be caused by using incorrect values of $\alpha$, the internal conversion coefficient; ${\tau }_m$, the mean life of the excited state; ${\Gamma }_A$ and ${\Gamma }_S$, the absorber and source linewidths; and $B$, the nonresonant background present in the detector at the energy of the Mössbauer $\gamma$ rays. In the present work, the use of a black resonant absorber and the technique x-$\gamma$ delayed coincidences combine to eliminate dependence on these parameters in first approximation. In particular, the results $f=0.455\mathrm{}\pm 0.010$ at 77.3°K and $f=0.72\mathrm{}\pm 0.01$ at 4.2°K are obtained. The errors are systematic, and are due largely to uncertainities in evaluating the residual resonant transmission of the black absorber, the total magnitude of which is about 5% for $T\le 100°$K. For the experimental temperature range of $1.3\le T\le 370°$K, $f$ values are obtained at over 300 points for two different source samples. The results are as much as 20% higher than some previously reported values, and also do not agree well with the theoretical calculations of DeWames, Wolfram, and Lehman for $T\le 150°$K. On the other hand, when the data are expressed in terms of a Debye temperature $\Theta$ derived at each temperature from the Debye formula for $f$, the $\Theta$ values show remarkably little variation with temperature, and fall on a smooth curve. The results at low temperature help to clarify the data of Wiedemann, Kienle, and Pobell in the superconducting region and immediately above.