Analytical study of quasidiscrete Stark levels in Rydberg atoms

A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\epsilon }_r$, widths ${\Gamma }_r$, 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 ${\mu }_l$ 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 $s\to p$ transitions. Isolated and interacting Stark manifolds with $m=0\mathrm{} \mathrm{and} 1$ are examined for systems with two nonnegligible ${\mu }_l$. 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 $F<\mathrm{}\frac{1}{3n^5}$ level positions are given analytically with respect to H levels of fixed $n$; $m=0\mathrm{}$ intensity distributions do not appear hydrogenic in Li since ${\mu }_0\sim \frac{1}{2}$. At $F>\mathrm{}\frac{1}{3n^5}$, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at $m=1\mathrm{}$ anticrossings in Li, as observed in ZLKK. For $m=0\mathrm{}$ the lower levels usually vanish instead. A full Stark map of calculated intensities ${\overline{f}}_r^F$ is presented for Li ($m=0\mathrm{}$) 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)].