We study the competition between the Kondo effect and the Ruderman-Kittel-K
asuya-Yosida interaction in the framework of the Anderson lattice model wit
h an extra intersite exchange term. By using an approximation based on an a
tomic expansion, we obtain, for the symmetric half-filled case, a phase dia
gram analog to the Doniach diagram for the Kondo lattice. The qualitative a
nd quantitative progress in the description of experimental results for the
cerium Kondo compounds with respect to previous approaches is discussed. W
e also calculate the specific heat which exhibits a two-peak structure as a
function of temperature.