Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous bound-state error estimates in the weak-field regime.

Abstract

Applying a method based on some results due to Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], we show that series of Rydberg eigenvalues and Rydberg eigenfunctions of hydrogen in a uniform magnetic field can be calculated with a rigorous error estimate. The efficiency of the method decreases as the eigenvalue density increases and as \ensuremath{\gamma}${\mathit{n}}^{3}$\ensuremath{\rightarrow}1, where \ensuremath{\gamma} is the magnetic-field strength in units of 2.35\ifmmode\times\else\texttimes\fi{}${10}^{9}$ G and n is the principal quantum number of the unperturbed hydrogenic manifold from which the diamagnetic Rydberg states evolve. Fixing \ensuremath{\gamma} at the laboratory value 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ and confining our calculations to the region \ensuremath{\gamma}${\mathit{n}}^{3}$1 (weak-field regime), we obtain extremely accurate results up to states corresponding to the n=32 manifold.