| 11. |
- Froese Fischer, Charlotte, et al.
(författare)
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Configuration interaction with separately optimized pair correlation functions
- 2010
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Variational methods produce one-electron radial functions that minimize the total energy of the system. Independent pair correlation functions (PCFs) designed to represent a specific correlation effect – valence, core-valence, or core-core – can be obtained from multiconfiguration Hartree-Fock (MCHF) or Dirac-Hartree-Fock (MCDHF) calculations [1,2]. These separately optimized and nonorthogonal PCFs may then be coupled by solving the associated generalized eigenproblem. In the present study, the Hamiltonian and overlap matrix elements are evaluated through biorthonormal orbital transformations and efficient counter-transformation of the configuration interaction eigenvectors [3]. The ground state of Be atom has been thoroughly tested by this method for various computational strategies and correlation models. It has been shown that the energy convergence is faster than with the usual SD-MCHF method of optimizing a single, orthonormal, one-electron orbital basis spanning the complete configuration space. Beryllium is a small system for which basis saturation can be achieved through complete active space MCHF expansions. But for larger systems describing electron correlation in all space by optimizing a common orthonormal set becomes hopeless whereas the calculation of additional PCFs is straight forward. Our independent optimization scheme, raises many questions related in the choice of the zero-order model to be used when building the interaction matrix. The present study is the first step in the current development of the extension of the atsp2K and grasp2K packages [1,2] that will adopt the biorthonormal treatment for energies, isotope shifts, hyperfine structures and transition probabilities.
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| 12. |
- Froese Fischer, Charlotte, et al.
(författare)
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Doublet-quartet energy separation in boron : a partitioned-correlationfunction- interaction method
- 2013
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 88:6
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Tidskriftsartikel (refereegranskat)abstract
- No lines have been observed for transitions between the doublet and quartet levels of B I. Consequently, energy levels based on observation for the latter are obtained through extrapolation of wavelengths along the isoelectronic sequence for the 2s22p 2Po 3/2 – 2s2p2 4P5/2 transition. In this paper, accurate theoretical excitation energies from a partitioned-correlation-function-interaction (PCFI) method are reported for B I that include both relativistic effects in the Breit-Pauli approximation and a finite mass correction. Results are compared with extrapolated values from observed data. For B I our estimate of the excitation energy 28 959 ± 5 cm−1 is in better agreement with the values obtained by Edl´en et al. (1969) than those reported by Kramida and Ryabtsev (2007). Our method is validated by applying the same procedure to the separation of these levels in C II.
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| 13. |
- Gaidamauskas, Erikas, et al.
(författare)
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Tensorial form and matrix elements of the relativistic nuclear recoil operator
- 2011
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Ingår i: Journal of Physics B. - : IOP Publishing Ltd. - 0953-4075 .- 1361-6455. ; 44:17
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Tidskriftsartikel (refereegranskat)abstract
- Within the lowest-order relativistic approximation (∼v2/c2) and to first order in me/M, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for calculating isotope shifts in the multiconfiguration Dirac–Hartree–Fock framework. Their calculation is illustrated for selected Li-, B- and C-like ions. This work underlines the fact that the relativistic corrections to the nuclear recoil are definitively necessary for obtaining reliable isotope shift values.
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| 14. |
- Gaigalas, Gediminas, et al.
(författare)
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Energies for States of the 2s22p5 and 2s2p6 in Fluorine-like Ions Between Si VI and W LXVI
- 2012
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Ingår i: Program and Abstracts. ; , s. 74-74
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The experimental energy levels and computed energies from the largest RCI calculations including QED corrections are displayed in Table 1. The computed energies agree very well with experimental values. Starting from Si VI the energy differences rapidly goes down to a few hundred cm−1 , which corresponds to an error of around 0.02 %. From Sr XXX to Sn XLII experimental energies are given with error bars between 1000 and 2000 cm−1 . The calculated values are within the stated experimental error bars except for Cd XL and Sn XLII. The reason for the difference in these two ions is not known. Experimental data for ions from Sb XLIII to Ta LXV are not available. For the W LXVI ion, the differences between theoretical and experimental transition energies are a few thousand cm−1 . As discussed by Kramida [1] the total uncertainties of the measured energies in W LXVI were dominated by the calibration uncertainties and varied in the range 1.0 - 2.3 eV, which translates to 8000 - 20000 cm−1 . Based on the comparison between theory and experiment for the lighter ions as well as for W LXVI we estimate that the errors in the calculated transition energies for ions in the range Sb XLIII - Ta LXV, for which no experimental data are available, are less than 0.08 %.
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| 15. |
- Gaigalas, Gediminas, et al.
