The long range van der Waals forces between non-identical systems

Abstract

The interaction energy between two dissimilar non-ionized molecules or atoms is calculated in fourth-order perturbation theory and dipole approximation. The interaction Hamiltonian involves the charge distribution with the complete Maxwell field and not only the Coulomb interaction between charges. At close separations between the two systems (still large compared with molecular diameters) the interaction energy is of course that corresponding to the London force. However, for separations large compared with the characteristic wavelengths associated with transitions within the molecules the London force is modified considerably. In the case of two molecules in the ground state this modification was first found by Casimir & Polder. If one of the molecules is in an excited state new effects appear at these large distances. The energy of interaction depends on the orientation of the transition moment in the excited molecule with respect to the vector displacement between the two systems. In both transverse and longitudinal orientations the potential law is considerably stronger than the R$^{-7}$ of the ground state-ground state interaction. For transverse orientations there is an unmodulated R$^{-2}$ energy dependence which though very weak individually could give rise to considerable effects when the excited molecule is in a macroscopic environment.