Analytical study of quasidiscrete Stark levels in Rydberg atoms

Abstract

A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths ${f}_{r}^{F}$ are derived in terms of matrices ${\mathit{H}}^{F}$ and ${\mathit{h}}^{F}$, which represent the hydrogenic density of states in a Stark field $F$. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements ${d}_{l}^{0}$. Normalized oscillator strengths ${\overline{f}}_{r}^{F}$ are defined which are independent of all ${d}_{l}^{0}$ for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with $m=0 \mathrm{and} 1$ are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields $F<\frac{1}{3{n}^{5}}$ level positions are given analytically with respect to H levels of fixed $n$; $m=0$ intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At $F>\frac{1}{3{n}^{5}}$, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at $m=1$ anticrossings in Li, as observed in ZLKK. For $m=0$ the lower levels usually vanish instead. A full Stark map of calculated intensities ${\overline{f}}_{r}^{F}$ is presented for Li ($m=0$) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include $\mathrm{ls}$ coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].