  We consider an Anderson lattice model with a spin 1/2 degenerated conduction
electron band and localized ionic CEF-levels, classified according to the
irreducible representation of the point group of the lattice. We present the
self-consistency equations for local approximations ("$d\rightarrow\infty"$
approximation) for the periodic Anderson model. It leads to a matrix
formulation of the effective local density of states and the lattice
$f$-Green's function. We derive the quasi-particle life-time which enters the
Boltzmann transport equations. The impact of a $k$-dependent hybridization is
discussed. We prove that vertex corrections will vanish, as long as all states
of an irreducible representation couple to the conduction electron band with a
hybridization matrix element of the same parity.
