Short Distance Relativistic Atom-atom Forces *

60 Garden Street, Cambridge, Massachusetts 02138 (March 1, 1999) About fifty years ago two important papers appeared describing novel interactions. One, by Casimir, discussed the case of two interacting walls [1] and the other, by Casimir and Polder, considered the interactions between an atom and a wall and between two atoms [2]. The history and some of the many interesting aspects of these interactions, their derivations, and their importance in field theory and atomic and molecular physics are summarized elsewhere [3–5]. Indeed, recent experiments give strong evidence of the reality of both the atom-wall [6] and the wall-wall interactions [7] predicted in those two papers. Here I will focus on the connection between the QED result of Casimir and Polder and other results for relativistic atom-atom interactions at short distances of the order of, say, 20 a0. The interaction between an electron and an ion will also be considered. For typical atomic systems these relativistic effects are very small corrections to the non-relativistic potentials arising from the van der Waals and Coulomb interactions for, respectively, the atom-atom interaction and the electron-ion interaction. Casimir and Polder used QED and old-fashioned perturbation theory and their result was subsequently duplicated by other authors with different methods, cf. [3]. One way to write their result for the interaction potential V (R) between two spherically symmetric atoms separated by a distance R is as a one-dimensional integral