Frequency dependence of the scattering probability of nearly monochromatic phonons

The scattering probability of acoustic phonons propagating in Sr${\mathrm{F}}_2$ containing 0.01-mole% ${\mathrm{Eu}}^{2+}$ has been investigated at three phonon frequencies. Superconducting fluorescer films of Sn, ${\mathrm{Pb}}_{0.5}$ ${\mathrm{Tl}}_{0.5}$, and Pb are used to obtain, respectively, phonon distributions with narrow-band maxima at frequencies of 287, 407, and 670 GHz. Time-of-flight measurements of phonon pulses are taken with carefully monitored Al superconducting bolometers. The fraction of the time-integrated bolometer response which arises from scattered phonons is taken as a measure of the scattering probability. The experimental results are compared to a theoretical analysis based on the $T$-matrix formalism of the frequency dependence of the scattering probability from a mass disturbance with local force constant changes. The experimental results are in over-all agreement with theory.