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 εᵣ, widths Γᵣ, and oscillator strengths fᵣF are derived in terms of matrices HF and hF, which represent the hydrogenic density of states in a Stark field F. Core effects appear through zero-field quantum defects μₗ and dipole matrix elements dₗ⁰. Normalized oscillator strengths f̄ᵣF are defined which are independent of all dₗ⁰ for s→p transitions. Isolated and interacting Stark manifolds with m=0 and 1 are examined for systems with two nonnegligible μₗ. 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<13n⁵ level positions are given analytically with respect to H levels of fixed n; $m=0$ intensity distributions do not appear hydrogenic in Li since μ₀~1/2. At F>13n⁵, 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 f̄ᵣF is presented for Li ($m=0$) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include 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)].