In this paper, the periodic Anderson Hamiltonian has been used to study the heavy-fermion behavior in the Rare-Earth and Actinide compounds. The mean-field approximation has been applied to the Coulomb correlation term between the f electrons and a self-energy term has been introduced to represent the effect of the many-body interaction. The single-site approximation has been used for the self-energy term. The properties of the systems have been discussed in a quasi-particle picture. The effective mass of the quasi-particles has been obtained through the self-consistent calculation of the average occupation number of the f electrons. The conditions necessary for the presence of the heavy fermions and the corresponding change of the magnetic properties have been discussed and numerical computation has been carried out. The calculated results have been compared with recent experiments.