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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 lowemittance 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 are 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 ͑535.2Ϯ8.5͒ K at 12 K and ͑519.0Ϯ10.8͒ K at 300 K has been derived. For germanium an increase from ͑232.7Ϯ12.8͒ K at 12 K to ͑292.0Ϯ16.4͒ 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

Polarization properties of parametric x radiation (PXR) produced by E 0 80.5 MeV electrons interacting with a 13 mm thick silicon crystal have been investigated. The direction and the degree of the linear polarization of PXR observed at about 20 ± with respect to the electron beam direction were determined by means of a novel method exploiting directional information of the photoelectric effect in a charge coupled device consisting of 6.8 3 6.8 mm pixels. Comparison of the results with a newly derived theoretical expression exhibits very good agreement if on top of the basic interaction process underlying PXR effects decreasing the polarization are taken into account. [S0031-9007(97)04605-X] PACS numbers: 41.60. -m, 07.85. -m, 41.75.HtParametric x radiation (PXR) is a highly monochromatic radiation produced by a relativistic charged particle traversing a crystal. It originates from the coherent superposition of the electromagnetic waves emitted due to the polarization of crystal atoms periodically distributed along the particle trajectory. For highly relativistic charged particles (Lorentz factor g 1 1 E 0 ͞mc 2 ¿ 1) the PXR intensity is concentrated predominantly within a small angular cone well separated from the electron beam. While PXR has already been predicted about three decades ago [1], it was first observed only in 1985 [2] and has attracted considerable interest ever since. The spectral and angular properties of PXR produced by electrons mostly in silicon and diamond crystals have been studied over a large range of electron energies from a few MeV up to several GeV. For recent investigations we refer to [3-13] and references therein. In general, the experimental results are well described by a so-called kinematical theory [3].So far the polarization character of PXR is largely unexplored. There exists only one experimental investigation [14,15] using 900 MeV electrons and a 370 mm Si crystal in which for three discrete points of the (220) reflex the linear polarization was measured. Away from the center of the reflex a high degree of polarization was found. The polarization was claimed [14] to have a radial distribution in analogy toČerenkov radiation. Since the applied theoretical approach [16] to the data does not contain explicit relations regarding the polarization properties of PXR, the quoted agreement [14,15] between experiment and theory appears to be fortuitous. It has been the aim of the work described in the present article to determine the polarization degree and direction of PXR for experimental conditions similar as in [14,15] applying a novel experimental technique which facilitates a continuous coverage of a substantial fraction of the diffraction pattern and to derive for the first time the appropriate expressions for the observables describing the polarization properties of PXR.Within the framework of the kinematical theory [3] it can be shown [17] that PXR is-under ideal conditions-

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