Finite Size Vertex Correction to the Strong Decay of η_c and x_c States and a Determination of α_s(m_c)

We calculate the correction to the two-gluon decay width due to the finite extension of the vertex function. We obtain the corrected factor to the zero-range vertex γ = 1.32, γ = 1.45, γ = 1.26 for η_c,x_c0, and x_c2, respectively. With the decay width Γ(η_c → 2g) we extract the value α_s(m_c) = 0.28±0.05 which agrees with that calculated from the same correction to the process Γ(J/ψ → 3g). This correction to the process Γ(η_c → 2g) is not as large as that to the process Γ(J/ψ → 3g).