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Physica Scripta

Angular Distribution of Radiation Following Photoionization of Polarized Atoms

Alicija Kupliauskienė, V Tutlys

Published Jan 1, 2004• 6 citations
Publisher

Abstract

A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.

DOI
10.1238/physica.regular.070a00241

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A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.
An expression for the probability of the excitation of polarized atoms by polarized radiation is obtained by using the graphical technique of angular momentum. In the case of pure states, the applied method is an alternative to that of density matrix formalism. The obtained expression enables one to describe the polarization state of an excited atom and can be used to derive formulas for the special cases under specific experimental conditions as well as for the photoexcitation as the first step process. The application of obtained expressions for the description of multistep processes is discussed. The photoexcitation of unpolarized atoms by polarized radiation and polarized atoms by unpolarized radiation is considered as the examples of practical application of the obtained general expression.
The angular correlation between the photoelectron and subsequent polarized fluorescent radiation measured in coincidence is analysed theoretically for atomic photoionization. Using the density matrix and statistical tensor formalism the general expression for the correlation function is obtained for an arbitrary polarized incident photon beam. The particular geometry of a recent experiment (Beyer et al., 1995) is considered and the parameters which determine the angular correlation are expressed in terms of photoionization amplitudes. It is demonstrated that the photoelectron- (polarized) fluorescence coincidence measurements reveal strong circular and linear dichroism. As an example the photoionization of Ca atoms near the 4p 2P3/2 threshold is calculated within the framework of multichannel quantum defect theory.
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.
A theoretical study of the angular correlation and angular variation of entanglement between a photoelectron and a fluorescent photon in photoionization of atoms is provided. The formulation is developed for experiments where spin polarization of a photoelectron and polarization of the subsequent fluorescent photon are detected in a coincidence measurement. The applied formalism of parameterization of all polarization sensitivities of the detectors using Stokes parameters and of the use of statistical and efficiency tensors provides straightforward implementation for any experimental geometry. The framework is demonstrated in the case of calcium photoionization followed by radiative decay.
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.