  The exclusive photoproduction of J/psi mesons, gamma p->J/psi p, has been
studied in ep collisions with the ZEUS detector at HERA, in the kinematic range
20<W<290 GeV, where W is the photon-proton centre-of-mass energy. The J/psi
mesons were reconstructed in the muon and the electron decay channels using
integrated luminosities of 38 pb^-1 and 55 pb^-1, respectively.
  The helicity structure of J/psi production shows that the hypothesis of
s-channel helicity conservation is satisfied at the two standard-deviation
level. The total cross section and the differential cross-section dsigma/dt,
where t is the squared four-momentum transfer at the proton vertex, are
presented as a function of W, for |t|<1.8 GeV^2. The t distribution exhibits an
exponential shape with a slope parameter increasing logarithmically with W with
a value b=4.15 \pm 0.05 (stat.)^{+0.30}_{-0.18} (syst.) GeV^-2 at W=90 GeV.
  The effective parameters of the Pomeron trajectory are alphapom(0) = 1.200
\pm 0.009(stat.)^{+0.004}_{-0.010}(syst.) and alphappom= 0.115 \pm
0.018(stat.)^{+0.008}_{-0.015}(syst.) GeV^-2.
