An analysis of inelastic photoproduction of J/Psi mesons is presented using
data collected at the ep collider HERA corresponding to an integrated
luminosity of above 80pb-1. Differential and double differential cross sections
are measured in a wide kinematic region: 60<W_gammap<260 GeV, 1<p_t^2< 60 GeV^2
and 0.05<z<0.9, where z is the fraction of the energy of the exchanged photon
transferred to the J/Psi meson in the rest frame of the target proton. Cross
sections at z<0.3 are presented for the first time. Theoretical calculations
within the Colour Singlet Model at NLO for direct photon processes are shown to
give a good description of the data in the medium z region (0.3<z<0.9) up to
the highest p_t^2 values. A calculation using a k_t factorisation approach in
LO in the Colour Singlet Model is also able to describe these data. The data in
the full z range are also compared to LO calculations within a non-relativistic
QCD framework including color octet and colour singlet contributions for direct
and resolved photons. It seems possible to reconcile data and theory with
modest contributions from colour octet processes. The polarisation of the J/Psi
meson is measured as a function of z and p_t,psi and is reasonably described by
the theoretical predictions.Comment: 30 pages, 11 figures, 11 table