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[References: 65 tit.]

We have studied the dominant radiative transitions of the charmonium S- and P-wave states within the covariant confined quark model. The gauge invariant leading-order transition amplitudes have been expressed by using either the conventional Lorentz structures, or the helicity amplitudes, where it was effective. The renormalization couplings of the charmonium states have been strictly fixed by the compositeness conditions that excludes the constituent degrees of freedom from the space of physical states. We use the basic model parameters for the constituent c-quark mass mc=1.80  GeV and the global infrared cutoff λ=0.181  GeV. We additionally introduce only one adjustable parameter ϱ>0 common for the charmonium states ηc(1S0), J/ψ(3S1), χc0(3P0), χc1(3P1), hc(1P1), and χc2(3P2) to describe the quark distribution inside the hadron. This parameter describes the ratio between the charmonium “size” and its physical mass. The optimal value ϱ=0.485 has been fixed by fitting the latest data for the partial widths of the one-photon radiative decays of the triplet χcJ(3PJ),J={0,1,2}. Then, we calculate corresponding fractional widths for states J/ψ(3S1) and hc(1P1). Estimated results are in good agreement with the latest data. By using the fraction data from PDG2020 and our estimated partial decay width for hc(1P1) we recalculate the “theoretical full width” Γtheorhc≃(0.57±0.12)  MeV in comparison with latest data Γexphc≃(0.7±0.4)  MeV. We also repeated our calculations by gradually decreasing the global cutoff parameter and revealed that the results do not change for any λ<0.181  GeV up to the “deconfinement” limit.