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Canadian Journal of Physics

Formal theory of multiphoton double ionization: Sequential and direct

Jerry B. Altzman, Marvin H. Mittleman

Published Jan 1, 1998• 0 citations
Publisher

Abstract

The rate parameters for double multiphoton ionization are obtained as functions of T matrices, which are derived from the S matrix by a generalization of the Fermi Golden Rule. The different T's appear, and are distinguished from each other as coefficients of different energy singularities, principal parts as well as delta functions, in S. These are connected to the rate parameters, which appear in threecoupled-rate equations. New terms are shown to contribute to the direct ionization process and new interference terms are also found to contribute to the direct ionization rate. A new interpretation of the shake-off term is given, and it is found to be a sequential process. {PACS Nos.: 32.80F, 32.80K}

DOI
10.1139/cjp-76-6-459

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The rate parameters for double multiphoton ionization are obtained as functions of T matrices, which are derived from the S matrix by a generalization of the Fermi Golden Rule. The different T's appear, and are distinguished from each other as coefficients of different energy singularities, principal parts as well as delta functions, in S. These are connected to the rate parameters, which appear in threecoupled-rate equations. New terms are shown to contribute to the direct ionization process and new interference terms are also found to contribute to the direct ionization rate. A new interpretation of the shake-off term is given, and it is found to be a sequential process. {PACS Nos.: 32.80F, 32.80K}
A general framework for description of quantum systems in strong external fields is established. The most important application of the theory is concerned with the multiphoton ionization of atoms and molecules. The adiabatic approximation is developed. The Hamiltonian of the system is diagonalized by a time-dependent unitary transformation, which generates an interaction energy vanishing for very slow fields. A general analysis of the photoionization rates is performed. A specific model is considered: one-dimensional motion in the δ-function potential and external harmonic electric field. This model allows the exact solution for time-dependent eigenvalues and eigenfunctions. These solutions are compared with the conventional free electron approach to the ionization states.
We investigate different processes which may be responsible for ejection of two electrons from the external shell of xenon through the absorption of two and three photons, namely two-photon direct double ionization and three-photon sequential double ionization via the ion in an excited state or in the ground state. We calculate the cross sections of the ionization processes involved, using many-body perturbation theory. These cross sections are then used within a rate equation model for comparing the relative efficiencies of the different double-ionization mechanisms.
In view of recent papers on two-photon double ionization of helium, pertaining to a perceived anomaly in the behavior of the sequential process and its influence on the direct process, as well as the dependence of both on the laser pulse duration, we show that upon the proper formulation, the sequential is well defined and free of divergence, and that the dependence on pulse duration is considerably more intricate. We also argue that the apparent sharp rise of the cross section for the direct process, around 54.4eV54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}54.4eV, is due to the unintended inclusion of the sequential process, which in any case is not properly describable in terms of a single cross section.