Retardation (Casimir) effects on high and not-so-high Rydberg states of helium

Abstract

The high-precision verification of a retardation effect on the interaction 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, with the electron in the 1s state, interacting with an electron in a state with n and l not too small, possibly in a high Rydberg state. We extend a previous calculation for this pair which made use of time-ordered Feynman diagrams, with the electrons treated nonrelativistically, and obtain an expression for V(r) valid for r greater than several $a_0$. [The V(r) obtained is identical to the main result of a recent dispersion theoretic approach.] Our approach can be interpreted as an extension of the physical argument that for r≳137$a_0$ 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, ${\alpha }_d$(ω); 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 ${\alpha }_d$(ω) but its frequency-dependent nonadiabatic dipole polarizability, β(ω). The simplicity of the approach, with the electrons again treated nonrelativistically and with physical insights relatively apparent, allows one, with some confidence, to guess at the form of V(r) for systems not yet studied; it strongly suggests that to include relativistic dynamical effects on the inner or outer electron, or to study the interaction of a Rydberg electron with either certain many-electron cores or a one-electron core in certain low-lying excited states, at least formally and to lowest order, one need merely use the corresponding forms of ${\alpha }_d$(ω) and of β(ω). Here we consider neither exchange nor higher multipole contributions.