Ionization distances of Rydberg atoms approaching solid surfaces in the presence of weak electric fields

The ionization distances R{sub c}{sup I} of slow hydrogenlike Rydberg atoms approaching solid surfaces in the presence of a weak external electric field are calculated. The ionization is treated as resonant electron tunneling in the very vicinity of the top of the potential barrier, created between the ionic core and polarized solid. We obtain both the complex energies and the ionization distances by solving the energy eigenvalue problem under the outgoing wave boundary condition towards the solid. The eigenvalue problem is studied in parabolic coordinates within the framework of an etalon equation method adapted to include the confluence of turning points. It is demonstrated that in a critical region R{approx_equal}R{sub c}{sup I}>>1 a.u. of ion-surface distances R, parabolic quantum numbers n{sub 1}, n{sub 2}, and m can serve as approximate, but 'sufficiently good' quantum numbers, at least for lower n{sub 1} values. The method offers asymptotically exact analytical expressions for the ionization rates and energies, which follow the theoretical predictions of the complex scaling method (CSM). It is also found that the resulting ionization distances R{sub c}{sup I} are in very good agreement with the results of CSM. The implications of using obtained results in analyzing the recent xenon experimental data for R{sub c}{sup I} are briefly discussed.