Resonance dispersion interaction of alkali metal atoms in Rydberg states

With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the 'Förster sphere' (R < R_F) this dependence transforms to the formula for electric dipole interaction energy ΔE_d-d = C₃/R³ and for R > R_F it transforms to the formula for the van der Waals interaction energy ΔE_VdW = –C₆/R⁶. The van der Waals constant C₆ is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J. The numerical values of the irreducible components of tensor C₆ were calculated for rubidium atoms in the same Rydberg states |nlJM⟩ with large quantum numbers n. We present the calculated resonance interaction energy of two rubidium atoms in the states |43D_{5/2 M}⟩, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P_{3/2 M}⟩ and of the other in the state |41F_7/2M⟩.