Transition-diffracted radiation and the Cerenkov emission of x rays

The x-ray radiation emitted by a charged particle as it penetrates a perfect crystal is studied. We find that in addition to the already known C {} {}{}erenkov radiation peak, there is a second peak which is due to the dynamical diffraction of the electromagnetic field associated with the electron. The theory developed here, which is an extension of the dynamical theory of x-ray diffraction, allows us to treat situations in which the direction of incidence of the electron, as well as the orientation of the crystal surface relative to the crystal planes, are kept arbitrary. Our equations apply also to situations in which the Bragg angle is close to {π}/2, where several of the approximations usually made in the dynamical theory are known to fail. Various features such as intensities, direction, frequency, and the spectral and angular widths of both the C {} {}{}erenkov and the ``transition-diffracted'' radiation are studied. A geometrical construction of the dispersion surfaces has been found to be very useful in visualizing the content of the theory. It is possible that these two processes of emission may find application as a tunable source of monochromatic and very directional x rays.