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Journal of Experimental and Theoretical Physics

Two-step excitation of an auto-ionized state of the Ba atom associated with two-photon excitation of an intermediate state

A. Yu. Elizarov

Published Mar 1, 1998• 0 citations
Publisher

Abstract

An experimental and theoretical study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2 ω -excited intermediate state 6 p 2 ( 1 S 0 ) and the auto-ionized state 6 p 8 s ( 3 P 1 ). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. The density-matrix formalism is used to obtain expressions for the angular dependence of the differential ionization probability. Possible experiments are discussed.

DOI
10.1134/1.558490

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An experimental and theoretical study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2 ω -excited intermediate state 6 p 2 ( 1 S 0 ) and the auto-ionized state 6 p 8 s ( 3 P 1 ). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. The density-matrix formalism is used to obtain expressions for the angular dependence of the differential ionization probability. Possible experiments are discussed.
An experimental and theoretically study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2(omega) -excited intermediate state 6p2 (1So) and the auto- ionized state 6p8s(3P1). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. Employing the density-matrix formalism, expressions have been obtained for angular dependence of the differential ionizations probability. Possible experiments are discussed.
An experimental and theoretical study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2ω-excited intermediate state 6p2(1S0) and the auto-ionized state 6p8s(3P1). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. Employing the density-matrix formalism, expressions have been obtained for angular dependence of the differential ionization probability. Possible experiments are discussed.
A theoretical investigation has been carried out on the dependence of the photoelectron angular distributions on laser intensity for the case of two-photon-resonant three-photon ionization of sodium. Good overall agreement is obtained with the experimental anisotropy parameters for ionization via the 4D3/2{D}_{3/2}D3/2​ and 4D5/2{D}_{5/2}D5/2​ intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
Calculated results for angular distribution and angular correlation of electrons produced in the process of two-photon double ionization of Xe are presented. In particular, a peculiar dependence of the angular distribution of the second step electrons on the alignment of the intermediate ionic state is predicted. The angular correlations of the electrons qualitatively depend on the term of the residual double charged ion. The results can be used in ongoing and future experiments with free-electron laser.
The Liouville representation is a formalism that describes quantum mechanical problems by using the space of density operators as kets and the space of observable operators as bras. It is useful for problems with complicated angular momentum coupling because it gives directly the probabilities and expectation values rather than probability amplitudes, so that some of the extended and tedious steps of the angular momentum algebra are eliminated. The graphical representation of angular momentum coupling has proved itself as another way to simplify and clarify calculations; graphical representation helps one to visualize the physics and simplifies and organizes the computations. By combining the graphical method and Liouville representation, we introduce a simple, transparent method to deal with problems of many coupled angular momenta. We use this formalism to derive the analytic expression for the angular distributions of photoelectrons. The angular distributions are represented by diagrams of density matrix and detector operators and a diagram of the transition matrix. The analytic expressions are then obtained from the diagrams by following simple general rules for the graphical reduction. A specific example, angular distributions of photoelectrons from resonant two-photon ionization of alkali atoms with hyperfine interaction, is also given.