  There are different approaches for diffractive photoproduction of charmonia.
Recently, a new approach is proposed, in which charm quarks are taken as heavy
quarks and the nonperturbative effect related to charmonia can be handled with
nonrelativistic QCD. The interaction between the $c\bar c$ pair and the initial
hadron is through exchange of soft gluons. The exchange of soft gluons can be
studied with heavy quark effective theory and an expansion in the inverse of
charm quark mass $m_c$ can be employed. In this approach a simple formula for
the S-matrix can be derived by neglecting higher orders in $m_c^{-1}$ and
relativistic correction related to charmonia. The S-matrix is related to the
usual gluon distribution $g(x)$ at small $x$. This result is different than
those from other approaches. Confronting experiment the result is not in
agreement with experimental measurement because large errors from higher order
in $m_c^{-1}$ and from relativistic corrections. Nevertheless the ratio of
cross sections of $\jpsi$ and $\psi(2S)$ can be predicted more precisely than
cross-sections. In this letter we show that the ratio predicted in this
approach with an estimation of relativistic corrections is in good agreement
with the recent measurement at HERA.
