  The diffractive t-slope, B_V, of elastic charmonia (V=J/psi, psi') photo- and
leptoproductions off a nucleon is studied at low |t| (< 1 GeV^2) in the leading
logarithmic approximation of perturbative QCD, with a special emphasis on the
space-time evolution of the c\bar{c}-dipole. We obey a framework based on QCD
factorization, which describes a certain Fermi motion effect due to the
$c(\bar{c})$-quarks in the proper manner and includes appropriately kinematical
corrections of the momentum transfer Delta_perp in the t-channel. Assuming the
universal two-gluon form factor of the nucleon, we show that the difference of
t-slopes for J/psi and psi' is dominated by the contribution from the
dipole-charmonium transition process. The calculated difference is found to be
B_J/psi-B_psi' \sim 0.53 GeV^-2 for the photoproduction, in agreement with HERA
data. We also calculate the t-dependence of the total cross sections for
several center-of-mass energies W. A good agreement of the results with the
available data demands that the mass scale appearing in the gluon form factor
should significantly decrease with increasing W.
