Self-consistent Treatment of Crystal-Electric-Field-Levels in the   Anderson Lattice
  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. 
F. B. Anders and D.L. Cox