Radiation spectra and angular distribution of emitted quanta for planar channelled particles: radiation of single particle

A method of calculating the radiation characteristics for the motion in an arbitrary one-dimensional potential is developed. Expressions for channelling radiation frequencies, polarization angles, and the number of emitted photons as functions of quanta angles, particle energy, amplitude of oscillations, and divergence in a plane parallel to the trapping crystal planes for any given harmonic number are found. The problem is treated in the classical approximation. Numerical examples of the application of the derived formulae for channelling in the (1,1,0) direction of a silicon crystal are given. The results are presented both for electrons and positrons. Comparison of the calculation results for two choices of continuum potential for positrons is also given