We investigate $phi$ meson photoproduction on the nucleon and the uclide[4]{He} targets within a dynamical model approach based on a Hamiltonian which describes the production mechanisms by the Pomeron-exchange, meson-exchanges, $phi$ radiations, and nucleon resonance excitations mechanisms. The final $phi N$ interactions are included being described by the gluon-exchange, direct $phi N$ couplings, and the box-diagrams arising from the couplings with $pi N$, $rho N$, $KLambda$, and $KSigma$ channels. The parameters of the Hamiltonian are determined by the experimental data of $gamma p to phi p$ from the CLAS Collaboration. The resulting Hamiltonian is then used to predict the coherent $phi$-meson production on the uclide[4]{He} targets by using the distorted-wave impulse approximation. For the proton target, the final $phi N$ rescattering effects, as required by the unitarity condition, are found to be very weak, which supports the earlier calculations in the literature. For the uclide[4]{He} targets, the predicted differential cross sections are in good agreement with the data obtained by the LEPS Collaboration. The role of each mechanism in this reaction is discussed and predictions for a wide range of scattering angles are presented, which can be tested in future experiments.
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