Interactions of $\omega$-Mesons in Nuclear Matter and with Nuclei

In--medium interactions of $\omega$--mesons are investigated microscopically by coupling to $NN^{-1}$ and $N^*N^{-1}$ particle--hole excitations of the medium, including elativistic mean--field dynamics by self--consistent scalar and vector fields. The resulting self--energies are transmitted to finite nuclei in local density approximation. Real and imaginary parts of longitudinal and transversal self--energies are discussed. The relation of the present approach to meson cloud models is addressed and an ambiguity is pointed out. Applications to recent data on the in--medium width of $\omega$ mesons scattered on a Niobium target serve to determine unknown $N^*N\omega$ in-medium coupling constants. The data are well described by $N^*N^{-1}$ self--energies containing S--wave and P--wave $N^*$ resonances. Exploratory investigations, however, show that the spectroscopic composition of self--energies depends crucially on the near--threshold properties of the width which at present is known only within large error bars. The calculations predict the prevalence of transversal self--energies, implying that vector current conservation is still maintained in the nuclear medium by slightly more than 90\%. Schr\"{o}dinger--equivalent potentials are derived and scattering lengths and effective range parameters are extracted for the longitudinal and transversal channel. Longitudinal and transversal spectral distributions are discussed and the dependencies on momentum and nuclear density are investigated. Schr\"{o}dinger--type $\omega+{}^{93}$Nb optical potentials are constructed. Low--energy parameters are determined, are used to study the pole structure of the S--matrix at threshold. The effective range expansion of the omega--nucleus K--matrix led to a $\omega +{}^{93}$Nb bound states with binding energy $Re(\varepsilon_B)=-448$~keV but of width $\Gamma_B=4445$~keV.