Multichannel quantum-defect theory of the Stark effect

Abstract

The spectra of hydrogen and nonhydrogenic Rydberg atoms in a dc electric field F are discussed in the framework of multichannel quantum defect theory (MQDT). Nonhydrogenic, many‐electron interactions are confined to the atomic core, where the field’s influence is nil. The Rydberg electron’s wave function is sensitive to F, but only outside the core. Hydrogen‐Stark eigenfunctions in a parabolic basis are required to represent the excited electron at r≫rF where z=−rF marks the classical saddle point and classical ionization limit ecil=−2√F (a.u.). A frame transformation connects spherical and parabolic bases for hydrogen. WKB phase and tunnelling integrals parametrize the field’s effects on wave function phases and amplitudes, and determine the hydrogenic density of states HF. The atom’s reaction matrix K (including quantum defects) then determines the nonhydrogenic density of states DF. At e<ecil, DF has a quasi‐discrete spectrum of Stark‐split and ‐broadened levels, whereas at e≳ecil all levels ionize. Th...