The van der Waals coefficient $C_6(\theta ;nlJM)$ of two like Rydberg atoms in their identical Rydberg states $|nlJM\rangle$ is resolved into four irreducible components called scalar $R_{ss}$, axial (vector) $R_{aa}$, scalar-tensor $R_{sT}=R_{Ts}$, and tensor-tensor $R_{TT}$ parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of $C_6(\theta ;nlJM)$ on the angle $\theta$ 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 $R_{\alpha \beta }$ of atoms in their Rydberg series of doublet states of the low angular momenta (${}^{2}S, {}^{2}P, {}^{2}D, {}^{2}F$). The polynomial presentations in powers of the Rydberg-state principal quantum number $n$ taking into account the asymptotic dependence $C_6(\theta ;nlJM)\propto n^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their $n{}^2{S}_{1/2}, n{}^2{P}_{1/2,3/2}, n{}^2{D}_{3/2,5/2}$, and $n{}^2{F}_{5/2,7/2}$ Rydberg states of arbitrary high $n$. The transformation of the van der Waals interaction law $-C_6/R^6$ into the dipole-dipole law $C_3/R^3$ 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 $\theta$ of the constant $C_3(\theta ;nlJM)$ are determined together with the ranges of interatomic distances $R$, where the transformation appears.

• Received 30 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.032716