Abstract
The radiation of a positron in a planar channel of a crystal is studied, considering the dependence of the medium polarization on the transverse coordinate. The expression for the spectral distribution of the number of radiated photons is obtained for a single positron. It is shown that because of the medium polarization in the soft and hard regions not all positrons make a contribution to the radiation formation. An analytical formula for the total spectral distribution of the number of photons is obtained.
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