  We calculate the shift, due to interatomic interactions, of an optical
transition in an atomic Fermi gas trapped in an optical lattice, as in recent
experiments of Campbell {\it et al.}, Science {\bf 324}, 360 (2009). Using a
pseudospin formalism to describe the density matrix of the internal two states
of the optical transition, we derive a Bloch equation which incorporates both
the spatial inhomogeneity of the probe laser field and the interatomic
interactions. Expressions are given for the frequency shift as a function of
the pulse duration, detuning of the probe laser, and the spatial dependence of
the electric field of the probe beam. In the low temperature semiclassical
regime, we find that the magnitude of the shift is proportional to the
temperature.
