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

An asymptotic expression for the van-der-Waals constant C-6 (n) approximate to -0.03n(12) K-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 n(1(2)) = n - 1, n(2(1)) = m = 0 in the case of collinear orientation of the Stark-state dipolar electric moments and the interatomic axis. The cubic polynomial K-3 (x) in powers of reciprocal values of the principal quantum number x = 1/n and quadratic polynomial K-2 (y) in powers of reciprocal values of the principal quantum number squared y = 1/n(2) were determined on the basis of the standard curve fitting polynomial procedure from the calculated data for C-6 (n). The transformation of attractive van-der-Waals force (C-6 > 0) for low-energy states n < 23 into repulsive force (C-6 < 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 -> infinity (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 C-6 (n) from the lower-energy two-atomic states, of the A(B)-atom principal quantum numbers n'(A(B)) = n - Delta n (where Delta n = 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 + Delta n make the joint contribution proportional to n(12). So, the hydrogen-like manifold structure of the energy spectrum is responsible for the transformation of the power-11 asymptotic dependence C-6(n) proportional to n(11) of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence C-6(n) proportional to n(12) for the dipolar states of the Rydberg manifold.