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[References.: 28 tit.]

In present work within the frame of dynamic theory for parametric X-ray radiation in two-beam approximation we have presented detailed studies on parametric radiation emitted by relativistic both electrons and ions at channeling in crystals that is highly requested at planned experiments. The analysis done has shown that the intensity of radiation at relativistic electron channeling in Si (110) with respect to the conventional parametric radiation intensity has up to 5% uncertainty, while the error of approximate formulas for calculating parametric X-ray radiation maxima does not exceed 1.2%. We have demonstrated that simple expressions for the Fourier components of Si crystal susceptibility χ0 and χgσ could be reduced, as well as the temperature dependence for radiation maxima in Si crystal (diffraction plane (110)) within Debye model. Moreover, for any types of channeled ions it is shown that the parametric X-ray radiation intensity is proportional to z2−b(Z,z)/z with the function b(Z,z) depending on the screening parameter and the ion charge number z=Z−Ze.