A variational theory for high Rydberg Stark ionization threshold scaling laws in atomic hydrogen

Abstract

We examine hydrogen atom Stark energies calculated with nonlinear variational theory using square‐integrable wavefunctions. The trial function for each state has a characteristic critical field (F*) above which the variational energy is complex. F* approximates the experimentally important Stark ionization threshold for Rydberg states and typifies critical fields encountered in mathematical ’’catastrophe theory.’’ Zero‐field wavefunctions yield analytic formulas for both threshold fields and energies in terms of parabolic quantum numbers. Aspects of the model suggest a ’’law of corresponding states’’ for Stark ionization near the critical field. The threshold fields scale as n⁻⁴ for all high Rydberg Stark states, while threshold energies scale as n⁻² for the most unstable Stark components, and as n^−8/3 for the most stable components. This variationally determined threshold behavior is compared with existing classical ionization criteria, perturbation theory, and semiclassical threshold orderings for different Stark components.