Angular distributions of photoelectrons from resonant two-photon ionization: A graphical approach
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.
- Research Organization:
- Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637
- OSTI ID:
- 6125486
- Journal Information:
- J. Chem. Phys.; (United States), Vol. 81:9
- Country of Publication:
- United States
- Language:
- English
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