Exclusive production of $rho^0$ and $J/psi$ mesons in e^+ p collisions has been studied with the ZEUS detector in the kinematic range $0.25 < Q^2 < 50 GeV^2, 20 < W < 167 GeV$ for the $rho^0$ data and $2 < Q^2 < 40 GeV^2, 50 < W < 150 GeV$ for the $J/psi$ data. Cross sections for exclusive $rho^0$ and $J/psi$ production have been measured as a function of $Q^2, W$ and $t$. The spin-density matrix elements $r^{04}_{00}, r^1_{1-1}$ and $Re r^{5}_{10}$ have been determined for exclusive $rho^0$ production as well as $r^{04}_{00}$ and $r^{04}_{1-1}$ for exclusive $J/psi$ production. The results are discussed in the context of theoretical models invoking soft and hard phenomena.
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