In the Jefferson Lab E12-16-007 (J/psi-007) experiment we measured the differential J/psi photo-production cross section as a function of photon energy, E_gamma and Mandelstam variable t - the momentum transfer from the initial photon to the produced J/psi - in the energy region where all the charm pentaquark states were discovered by the LHCb (Large Hadron Collider beauty) collaboration. The J/psi-007 experiment was conducted in the experimental Hall C of the Thomas Jefferson National Accelerator Facility using a high-intensity real photon beam generated by a 10.6 GeV incident electron beam traversing a copper radiator upstream of a liquid hydrogen target. Two arm spectrometers of Hall C, HMS (High Momentum Spectrometer), and SHMS (Super High Momentum Spectrometer) were used to detect the e+ e- di-lepton J/psi decay pairs in coincidence. The spectrometers' four momentum and angle settings scanned a photon beam energy range between 9.1 and 10.6 GeV and |t| up to 5 GeV^2. An enhanced sensitivity to the s-channel resonant J/psi photo-production was achieved by optimizing the spectrometer settings at a higher t region where the non-resonant standard t-channel J/psi production cross section is strongly suppressed. No evidence for pentaquarks was observed and, the cross section upper limits for each LHCb pentaquark candidate were determined and are presented in this document. / Physics