(författare)
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Energy Level Structure and Transition Data of Er2
- 2020
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Ingår i: Astrophysical Journal Supplement Series. - : Institute of Physics Publishing (IOPP). - 0067-0049 .- 1538-4365. ; 248:1
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Tidskriftsartikel (refereegranskat)abstract
- A majority of Er in the universe is synthesized by the r-process, which can occur in the mergers of neutron stars (NSs). The contribution of this element to the opacity of NS ejecta should be tested, but even the energy levels of first excited configuration have not been fully presented. The main aim of this paper is to present accurate energy levels of the ground [Xe]4f(12) and first excited [Xe]4f(11)5d configurations of Er2+. The energy level structure of the Er2+ ion was computed using the multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction (RCI) methods, as implemented in the GRASP2018 program package. The Breit interaction, self-energy, and vacuum polarization corrections were included in the RCI computations. The zero-first-order approach was used in the computations. Energy levels with the identification in LS coupling for all (399) states belonging to the [Xe]4f(12) and [Xe]4f(11)5d configurations are presented. Electric dipole (E1) transition data between the levels of these two configurations are computed. The accuracy of these data is evaluated by studying the behavior of the transition rates as functions of the gauge parameter, as well as by evaluating the cancellation factors. The core electron correlations were studied using different strategies. The rms deviations obtained in this study for states of the ground and excited configurations from the available experimental data are 649 and 754 cm(-1), respectively.
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| 16. |
- Gaigalas, Gediminas, et al.
(författare)
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Energy level structure of Er3+ free ion and Er3+ ion in Er2O3 crystal
- 2014
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Ingår i: National Institute for Fusion Science, Research Report NIFS-DATA. - : National Institute for Fusion Science. - 0915-6364. ; :115, s. 1-25
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The latest version of the GRASP2K atomic structure package [P. J¨onsson, G. Gaigalas, J. Biero´n, C. Froese Fischer, I.P. Grant, Comput. Phys. Commun. 184 (2013) 2197], based on the multiconfigurational Dirac-Hartree-Fock method, is extended to account for effects of crystal fields in complex systems. Energies from relativistic configuration interaction calculations are reported for the Er3+ free ion. E2 and M1 line strengths, weighted oscillator strengths, and rates are presented for transitions between states of the [Xe]4f11 configuration. Also Stark levels of the Er3+ 4Io 15/2 state in Er2O3 are calculated in the ab initio point charge crystal field approximation. In all calculations the Breit interaction and leading QED effects are included as perturbations. Different strategies for describing electron correlation effects are tested and evaluated. The final results are compared with experiment and other methods.
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| 17. |
- Gaigalas, Gediminas, et al.
(författare)
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JJ2LSJ Transformation and Unique Labeling for Energy Levels
- 2017
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 5:1
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Tidskriftsartikel (refereegranskat)abstract
- The JJ2LSJ program, which is important not only for the GRASP2K package but for the atom theory in general, is presented. The program performs the transformation of atomic state functions (ASFs) from coupled CSF basis. In addition, the program implements a procedure that assigns a unique label to all energy levels. Examples of how to use the JJ2LSJ program are given. Several cases are presented where there is a unique labeling problem.
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| 18. |
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| 19. |
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| 20. |
- Jönsson, Per, et al.
(författare)
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Accurate Transition Probabilities from Large-scale Multiconfiguration Calculations
- 2012
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Ingår i: Program and Abstracts. ; , s. 40-40
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The quality and resolution of solar, stellar, and other types of plasma observations, has so improved that the accuracy of atomic data is frequently a limiting factor in the interpretation of these new observations. An obvious need is for accurate transition probabilities. Laboratory measurements, e.g. using ion/traps, beam-foil or laser techniques, have been performed for isolated transitions and atoms, but no systematic laboratory study exists or is in progress. Instead the bulk of these atomic data must be calculated. Multiconfiguration methods, either non-relativistic with Breit-Pauli corrections (MCHF+BP) or fully relativistic (MCDHF), are useful to this end. The main advantage of multiconfiguration methods is that they are readily applicable to excited and openshell systems, including open f-shells, across the whole periodic table, thus allowing for mass production of atomic data. The accuracy of these calculations depends on the complexity of the shell structure and on the underlying model for describing electron correlation. By systematically increasing the number of basis functions in large-scale calculations, as well as exploring different models for electron correlation, it is often possible to provide both transition energies and transition probabilities with some error estimate. The success of the calculations also depends on available computer software. In this talk we will describe a collaborative effort to continue the important and acclaimed work of Prof. Charlotte Froese Fischer and to develop state-of-the-art multiconfiguration codes. In the latest versions of the non-relativistic (ATSP2K) and relativistic (GRASP2K) multiconfiguration codes angular integration is performed using second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique that allows open f-shells. In addition it is possible to transform results given in the relativistic j j-coupling to the more useful LSJ-coupling. Biorthogonal transformation techniques are implemented and initial and final states in a transition can be separately optimized. The main parts of the codes are also adapted for parallel execution using MPI. Results from recent large-scale calculations using these codes will be presented for systems of different complexity. Of special interest are spectrum calculations, where all states up to a certain level are computed at the same time. Finally, we look at new computational developments that allow basis functions in multiconfiguration methods to be built on several independent and non-orthogonal sets of one-electron orbitals. Initial calculations indicate that the increased flexibility of the orbital sets allows transition energies, as well as other atomic properties, to be predicted to a much higher accuracy than before.
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