# Quantum-Electrodynamic Level Shifts between Parallel Mirrors: Applications, Mainly to Rydberg States

G. Barton

## Abstract

Hydrogen atoms in Rydberg states (principal quantum number n $\gg$ 1) inserted between parallel mirrors separated by a distance L suffer level shifts now becoming measurable. The analysis in the preceding paper is applied to predict these shifts $\Delta$. When L < n$^3$a/$\alpha$ (a is the Bohr radius; $\alpha = e^2/\hslash c \approx \frac{1}{137}), \Delta$ is basically electrostatic (non-retarded'), and of order (n$^4$/L$^3_{mm}$) x 10$^{-6}$ Hz (with L expressed in millimetres). When L > n$^3$a/$\alpha$, $\Delta$ is basically radiative (retarded'), and of order (2/n$^2$L$_{mm}$) x 10$^4$ Hz. Fine structure and hyperfine structure are taken into account, considering the extreme cases of low orbital angular momenta (l = 0, 1), and, more briefly, very high l (with $(n - l)/n = O(1/n))$. Explicit formulae are given in the non-retarded regime, except for very small L, where $\Delta$ becomes comparable with the fine structure. In the retarded regime for low l, the requisite radial integrals are not available accurately, and only rough predictions can be made.