Retardation or Casimir Effects in a Rydberg Helium Atom and Other Atomic Systems.

A retardation effect, an effect due to the finiteness of the speed of light, can manifest itself in the interaction between two polarizable systems as a change in the form of the long-range interaction potential. With the interaction viewed as mediated by virtual photons, retardation effects become important when the time required for a photon to travel back and forth between the two systems becomes larger than or of the order of the characteristic period of the motion of either system. The form of the potential under retardation is characterized in general by the dynamic electric dipole polarizabilities alpha_ {d}(omega) of each of the systems, where omega is the virtual photon frequency, the separation r of the systems, hbar, and c. The high-precision verification of a retardation effect on the potential V(r) between a pair of systems probably demands that the systems be microscopic and form a bound state. The ideal pair would seem to be a helium ionic core (an alpha particle and an electron in the 1 s state) interacting with an electron in a state with n and l not too small, possibly in a high Rydberg state. Making use of time-ordered Feynman diagrams, with the electrons treated nonrelativistically, an expression for V(r) valid for r greater than several a _0 is obtained. The approach can be interpreted as an extension of the physical arguement that for r > 137alpha_0 the retardation component of V(r) follows easily from considerations of the interactions between electromagnetic vacuum fluctuations and each member of the pair, with each member characterized solely by its frequency-dependent electric dipole polarizability, alpha_{d}(omega); the extension from r > 137 a_0 down to just several a _0 is achieved by including in the characterization of each member not only its alpha_ {d}(omega), but its frequency-dependent nonadiabatic dipole polarizability, beta( omega). Effects originating in the finite nuclear mass are discussed. Retardation effects for Rydberg systems with many-electron cores are also of interest and so a qualitative discussion of retardation effects is provided to help one guess, for a given system with l ~ n gg 1, whether the size of the retardation energy shift is such as to warrant consideration.