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van der Waals interaction of atoms in circular Rydberg states


Analytical expressions for the constants of resolution in powers of inverse interatomic distance 1∕R are determined for the energy of the long-range interaction between two atoms A and B in their circular Rydberg states of equal principal quantum numbers nA = nBn ≫ 1, maximal angular momenta and magnetic quantum numbers lA = lB = |mA| = |mB| = n − 1 in the case of arbitrary orientation of the interatomic axis relative the axis of the m-quantization. Coefficients of the odd-power terms CkRk are derived for k = 5, 7, 9 from the first-order perturbation theory (PT) for the interaction Hamiltonian. The constant C6 of the van der Waals interaction ΔEvdW = −C6R6, determined from the second-order PT, is resolved into irreducible components. The combinations of irreducible components determine coefficients at Legendre polynomials and/or cosine functions describing the dependence of C6 on the angle between the interatomic and quantization axes. The asymptotic dependence on the principal quantum number C6n12 is demonstrated analytically. Polynomials in powers of n are derived for extrapolation of calculated data to the case of arbitrary n. The transformation of attractive van der Waals force (C6 > 0) for low-energy states n < 6 into repulsive force (C6 < 0) for all higher-energy states of n ≥ 8 is demonstrated in numerical calculations.

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Correspondence to Vitaly D. Ovsiannikov.

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Kamenski, A.A., Manakov, N.L., Mokhnenko, S.N. et al. van der Waals interaction of atoms in circular Rydberg states. Eur. Phys. J. D 72, 174 (2018).

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