Quantum-electrodynamic level shifts between parallel mirrors: applications, mainly to Rydberg states

Abstract

Hydrogen atoms in Rydberg states (principal quantum number n ≫ 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 ⊿. When L < n 3 a /α ( a is the Bohr radius; α = e 2 / ħc ≈ 1/137), ⊿ 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 /α, ⊿ 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 régime, except for very small L , where ⊿ becomes comparable with the fine structure. In the retarded régime for low l , the requisite radial integrals are not available accurately, and only rough predictions can be made.