Van-der-Waals interaction of atoms in dipolar Rydberg states

Abstract

An asymptotic expression for the van-der-Waals constant C6(n) ≈ –0.03n12K p (x) is derived for the long-range interaction between two highly excited hydrogen atoms A and B in their extreme Stark states of equal principal quantum numbers n A = n B = n ≫ 1 and parabolic quantum numbers n1(2) = n - 1, n2(1) = m = 0 in the case of collinear orientation of the Stark-state dipolar electric moments and the interatomic axis. The cubic polynomial K3(x) in powers of reciprocal values of the principal quantum number x = 1/n and quadratic polynomial K2(y) in powers of reciprocal values of the principal quantum number squared y = 1/n2 were determined on the basis of the standard curve fitting polynomial procedure from the calculated data for C6(n). The transformation of attractive van-der-Waals force (C6 > 0) for low-energy states n < 23 into repulsive force (C6 < 0) for all higher-energy states of n ≥ 23, is observed from the results of numerical calculations based on the second-order perturbation theory for the operator of the long-range interaction between neutral atoms. This transformation is taken into account in the asymptotic formulas (in both cases of p = 2, 3) by polynomials K p tending to unity at n → ∞ (K p (0) = 1). The transformation from low-n attractive van-der-Waals force into high-n repulsive force demonstrates the gradual increase of the negative contribution to C6(n) from the lower-energy two-atomic states, of the A(B)-atom principal quantum numbers n′A(B) = n-Δn (where Δn = 1, 2, … is significantly smaller than n for the terms providing major contribution to the second-order series), which together with the states of n″B(A) = n+Δn make the joint contribution proportional to n12. So, the hydrogen-like manifold structure of the energy spectrum is responsible for the transformation of the power-11 asymptotic dependence C6(n) ∝ n11of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence C6(n) ∝ n12 for the dipolar states of the Rydberg manifold.