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Physical Review A

Theory of two-photon autoionization of H2

Krishna Rai Dastidar, P. Lambropoulos

Published Jan 1, 1984• 21 citations
Publisher

Abstract

We present a model calculation for two-photon autoionization of ${\mathrm{H}}_{2}$ to the $X^{1}\ensuremath{\Sigma}_{g}$ state of ${\mathrm{H}}_{2}^{+}$. The theory is based on a formulation that allows for strong-field effects. It is shown that, as a result of such effects, the autoionization profile will in general exhibit qualitatively new behavior at laser intensities needed for two-photon ionization. The magnitude of these effects depends significantly on the presence of resonance with intermediate states. The notion of autoionization width and $q$ parameter are generalized to include this new behavior. Detailed calculations are reported for intensity effects on the line profile, the role of intermediate resonances, and the separate contribution of the vibrational states of ${\mathrm{H}}_{2}^{+}$ as final states. The feasibility of observation with currently available sources is discussed.

DOI
10.1103/physreva.29.183

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Detailed descriptions of one- and two-photon ionization are presented. We go beyond conventional perturbation theory to investigate the dynamics of both processes for a broad range of field intensities. The general theory of unstable decaying states is applied to the problem of one-photon ionization (the photoeffect). It is found that a non-trivial dependence of the transition dipole moment on the continuum state energy can lead to corrections to exponential decay, and even oscillations in the bound state population. As examples we consider the photoionization of hydrogen and atoms with autoionizing states. Only in the absence of autoionizing states corrections to exponential decay remain inconsequential for any experimentally relevant intensity. Our description of two-photon ionization is formulated in the Heisenberg picture. Besides the usual two-level atom projection operators we introduce explicitly the operators referring to the atomic continuum. By eliminating from the equations of motion the terms related to the electromagnetic self field as well as the terms referring to the continuum, transverse and longitudinal damping corresponding to spontaneous emission and photoionization is obtained. The use of field correlation functions allows us to account for the partial coherence of the applied field. We develop a technique to extract from the equations of motion a unique two-photon ionization rate. Such a characterization of the ionization process is not only instructive because of its simplicity, it is also in many cases completely satisfactory. The resulting general expression for the two-photon ionization rate is the central result of our treatment. From it we recover several familiar results in different limiting cases. In addition, our general rate expression provides the first description of the complete hierarchy of saturation effects that one should expect. We present a number of examples where we calculate the two-photon ionization rate as a function of the detuning, and where we emphasize the saturation and field correlation effects.
We derive a parametrized formula for the photoionization cross section in the vicinity of an autoionizing state (AIS) coupled with another AIS by a strong laser field. The rotating-wave approximation is used and adiabaticity is assumed. In the probe field spectrum two Fano resonances contribute to the cross section, while a single resonance occurs in the strong-field spectrum. The correlation between the resonance shape and the complex energies of the laser-driven two-level system is described. Calculations are performed for the and AIS pair in He and for the and pair in Mg. The results agree with those obtained using time-dependent approaches. The formula for the cross section describes the spectral features of the ion yield measured in the two-photon ionization of the Mg atom via the AIS coupled with the state. The appearance of laser-induced degenerate states in the cross section shape is studied.