We report the first measurements of microwave excitation and ionization of excited hydrogen atoms for scaled frequencies n$co up to 2.8. Classical 3D calculations which directly model this 36.021-GHz experiment agree quite well for n$o) < 1, agree less well for 1 < n$co< 2, and do not agree for n$co > 2. This supports theoretical predictions that as n$co rises above 1, quantal ionization threshold fields rise above those for the onset of classical chaos; however, the data continue to reveal local stability near certain rational frequency ratios that recalls classical behavior.

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New data for no=24, . . . , 32 H atoms ionized b' a linearly polarized, 9.908-6Hz electric field are compared with calculations.Being more precise than laser multiphoton ionization experiments with tightly bound atoms, our experiments distinguish between tunneling through and classical escape o[.er a slowly oscillating barrier and between oneand many-state dynamical processes. Formulas used to interpret low-frequency laser multiphoton ionization data poorly describe our results. Our data delineate ranges of validity of other partly successful models and are best reproduced by a new 30 semiclassical model. PACS numbers: 32.80.Rm, 03.65.Sq, 73.40.Gk While the realization that a "particle" could traverse a classically impenetrable, static potential barrier arose early in the development of quantum mechanics, there has been continuing interest in (and some controversy [I] over) quantum-mechanical tunneling. Questions being raised [I] include the definition of tunneling time(s) and how a nonstationary barrier is traversed. Several theories [2-4] address the tunneling ionization of atoms in an oscillatory electric field with amplitude F. Tunneling interpretations have been applied to some intense-laser multiphoton ionization (LMPI) experiments [5-8], often with noble gas atoms or their positive ions. However, given that tunneling rates increase exponentially with F and that absolute determination of relevant peak intensities & 10' W/cm in focused laser beam pulses is said [8,9] to be diNcult even to a factor of 2, LMPI experiments have not provided sensitive tests of' dynamic tunneling theory. Indeed, the term tunneling ionization was even ascribed to LMPI experiments that were analyzed with a model based on classical, over-the-barrier escape [6(a)].In this Letter we use tunneling to refer specifically to a transition through a barrier, where the transition connects two states having the same total energy; we also contrast this with mechanisms, such as MPI, involving transitions to states with other energies.Our dat I come from micro~ave ionization of excited H atoms. Micro~ave technology facilitates precise determinations [10] of the field amplitude and pulse shape, a major advantage over LMPI experiments. Moreover, the simplicity of the hydrogen atom allows us to model details of the ionization process and make a direct comparison between experiment and theories. We find that a theory [4] often used [6-8] to model laser tunneling ion-Ization experiments fails to describe the present data. lt is convenient to use classically scaled variables [11] (r)t, .FO) for the f'requency to and amplitude F (atomic units are used throughout) of the applied field, where t&o=njj'to and Fo=noF The classical dyn. amics [11,12] depends on only these and not separately on m, F, and the principal classical action 10, here set equal (in a.u. ) to no Using results from Ref. [13] for each parabolic substate n =(no, n~,~m~), the highest [lowest] critical field F, '. ("(n) for classical escape is F0=0.38 [Fo=0.13] for the extremal upward-g...