Scale Dependence of the Retarded van der Waals Potential

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $α\to 0$ together with the relative distance between the atoms increasing as $α^{-γ} R$, $γ> 0$. 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 $α^{-2} R$.

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