Effect of the periodic crystal structure on the emission by channeled particles

The effect of the periodic structure of a single crystal on the intensity and spectrum of the emission of channeled particles is examined theoretically. The discrete structure of the atomic rows or planes forming the channel is taken into account through the expansion of the actual potential in a Fourier series. A system of nonlinear differential equations is used to describe the continuous potential of the periodic structure, and a dipole approximation is derived to express the spectral density of the emission from a relativistic particle. Calculations of the spectral density of positrons at 1 GeV and 56 MeV in silicon during plane and axial channeling were found to agree with known experimental data. The complicated structure of the spectral density of the emission of channeled particles after the maximum is thus attributed to a longitudinal modulation of the potential well inside the channel.