Quantum-electrodynamic level shifts between parallel mirrors: analysis

Abstract

Atoms inserted between parallel conducting planes (mirrors) separated by a distance L suffer level shifts that can be understood only through a careful quantum-electrodynamic calculation embracing both electrostatics and electromagnetic retardation. The basic theory is reformulated with a view to spectroscopic experiments now under way. The requisite mathematics is systematized and made more accessible; special attention is paid to the symmetry properties of the shifts; the asymptotically leading terms are given in full for small and for large L ; the role of the characteristic hydrogenic degeneracies is explored, and is found to be surprisingly unimportant in almost all situations of potential interest. For small L , the shifts are dominated by essentially electrostatic effects, of order 1/ L 3 . For large enough L , all frequency shifts are dominated by energy shifts peculiar to excited states, and decreasing only as 1/ L ; a simple classical model helps to elucidate this effect, and a kind of resonant enhancement to which it can lead. The following paper applies the results specifically to Rydberg (high- n ) states, which present some interesting problems of their own.