The asymptotic Casimir–Polder potential from second‐order perturbation theory and its generalization for anisotropic polarizabilities

It is shown how the leading term for very large R of the Casimir–Polder potential, that is the term varying as R −7 , arises in second‐order perturbation theory applied to the interaction Hamiltonian − \documentclass{article}\pagestyle{empty}\begin{document}$ - \sum\limits_\sigma {\frac{1}{2}\alpha (\sigma){\rm E}^{ \bot ^2 } (\sigma)} $\end{document} . The generalization to anisotropic molecules is calculated and the angular dependence of the long range intermolecular potential in this case is given explicitly in terms of the principal polarizabilities and their corresponding directions of the two molecules.