The existence of a bound pion-nucleus system has been experimentally demonstrated by embedding negatively charged pions in different nuclei. These bound systems are formed by the interplay of the Coulomb and strong interaction. In this thesis the possible formation of omega-mesic states was investigated which are governed solely by the strong interaction since the omega-meson is electrically neutral.At the electron stretcher ELSA at Bonn the photoproduction of omega-mesons on a liquid hydrogen as well as on a carbon target has been studied for incident photon energies of 1250 - 3110 MeV. The combined setup of the Crystal Barrel and the MiniTAPS detector systems, which form a 4pi electromagnetic calorimeter, was used for detecting the possible omega-mesic state via the omega -> pi0 + gamma decay mode. The recoiling proton of the gamma + p -> omega + p reaction was identified with an aerogel-threshold-Cherenkov detector in veto-mode and the forward angle spectrometer MiniTAPS, exploiting the characteristic correlation between deposited energy and time-of-flight for protons. Measurements on liquid hydrogen are used as a reference for understanding background reactions and studying systematic uncertainties. Several kinematical cuts have been applied to reduce the background which mainly stems from pi0-pi0- and pi0-eta-production where one of the four decay photons escaped detection.The kinematics of the reaction channel and the detector acceptance have been calculated based on Monte Carlo simulations. Different incident photon energies, diverse target materials as well as the Fermi momentum of the nucleons in a carbon nucleus have been considered.Structures in the total energy distribution of the pi0-gamma-pairs, which would indicate the population and decay of bound omega-Boron-11 states, are not observed. The differential pi0gamma-cross section of 0.3 nb/MeV/sr found in the bound state energy regime between -100 and 0 MeV may be accounted for by yield leaking into the bound state regime because of the large in-medium width of the omega-meson.Theoretical predictions exist only for the formation of quantum-mechanical states of omega-mesic nuclei and for quasi-free omega-production. Both, decay and possible final state interaction of the decay products have to be considered for a direct comparison to experimental data. Therefore, calculations with the Giessen Boltzmann-Uehling-Uhlenbeck transport model (GiBUU) have been performed to determine the effective branching ratio of an omega-mesic state into the pi0-gamma-channel. It turns out that the kinetic energy distribution of the omega-mesons is sensitive to the depth of the optical potential, even in the quasi-free region. Depending on its real part, the peak position is shifted: For an attractive omega-nucleus interaction the omega-meson is slowed down, while for a repulsive interaction the kinetic energy of the omega-meson is increased. A comparison of the measured total energy distribution with calculations, extending into the regime of quasi-free omega-production, suggests the real part V0 of the optical meson-nucleus potential to be small and only weakly attractive with V0(rho = rho_0) = -15 ± 35 (stat) ± 20 (syst) MeV in contrast to several theoretical predictions of attractive potentials with a depth of 100 - 150 MeV.
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