On the Cooper-Stacey reduction in Dicke coherence due to relative motion

The lifetime for a pair of atoms with one quantum of excitation is calculated by conventional perturbation theory without the assumption of fixed separation between the atoms. Several cases for the initial preparation of the state of relative motion are considered. For plane wave states there is no coherence, for the state with locked-in relative displacement the usual coherence is deduced, while for a nearly classical state with minimum dispersion in both relative displacement and relative momentum the result of Cooper and Stacey (see abstr. A19687 of 1974) is confirmed. The resonance energy is shown to be unaffected by the relative motion.