  We study the coupling of internal electronic excitations to vibrational modes
of the external motion of ultracold atoms in an optical lattice. For different
ground and excited state potentials the on-site coupling of excitations and
vibrations term renormalizes the effective electronic transition energy, which
appears e.g. in clock transitions. In addition in the Mott state with filling
factor one, the dipole-dipole coupling between neighbouring sites includes
emission and absorption of vibrational quanta. Such processes create a
significant mechanism for excitation of vibrations leading to motional heating
of the lattice atoms by resonant light interaction. We calculate estimates of
the corresponding parameters from a perturbation expansion in small atomic
displacements.
