Some peculiarities of the optical transition radiation from high-energy particles at inclined incidence (III)

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General formulas for the intensities of transition radiation (TR) at inclined particle incidence on the separation boundary of media with various ε 1 ≠ 1 and ε 2 ≠ 1 have been obtained. Modified formulas, simplifying the calculations of various properties of transition radiation at inclined incidence are given. Angular properties of the optical transition radiation for the particle incidence at ψ = 45° on a thick Ni foil plate in vacuum have been calculated for a wide range of γ (from 27.5 to 5.88 × 10 4). The calculations confirm theoretical predictions, that at large values of γ a considerable part of transition radiation emitted “forward” concentrates near the direction of the particle velocity in a narrow cone of 2θ∼ 2 γ opening; transition radiation emitted “backward” tightens into a narrow cone with an axis which is the mirror reflection in the separation boundary of media. This part of transition radiation is increased with energy ∼lnγ. In addition to “forward” and “backward” narrow-directed cones, a fraction of TR has a wide angle distribution (±45°), whose intensity does not, practically, depend upon γ. From calculations it follows that transition radiation intensity, emitted in the direction of the particle velocity, does not reach a zero value. The full number of transition radiation photons emitted both “forward” and “backward” has a dependence of ∼lnγ, beginning from γ⪸10 2 . The efficiency of the particle detection in Cherenkov counters is evaluated on account of the optical TR. The investigation has been performed in the Laboratory of Nuclear Problems, JINR.