A functional approach to the Van der Waals interaction

Abstract

We evaluate the quantum interaction energy between two neutral atoms, using a functional integral approach. In our setup, each atom has an electron bound to the nucleus via a harmonic potential. The resulting expression for the vacuum energy becomes the Van der Waals interaction at the first non-trivial order in an expansion in powers of the fine structure constant, encompassing both the long and short distance behaviours. We also explore the opposite, strong-coupling limit, which yields a result for the interaction energy as well as a threshold for the existence of a vacuum decay probability, manifested here as an imaginary part for the effective action. In the weak-coupling limit, we also study the effect of using a general central potential for the internal structure of the atoms.