https://doi.org/10.1140/epjd/e2017-80477-x

Regular Article

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

Department of Physics, Voronezh State University,
394006
Voronezh, Russia

^{a} e-mail: ovd@phys.vsu.ru

Received:
18
July
2017

Received in final form:
20
November
2017

Published online: 6
February
2018

An asymptotic expression for the van-der-Waals constant *C*_{6}(*n*) ≈ –0.03*n*^{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* → *∞* (*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*-Δ*n* (where Δ*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*+Δ*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*) ∝ *n*^{11}of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence *C*_{6}(*n*) ∝ *n*^{12} for the dipolar states of the Rydberg manifold.

Key words: Atomic Physics

*© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2018*