  We consider the resonant interaction energy and force between two identical
atoms, one in an excited state and the other in the ground state, placed inside
a photonic crystal. The atoms, having the same orientation of their dipole
moment, are supposed prepared in their symmetrical state and interact with the
quantum electromagnetic field. We consider two specific models of photonic
crystals: a one-dimensional model and an isotropic model. We show that in both
cases the resonant interatomic force can be strongly enhanced by the presence
of the photonic crystal, as a consequence of the modified dispersion relation
and density of states, in particular if the transition frequency of the atoms
is close to the edge of a photonic gap. Differences between the two models
considered of photonic crystal are discussed in detail, as well as comparison
with the analogous system of two impurity atoms in a quantum semiconductor
wire. A numerical estimate of the effect in a realistic situation is also
discussed.
