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.