Weak-field versus Born-Oppenheimer asymptotics in the theory of tunneling ionization of molecules

Abstract

The weak-field asymptotic theory (WFAT) and the Born-Oppenheimer approximation (BOA) provide two general approaches to the theory of tunneling ionization of molecules enabling one to treat the internuclear motion quantum mechanically on an equal footing with the electronic motion. The approaches are based on the asymptotic expansions in field strength and electron-to-nuclear mass ratio, respectively. The problem is that they yield quite different formulas for the ionization rate, which causes an ambiguity for applications in strong-field physics. A recent experimental observation of the isotope effect in tunneling ionization of hydrogen molecules [X. Wang et al., Phys. Rev. Lett. 117, 083003 (2016)] motivates us to address this theoretical ambiguity. The WFAT and BOA have different but overlapping regions of applicability in the field strength---nuclear mass plane. We link the approaches analytically, in particular showing that the rate formulas in fact coincide in the overlap region where they both apply, and compare their predictions quantitatively.