beams of highly excited hydrogen atoms were passed through a microwave cavity. The probability of ionization was measured 1 and excitation to states higher than the initial states detected. 2 The experiments were suggested by them to be a useful scaled model of laser ionization of atoms in low states.Their experimental results can be summarized as follows: (EX1) For given field frequency (i.e., microwave) the ionization probability rises from zero to unity with increasing field strength. Considerable ionization is observed even when the peak electric field strength is small by comparison with the static electric field strength needed to ionize the atom. (EX2) The ionization probability depends on the field frequency u F . (EX3) Multiphoton excitations take place.It is clear that very large numbers of quantum states are involved. The usual theories of laser ionization 3 have not been applied. The Keldysh dynamic barrier-penetration theory 4 * 5 is clearly inadequate because barrier penetration decreases approximately as exp(-^) and is utterly negligible for n «66. However the parameter y introduced by Keldysh has a classical interpretation which is important in this Letter.In our theory both atom and microwave field are treated classically and the magnetic effects of the field neglected. While the atom is in the interior of the microwave cavity its electron moves in a classical orbit satisfying Hamilton's 13 M" Glass-Maujean, L. Julien, and T. Dohnalik, (to be published), and to be published.
equations with the Hamiltonian functionH(?,p) = H> 2 -r-1 + zF max cosut 9 (1)where r is the position and p the momentum of the electron and units have been chosen for which the charge and mass of the electron are unity. Entry to and exit from the cavity are represented by adiabatic increase and decrease of the envelope of the oscillating field. The initial conditions are chosen by a Monte Carlo method from a classical microcanonical distribution corresponding to equal population of the degenerate (Z, m) states of a given n. The equations of motion are solved by stepwise numerical integration. Details of the method and checking procedures are given by Leopold and Percival. 6 The theory and method were both adapted from well-tried procedures for collision processes. 7 The method was subject to the following errors: (El) The precise conditions of the laboratory experiment, such as the initial distribution over (Z, m) states produced by charge transfer, and the form of the rise and fall of the microwave field, were not known. (E2) The quantized atom and field are represented by a classical model. (E3) There are errors in computation, mainly inadequate statistics.Experimental results without errors El were unavoidable to us, the errors E3 are probably slightly smaller, and the errors E2 are certainly completely negligible by comparison. Thus the theoretical model adequately represents the A classical theory gives excellent agreement with the Bayfield-Koch experiment on microwave ionization of Rydberg hydrogen atoms. The time de...
Ionization of hydrogen atoms with principal quantum number n =32, 40, and 51-74^by a 9.92-GHz electric field F(/) = z/ocoscof was studied with a superimposed static electric field F s = 0, 2, 5, and 8 V/cm. The measured field strengths Fo(\0°/o) at which 10% of the atoms were ionized are in excellent agreement with classical calculations in both one and two spatial dimensions. Covering finer detail as well as gross structure of the n dependence of FoOOo/o), the agreement supports the application of classical dynamics to the analysis of this strongly perturbed quantum system.
For periodically forced systems we show that the scarred state corresponding to the unstable periodic orbit of the main m o m c e has a lower ionization nte thm adjacent states because a representation exists in which coupling to &er sfateS is minimal. Our results explain why this scyred state h a been observed in recent experiments on the microwave ionization of excited hydrogen atoms; other previously unexplained features are also elucidated.
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