### ?

## Energy of van der Waals and dipole-dipole interactions between atoms in Rydberg states

The van der Waals coefficient C6(θ;nlJM) of two like Rydberg atoms in their identical Rydberg states |nlJM⟩ is resolved into four irreducible components called scalar Rss, axial (vector) Raa, scalar-tensor RsT=RTs, and tensor-tensor RTT parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of C6(θ;nlJM) on the angle θ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components Rαβ of atoms in their Rydberg series of doublet states of the low angular momenta (2S, 2P, 2D, 2F). The polynomial presentations in powers of the Rydberg-state principal quantum number n taking into account the asymptotic dependence C6(θ;nlJM)∝n11 are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their n2S1/2, n2P1/2,3/2, n2D3/2,5/2, and n2F5/2,7/2 Rydberg states of arbitrary high n. The transformation of the van der Waals interaction law −C6/R6 into the dipole-dipole law C3/R3 in the case of close dipole-connected two-atomic states (the Förster resonance) is considered and the dependencies on the magnetic quantum numbers M and on the angle θ of the constant C3(θ;nlJM) are determined together with the ranges of interatomic distances R, where the transformation appears.