For pt.III see ibid., vol.23, no.1, p.21-43 (1990). The differential cross section for the photoionization of an atom in a uniform electric field can be observed if the photocurrent is registered on the plane screen perpendicular to the uniform field axis. In the photodetachment case the differential cross section structure is interpreted exclusively in terms of the interference between two photoelectron classical trajectories passing through a given point on the screen. When the photoionization of the neutral atom is considered the resonance effects should be taken into account. If the photon energy is chosen so that the photoionization proceeds into a particular resonance state then the differential cross section represents essentially the squared resonance wavefunction in the parabolic coordinate xi .

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The photoionisation cross section for a hydrogen atom placed in a uniform electric field is calculated using separation of the variables in parabolic coordinates and the semiclassical approximation with account for the tunnelling and reflection above the top of the potential barrier. The corrections to the semiclassical approximation are established accounting for the peculiarities of the effective potential barrier form. The approximate separation of the centrifugal terms contribution in the phase barrier form. The approximate separation of the centrifugal terms contribution in the phase integrals allows the latter to be expressed via hypergeometric functions. The structure in the energy dependence of the cross section is associated with its complex poles. The motion of the poles under variation of the photon energy is investigated. The equations defining the resonance positions and widths are obtained and analysed for energies below and above the potential barrier. The boundary between these two regions is described. The analytical expressions for the parameters of resonances lying above the barrier are obtained for the first time. In the vicinity of the resonance the cross section can be well parameterised by Fano's formula. The approximate expressions for the profile index are deduced. The analytical results are compared with numerical calculation data. The recent experiments on the photoionisation of rubidium and sodium atoms are discussed.

We report the results of an experimental and theoretical investigation of the recurrence spectra of Rydberg atoms in a static plus weak oscillating electric field. Experiments reveal the systematic weakening of orbits in a recurrence spectrum as the oscillating field strength and frequency are changed. We describe a generalization of closed orbit theory to time-dependent systems and show that it provides a qualitative and quantitative description of the phenomena. [S0031-9007 (97)03947-1] PACS numbers: 32.60. + i, 03.65.Sq, 05.45. + bIn the quest for a satisfactory understanding of the connections between quantum and classical descriptions of simple Hamiltonian systems, Rydberg atoms in applied fields provide prototypes for experiment and theory [1]. Recurrence spectroscopy and closed orbit theory have proven to be powerful tools for these studies [2][3][4]. A recurrence spectrum is the Fourier transform of a photoexcitation spectrum that is taken with the field varying with energy according to a classical scaling rule that keeps the classical motion unchanged at all points in the spectrum [2]. It can be shown that each closed classical orbit of the electron generates a peak in the recurrence spectrum at the action of the orbit. Consequently, the recurrence spectrum provides a quantum picture of classical behavior. Studies of recurrence spectra have led to observations of the creation of new orbits through bifurcations [5,6], the onset of irregular behavior through core scattering [7-10], symmetry breaking in crossed fields [11], and the identification of numerous closed orbits [1].We have extended this line of inquiry by investigating the recurrence spectrum of a Rydberg atom in a field that is oscillating with a period which is comparable to the period of its classical orbits. The underlying thought is that periodic orbits should be sensitive to periodic perturbations, and that this sensitivity should be revealed by recurrence spectra. Recurrences with periods that are integer multiples of the period of the perturbing field might be expected to be most affected. We report here the first results of such a study. The experimental observations are surprising: Recurrences with periods near integer multiples of the period of the perturbation survive, while those that are out of "resonance" with the field are weakened or eliminated. We have been able to interpret these results by generalizing closed orbit theory to incorporate periodic fields, obtaining both a qualitative and quantitative description of the phenomena.Our study employs a lithium Rydberg atom in a static electric field-a system we have previously studied [8]but now with the addition of an oscillating field. At the low actions studied in these experiments, the spectrum is regular and can be understood by considering only the closed orbits of hydrogen. Experimentally, introducing an rf field is a straightforward task. (We use "rf" to signify the oscillating field though the actual frequency may be in the microwave regime.)