Theoretical Studies of Atomic Transitions
C. Froese Fischer, Vanderbilt University
Research Objectives
Accurate computational procedures are being developed for atomic structure calculations that can predict properties such as energy levels, binding energies, transition probabilities, lifetimes, hyperfine structure, isotope shifts, and photoionization cross sections.
Computational Approach
Our approach is a variational one, starting either from nonrelativistic theory and adding the low-order relativistic corrections, or from a fully relativistic Dirac-Fock theory including Breit and quantum electrodynamics corrections. These are referred to as MCHF (multiconfiguration Hartree-Fock) and MCDF (multiconfiguration Dirac-Fock) methods, respectively. Rule-based schemes are being devised for expanding the wavefunction, describing the electronic charge distribution in terms of a basis of configuration states, a basis which is then optimized.
An important part of the calculation is the matrix eigenvalue problem for which we use the Davidson algorithm for finding a few selected eigenvalues of the sparse symmetric interaction matrix. Since this algorithm relies primarily on matrix-vector multiplication, a parallel version on the T3E could readily be implemented, and cases as large as 100,000 x 100,000 have been considered.
Accomplishments
The MCHF codes had been parallelized previously using MPI. This year the MCDF matrix eigenvalue problem was also converted. These codes were used on the T3E in two important applications:
1. Spectrum calculations for the lithium-like sequence for nuclear charges, Z=3-10, for decay from 2p, 3s, 3p, and 3d levels. This allows for the calculation of not only the individual transition rates, but also the lifetime of the excited levels, which often is the measured experimental quantity. Only in Li are experimental lifetimes available. Our computed results appear to be more accurate than experiment.
2. Forbidden E2 and M1 transitions in Fe+3 3d5. For the former, the MCHF method was most efficient, but for the latter, where there are many closely spaced levels, both methodologies were tested. Currently, the MCHF calculations are better able to account for many-body effects, though MCDF provides a better description of relativistic effects.
The accuracy that can be achieved by MCDF studies for both light and heavy elements of the Be-like sequence was investigated without the use of the T3E, but comparison with experiment provides a benchmark study of the reliability of our methods. The figure shows that for some four-electron systems, atomic properties can be computed to experimental accuracy.
A comparison of computationally predicted atomic transition data with experiment for four electron ions of nuclear charge Z, plotted against 1/Z. For the top graph, relativistic effects are small for Z < 20, but they are crucial for all Z in the bottom graph.
Significance
Atomic data are needed in many scientific endeavors, for example, in plasma diagnostics and astrophysical applications. Of particular interest has been the prediction of lifetimes of excited states that decay through the emission of a photon. Such data for the rare earths are currently of interest in the lighting industry. Iron is produced predominantly in supernovae, with measurements of the Fe abundance providing fundamental information on nucleosynthesis and galactic chemical evolution. Data for Fe at several stages of ionization are needed in modeling studies.
Publications
C. Froese Fischer and R. H. Rubin, "Transition rates for some forbidden lines in Fe~IV," J. Phys. B 31, 1657 (1998).
C. Froese Fischer, M. Saparov, G. Gaigalas, and M. Godefroid, "Breit-Pauli energies, transition probabilities, and lifetimes for 2s,2p,3s,3p,3d,4s 2L levels of the lithium sequence, Z=3-8," Atomic Data and Nuclear Data Tables 70, 1 (1998).
P. Jonsson, C. Froese Fischer, and E. Trabert, "MCDF calculations of transition probabilities in the Be isoelectronic sequence," J. Phys. B 31, 3497 (1998).