Abstract: In this work we consider the Coqblin-Schrieffer model when the spin is S=1/2. The atomic solution has eight states: four conduction and two localized states, and we can then calculate the eigenenergies and eigenstates analytically. From this solution, employing the cumulant Green's functions results of the Anderson model, we build a "seed", that works as the input of the atomic approach, developed earlier by some of us. We obtain the T-matrix as well as the conduction Green's function of the model, both for the impurity and the lattice cases. The generalization for other moments within N states follows the same steps. We present results both for the impurity as well as for the lattice case and we indicate possible applications of the method to study ultra cold atoms confined in optical superlattices and Kondo insulators. In this last case, our results support an insulator-metal transition as a function of the temperature Ver menos