Two-level systems in electron-irradiated quartz

The longitudinal ultrasonic attenuation in electron-irradiated crystalline quartz (dose of 1.0×${10}^{20}$ e/${\mathrm{cm}}^2$, $E=2\mathrm{}$ MeV) was measured in the temperature range 1.4-300 K, at a frequency of 640 MHz. The data show conclusive evidence for the existence of two-level systems, similar to those in glasses. A relaxation attenuation is observed, giving rise to a $T^3$ behavior at the lowest temperatures that levels off to a shoulder at about 10 K. The derived density of states is smaller than that in vitreous silica.