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Physical Review A

Two-photon ionization of colliding atoms

Munir Hasan Nayfeh

Published Sep 1, 1977• 21 citations
Publisher

Abstract

Semiclassical expressions of two-photon ionization of two colliding atoms are derived for a wide range of electromagnetic field intensity and detunings from the isolated atom line. The dependence of the ionization yield on the details of the interaction potential of the system is derived. This process promises an extremely sensitive method for studying line broadening on the far wing, especially when absorption or fluorescence becomes very weak.

DOI
10.1103/physreva.16.927

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Semiclassical expressions of two-photon ionization of two colliding atoms are derived for a wide range of electromagnetic field intensity and detunings from the isolated atom line. The dependence of the ionization yield on the details of the interaction potential of the system is derived. This process promises an extremely sensitive method for studying line broadening on the far wing, especially when absorption or fluorescence becomes very weak.
Semiclassical expressions of two-photon ionization of atoms induced by radiative collisions are derived. The dependence of the ionization yield on the atomic forces, field intensity, and energy gap is derived. Although absorption tends to decrease as the field intensity rises due to stimulated emission at the second crossing, the two-photon ionization yield can be nearly saturated at the first crossing, thus enhancing the absorption. Both regions, ionization in single collisions and ionization between collisions, are treated. In the latter we find that saturation of the ionization can be achieved at much reduced intensities. This process promises an extremely sensitive method for studying radiative collisions, especially when absorption or fluorescence becomes extremely weak.
A semiclassical treatment of collision-induced three-photon ionization of atoms with a near two-photon resonance is presented. The system is described by an effective two-level system. The wavelength dependence of the ionization yield does not obey a power law. When the first excited state is far from resonance, and with a C6R6\frac{{C}_{6}}{{R}^{6}}R6C6​​ interatomic potential, a first-order correction to the expected $\ensuremath{-}\frac{3}{2}$ power law obeys a - \textonehalf{} power law. This three-photon process promises to be an extremely sensitive method for the study of collisional effects in the far wing of two-photon $S\ensuremath{-}S$ and $S\ensuremath{-}D$ transitions, and without the requirement of high densities.
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.
The first analysis is made of stimulated Raman scattering and two-photon absorption (emission) processes resulting in a change in the states of two colliding particles. These processes are caused the by interaction between dipole moments induced as a result of polarization of the particles by the radiation. Equations are derived to describe multiphoton transitions during a collision between two particles in a radiation field. Using the approximation of rectilinear trajectories, expressions are derived and analyzed for the cross section of collisional two-photon transitions in weak and strong fields. It is shown that in fields of ≈103 cgs esu, the cross section of these transitions may reach 10–4 cm2
Two-photon absorption is theoretically analyzed within the semiclassical formalism of radiation-matter interaction. We consider an ensemble of inhomogeneously broadened three-level atoms subjected to the action of two counterpropagating fields of the same frequency. By concentrating in the limit of large detuning in one-photon transitions, we solve perturbatively the Bloch equations in a non-usual way. In this way we derive an analytical expression for the width of the two-photon resonance that makes evident sub-Doppler two--photon spectroscopy. We also derive an analytical expression for the Stark shift of the two-photon resonance.
The photoionization of atoms in a strong electromagnetic field leads to the effect of "above-threshold" ionization, displaying a number of peaks in the energy spectrum of the photoelectrons. In the case of a one-electron model atom in a circularly polarized field, we derive expressions that describe the position as well as the intensity of those peaks as a function of the field parameters by means of a nonperturbative method. It is immediately clear from our formulas that the lowest-energy peaks in general disappear with increasing field intensity, for Coulomb-like as well as shortrange potentials. For a zero-range potential, a numerical evaluation is easily performed, leading to results that are in every respect qualitatively similar to the experimental results obtained thus far on these kinds of processes.