Correlated Motion in Atomic Many-Body Systems

H. W. van der Hart, JILA
C. H. Greene, University of Colorado

Research Objectives

To describe in detail the motion of electrons in complex open-shell atoms and to extend the application of our computational approach to more complicated species and to frequencies where the atomic structure is more complicated.

Computational Approach

For the calculation of complex spectra, we employ the R-matrix approach. In this approach, configuration space is divided into two regions. In the inner region, we use a large basis set to describe all interactions in the atom. After setting up the Hamiltonian, we use a full diagonalization to obtain all the eigenvectors and eigenvalues of the Hamiltonian. These eigenvectors and eigenvalues provide the R-matrix. In the outer region, asymptotic solutions for one outgoing electron are obtained. By matching these solutions with the R-matrix, we obtain all the photoionization properties of the atom. All calculations are performed on the J-90 cluster.

Accomplishments

We have employed the R-matrix approach for photoionization studies of Ar, with special emphasis on the resonances observed experimentally in the frequency range between 30 and 38 eV. Many excited Ar⁺ thresholds lie in this region, so that photoionization can leave Ar⁺ in a wide variety of excited states. To determine the excitation of these Ar⁺ states, we must obtain a good description of many Ar⁺ states simultaneously. Consequently, extensive basis sets are required.

In a first study, we have compared our spectra for emission of 3p and 3s electrons with experiment and obtained excellent agreement. The complex resonance spectrum for photon energies between 30 and 38 eV is reproduced in great detail. In addition, we have determined spectra for observing ejected electrons with nearly zero energy, so-called threshold photoelectron spectra. These spectra are strongly affected by the interactions in both Ar and Ar⁺. The good agreement with experiment shows our success in describing the complex interreactions in Ar.

In a second study, we have emphasized the photoionization cross sections while leaving Ar⁺ in the 3p⁴(³P)4p states. Using fluorescence spectroscopy, experimentalists have provided detailed spectra for these processes. The present calculations reproduce the experimental spectra well, and also provide good predictions for the polarization of the fluorescence. Through frame transformation techniques, we can also determine the influence of relativistic effects on the photoionization spectra.

Theoretical (red) and experimental (blue) spectra for photoemission of a 3s electron from the Ar ground state. The top figure shows a theoretical spectrum obtained with infinite resolution, while the theoretical results in the bottom figure have been convoluted with the experimental resolution.

Significance

The interactions between the electrons are very significant in complex open-shell atoms and need to be described accurately to predict the atomic spectra reliably. Theoretical calculations are valuable to identify the observed features in experiment. The comparison of theory with experiment also facilitates the identification of relativistic effects in the experimental spectra. Ultimately, we hope that these critical tests will lead to an improved theoretical methodology that can be used to describe the nonseparable quantum mechanical behavior of complex many-body systems.

Publications

H. W. van der Hart and C. H. Greene, "Multichannel photoionization spectroscopy of Ar: Total cross section and threshold photoelectrons," Phys. Rev. A 58, 2097 (1998).