Temperature dependence of planar channeling radiation in silicon, germanium, and beryllium between 12 and 330 K

The temperature dependence of planar channeling radiation of 62.8 MeV electrons has been studied for silicon, germanium, and beryllium. The measurements have been performed using an uncollimated low-emittance cw beam from the superconducting electron linac S-DALINAC at the Technische Hochschule Darmstadt. Energies and linewidths of transitions between transverse bound states have been determined in the energy range between 40 and 230 keV for silicon and beryllium at temperatures between 12 and 330 K, and for germanium between 12 and 223 K. From the shift of the transition energies with temperature the mean thermal vibrational amplitudes of the atoms transverse to the channeling planes rue determined by comparison with calculations using the many-beam;formalism. Within experimental errors no directional dependence of the vibrations is observed. For silicon a Debye temperature of (535.2+/-8.5) K at 12 K and (519.0+/-10.8) K at 300 K has been derived. For germanium an increase from (232.7+/-12.8) K at 12 K to (292.0+/-16.4) K at 223 K is observed. Planar channeling radiation spectra from a beryllium crystal taken at 12, 220, and 300 K have been analyzed the same way yielding a Debye temperature of (1060+/-50) K.