Precision Determinations of the Mössbauer Recoilless Fraction for Metallic Gold in the Temperature Range4.2≤T≤100°K

Abstract

Mössbauer spectra for thick gold absorbers have been measured as a function of absorber temperature $T$ in the range $4.2\le T\le 100$ °K. By fitting these spectra with an appropriate theoretical line-shape function, values of $\frac{f\left(T\right)\mathrm{}}{(1+\alpha )}$ have been obtained, where $f\left(T\right)\mathrm{}$ is the recoilless fraction for metallic gold and $\alpha$ is the internal-conversion coefficient for the 77.3- keV state in ${\mathrm{Au}}^{197}$. The precision in these values is about 1%, except at the higher absorber temperatures. Because of its importance in the thick-absorber line-shape analysis, the natural linewidth ${\Gamma }_0$ for the 77.3-keV state has been redetermined to be 0.923 ± 0.006 mm/sec. Values of $f\mathrm{}\left(T\right)\mathrm{}$ for metallic gold have been obtained by reducing our thick-absorber data with $\alpha =4.\mathrm{}30$. This value of $\alpha$ is based on two independent estimates which show good agreement. One estimate uses conversion-intensity data and theoretical internal-conversion coefficients, while the other estimate uses our $\frac{f\left(T\right)\mathrm{}}{(1+\alpha )}$ data and predictions of $f\left(T\right)\mathrm{}$ from a recent quasiharmonic analysis of gold thermodynamic data. The recoilless fraction for metallic gold as determined in our treatment is found to vary from $f\left(4.\mathrm{}2{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}\right)=0.\mathrm{}189$ to $f\left(100\mathrm{}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}\right)=0.\mathrm{}0097$. Effective Debye temperatures ${\Theta }^M\mathrm{}\left(T\right)\mathrm{}$ are determined from these recoilless fractions for gold and are compared with corresponding effective Debye temperatures ${\Theta }^C\mathrm{}\left(T\right)\mathrm{}$ determined from specific-heat measurements.