Are the ψ′→η_cγ,ψ″→η_cγ decays due to the gluon admixture?

We propose a new method for estimating the radiative transitions between the excited 1^- charmonium levels and η_c. The method is based on QCD (plus the hypothesis of local duality) and makes no reference to the standard potential picture. It is argued that the decay ψ′(3.698)→η_cγ is essentially due to the gluon admixture in the Ψ′ wave function. The most naive analysis yields approximately 0.15 keV for the ψ′→η_cγ decay width, five times smaller than preliminary data. The experimental number for Γ(ψ′→η_cγ)-0.7 keV-can be reproduced only at a price of introducing a rather large ψ″(3.772)→η_cγ amplitude, Γ(ψ″→η_cγ)∼1 keV. As a byproduct, we get a reliable prediction for the ρ→πγ decay rate, Γ(ρ→πγ)≈70 keV, in good agreement with a recent measurement.