  We analyze the two Anderson impurity problem, in the strong Coulomb repulsion
limit, by means of variational wave functions whose equations we solve
analytically. We found two pairs of Doublet states, one odd and one even with
respect to the midplane between the impurities. These Doublets make a
significatively strong use of the hybridization terms of the Hamiltonian, and
have a much larger Kondo-like correlation energy than a single impurity (the
Kondo energy). Furthermore, these Doublets combine to form a Super-Singlet.
This Super-Singlet makes use of the remaining hybridization probability to
improve its energy with respect to the Doublets energy, but for low-Dimensional
systems and at the inter-impurity distances where the Doublets are full
developed, its energy gain is exponentially small. The interaction behind the
Doublets is a first-order (in the effective Kondo coupling) one, it also
generates a parallel alignment of the impurity-spins. This ferromagnetic
impurity-impurity response is thus generated without resort to the RKKY
interaction. The effective range of this first-order Doublet interaction is
also much larger than the one of the RKKY interaction.
