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

Doppler-shift measurements of M\"ossbauer recoilless fractions f in β-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 α, the internal conversion coefficient; τₘ, the mean life of the excited state; ΓA and ΓS, the absorber and source linewidths; and B, the nonresonant background present in the detector at the energy of the M\"ossbauer γ rays. In the present work, the use of a black resonant absorber and the technique x-γ delayed coincidences combine to eliminate dependence on these parameters in first approximation. In particular, the results f=0.455±0.010 at 77.3^∘{}K and f=0.72±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≤100^∘K. For the experimental temperature range of 1.3≤T≤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≤150^∘K. On the other hand, when the data are expressed in terms of a Debye temperature Θ derived at each temperature from the Debye formula for f, the Θ 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.