Retardation in the resonant interaction of two identical atoms

Abstract

The problem considered is that of two identical two-level atoms a fixed distance $r$ apart, one of which is excited at $t=0$. A simple improvement on the usual on-shell approximation (which in the single-atom case is part of the Weisskopf-Wigner approximation) yields new solutions for the various probability amplitudes in the form of infinite series involving all the retardation times $\frac{\mathrm{nr}}{c}$. The truncated solutions involving only the single retardation time $\frac{r}{c}$ are compared with previously published results both when all photon modes are allowed and when only photons propagating along the interatomic axis are allowed. When the retardation times are neglected, the series are summed to give the well-known results of Stephen and others.