a1 Mathematics Department, University College, London.
In the theory of the interaction between simple electrically neutral systems with dipole moments, the interaction energy between two such systems when they are identical, one in an excited state and the other in the ground state, is of current interest. It is well-known that, within the Coulomb force approximation for the electron-electron interaction, the energy varies as
where q(r) is the electric dipole moment of the system r = 1, 2, and R is the vector displacement of system 2 from system 1. This is the so called resonance attraction between the systems. On the other hand it has been known since 1948 (see ) that for two systems both in their ground states the potential of interaction falls off at large separation faster than the London formula for the energy, namely
predicts. In equation (2) α(r) is the polarization of the system r, in terms of the dipole moments (here induced)
where E is the energy separation between the two states considered, i.e., the ground state and the excited state reached from the ground state by electric dipole transitions. In fact the asymptotic form of the potential energy at separation was given by Casimir and Polder as
(Received May 14 1964)