Quantum-radiation spectra of relativistic particles derived by the correspondence principle

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Abstract
It is known that ultrarelativistic electrons, when moving nearly parallel to an axis in a single crystal, will emit very intense radiation containing high-energy quanta. The radiation spectra are connected to synchrotron spectra in excessively strong magnetic fields. The latter spectra have previously been calculated by quantum perturbation theory, and are much reduced compared to the corresponding classical spectra. By application of the correspondence principle, it is shown that, for spin-zero particles, the complete quantum spectrum is obtained exactly from the classical spectrum by a simple modification of the frequency variable. The result holds for arbitrary external fields and with respect to angular distribution, polarization, and frequency distribution. Agreement with previous calculations of the synchrotron case is verified. For spin-1/2 particles the quantum frequency spectrum can be expressed with satisfactory accuracy by the classical radiation of spin-zero particles. These results may be of assistance in our understanding of radiation by ultrarelativistic particles.