Scale dependence of the retarded van der Waals potential

Abstract

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit α → 0 together with the relative distance between the atoms increasing as α−γR, γ > 0. In particular we determine explicitly the crossover function from the R−6 van der Waals potential to the R−7 retarded van der Waals potential, which takes place at scale α−2R.