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A program for accurate solutions of two-electron atoms
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics, Condensed Matter Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics, Condensed Matter Theory.
2005 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 165, no 3, 260-270 p.Article in journal (Refereed) Published
Abstract [en]

We present a comprehensible computer program capable of treating non-relativistic ground and excited states for a two-electron atom having infinite nuclear mass. An iterative approach based on the implicitly restarted Arnoldi method (IRAM) is employed. The Hamiltonian matrix is never explicitly computed. Instead the action of the Hamiltonian operator on discrete pair functions is implemented. The finite difference method is applied and subsequent extrapolations gives the continuous grid result. The program is written in C and is highly optimized. All computations are made in double precision. Despite this relatively low degree of floating point precision (48 digits are not uncommon), the accuracy in the results can reach about 10 significant figures. Both serial and parallel versions are provided. The parallel program is particularly suitable for shared memory machines such as the Sun Starcat series. The serial version is simple to compile and should run on any platform.

Place, publisher, year, edition, pages
2005. Vol. 165, no 3, 260-270 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-91424DOI: 10.1016/j.cpc.2004.01.007OAI: oai:DiVA.org:uu-91424DiVA: diva2:164145
Available from: 2004-02-25 Created: 2004-02-25 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Transition Properties of f-electrons in Rare-earth Optical Materials
Open this publication in new window or tab >>Transition Properties of f-electrons in Rare-earth Optical Materials
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main purpose of this thesis is to theoretically study energy levels and intra-electronic transition intensities for various f-electron systems. The f-f electronic dipole transitions are parity-forbidden for a free ion but become non-zero when the ion is subject to a crystal-field. This is commonly described within the framework of Judd-Ofelt theory which accounts for the mixing of odd parity into the wave-functions.

Some refinements and quantitative studies have been made by applying many-body perturbation theory, or the perturbed functions approach, to obtain effective dipole operators due to correlation, spin-orbit and higher order crystal-field effects not included in Judd-Ofelt theory. A software for the computation of f-electron multiplets and Stark levels was implemented and published as well.

The single- and pair-functions used for the evaluation of intensity parameters were obtained by solving various inhomogeneous Schrödinger equations. The wave-functions and energies obtained by diagonalizing an effective Hamiltonian have been used together with the oscillator strength methods to simulate absorption spectrum. Consistent crystal-field parameters applied in some of the papers were obtained by fitting crystal polarizabilities to reflect the experimental Stark levels. The same crystal model was then used to generate odd crystal field parameters needed for the f-f transition intensities. The total effect of these refinements are spectral features that usually agree well with experimental findings. Some of these methods have also been applied and seen to be quite useful for the understanding of optical fiber amplifiers frequently used in today's optical networks.

Finally, a finite-difference approach was applied for the Helium iso-electronic sequence. The exact wave-function was expanded in a sum of partial waves, and accurate ground- and excited state energies were obtained by using the iterative Arnoldi approach.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2004. 50 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 944
Keyword
Physics, rare-earth ions, oscillator strengths, correlation, crystal field, f-electrons, Fysik
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-4014 (URN)91-554-5890-4 (ISBN)
Public defence
2004-03-19, Siegbahnsalen, Ångström laboratory, Lägerhyddsvägen 1, Polacksbacken, Uppsala, 14:00
Opponent
Supervisors
Available from: 2004-02-25 Created: 2004-02-25 Last updated: 2012-04-04Bibliographically approved

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