  We report on high-resolution optical spectroscopy of interacting bosonic
$^{174}$Yb atoms in deep optical lattices with negligible tunneling. We prepare
Mott insulator phases with singly- and doubly-occupied isolated sites and probe
the atoms using an ultra-narrow "clock" transition. Atoms in singly-occupied
sites undergo long-lived Rabi oscillations. Atoms in doubly-occupied sites are
strongly affected by interatomic interactions, and we measure their inelastic
decay rates and energy shifts. We deduce from these measurements all relevant
collisional parameters involving both clock states, in particular the intra-
and inter-state scattering lengths.
