Further investigations on doubly excited four-electron ions: beam-foil experiment and MCDF theory

In continuation of our previous work on the quintet transitions 1s2s2p^2 ^5 P-1s2s2p3d ^5 P^0, ^5 D^0, results on other n = 2 - n' = 3 quintet transitions for elements N, 0 and F are presented. Assignments have been established by comparison with Multi-Configuration Dirac-Fock calculations. High spectral resolution on beam-foil spectroscopy was essential for the identification of most of the lines. For some of the quintet lines decay curves were measured, and the lifetimes extracted were found to be in reasonable agreement with MCDF calculations.

Ground state correlation energy of the Be-sequence for Z = 4-20 in MCDF approximation

The ground state (J = 0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation for Z = 4-20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

QED and relativistic corrections in superheavy elements

In this paper we review the different relativistic and QED contributions to energies, ionic radii, transition probabilities and Landé g-factors in super-heavy elements, with the help of the MultiConfiguration Dirac-Fock method (MCDF). The effects of taking into account the Breit interaction to all orders by including it in the self-consistent field process are demonstrated. State of the art radiative corrections are included in the calculation and discussed. We also study the non-relativistic limit of MCDF calculation and find that the non-relativistic offset can be unexpectedly large.

Mode-Controlled Data-Flow Modeling of Real-Time Memory Controllers

Accepted in 13th IEEE Symposium on Embedded Systems for Real-Time Multimedia (ESTIMedia 2015), Amsterdam, Netherlands.

Systematic multi-configuration calculations on structures and properties of complex atoms

Die relativistische Multikonfigurations Dirac-Fock (MCDF) Methode ist gegenwärtig eines der am häufigsten benutzten Verfahren zur Berechnung der elektronischen Struktur und der Eigenschaften freier Atome. In diesem Verfahren werden die Wellenfunktionen ausgewählter atomarer Zustände als eine Linearkombination von sogenannten Konfigurationszuständen (CSF - Configuration State Functions) konstruiert, die in einem Teilraum des N-Elektronen Hilbert-Raumes eine (Vielteilchen-)Basis aufspannen. Die konkrete Konstruktion dieser Basis entscheidet letzlich über die Güte der Wellenfunktionen, die üblicherweise mit Hilfe einer Variation des Erwartungswertes zum no-pair Dirac-Coulomb Hamiltonoperators gewonnen werden. Mit Hilfe von MCDF Wellenfunktionen können die dominanten relativistischen und Korrelationseffekte in freien Atomen allgemein recht gut erfaßt und verstanden werden. Außer der instantanen Coulombabstoßung zwischen allen Elektronenpaaren werden dabei auch die relativistischen Korrekturen zur Elektron-Elektron Wechselwirkung, d.h. die magnetischen und Retardierungsbeiträge in der Wechselwirkung der Elektronen untereinander, die Ankopplung der Elektronen an das Strahlungsfeld sowie der Einfluß eines ausgedehnten Kernmodells erfaßt. Im Vergleich mit früheren MCDF Rechnungen werden in den in dieser Arbeit diskutierten Fallstudien Wellenfunktionsentwicklungen verwendet, die um 1-2 Größenordnungen aufwendiger sind und daher systematische Untersuchungen inzwischen auch an Atomen mit offenen d- und f-Schalen erlauben. Eine spontane Emission oder Absorption von Photonen kann bei freien Atomen theoretisch am einfachsten mit Hilfe von Übergangswahrscheinlichkeiten erfaßt werden. Solche Daten werden heute in vielen Forschungsbereichen benötigt, wobei neben den traditionellen Gebieten der Fusionsforschung und Astrophysik zunehmend auch neue Forschungsrichtungen (z.B. Nanostrukturforschung und Röntgenlithographie) zunehmend ins Blickfeld rücken. Um die Zuverlässigkeit unserer theoretischen Vorhersagen zu erhöhen, wurde in dieser Arbeit insbesondere die Relaxation der gebundenen Elektronendichte, die rechentechnisch einen deutlich größeren Aufwand erfordert, detailliert untersucht. Eine Berücksichtigung dieser Relaxationseffekte führt oftmals auch zu einer deutlich besseren Übereinstimmung mit experimentellen Werten, insbesondere für dn=1 Übergänge sowie für schwache und Interkombinationslinien, die innerhalb einer Hauptschale (dn=0) vorkommen. Unsere in den vergangenen Jahren verbesserten Rechnungen zu den Wellenfunktionen und Übergangswahrscheinlichkeiten zeigen deutlich den Fortschritt bei der Behandlung komplexer Atome. Gleichzeitig kann dieses neue Herangehen künftig aber auch auf (i) kompliziertere Schalensstrukturen, (ii) die Untersuchung von Zwei-Elektronen-ein-Photon (TEOP) Übergängen sowie (iii) auf eine Reihe weiterer atomarer Eigenschaften übertragen werden, die bekanntermaßen empflindlich von der Relaxation der Elektronendichte abhängen. Dies sind bspw. Augerzerfälle, die atomare Photoionisation oder auch strahlende und dielektronische Rekombinationsprozesse, die theoretisch bisher nur selten überhaupt in der Dirac-Fock Näherung betrachtet wurden.

Study of 3d - 4f and 3d - 5f quartet and doublet transitions of doubly excited three-electron ions

We present the first observation of optical transitions between doubly excited doublet states in the term systems N V, 0 VI and F VII. The spectra were produced by foil excitation of fast ion beams. The assignment of the spectral lines was made by comparison with the results of MCDP calculations along the isoelectronic sequence. The same method also led to the identification of two 3d - 4f quartet transitions in Mg X.

Analysis of the electronic structure, hyperfine structure, and volume isotope shifts in the low lying states of BA I and BA II

Relativistic multi-configuration Dirac Fock (MCDF) wavefunctions coupled to good angular momentum J have been calculated for low lying states of Ba I and Ba II. These wavefunctions are compared with semiempirical ones derived from experimental atomic energy levels. It is found that significantly better agreement is obtained when close configurations are included in the MCDF wavefunctions. Calculations of the electronic part of the field isotope shift lead to very good agreement with electronic factors derived from experimental data. Furthermore, the slopes of the lines in a King plot analysis of many of the optical lines are predicted accurately by these calculations. However, the MCDF wavefunctions seem not to be of sufficient accuracy to give agreement with the experimental magnetic dipole and electric quadrupole hyperfine structure constants.

On the total energy of two-electron atoms

Using the Multi-Configuration Dirac-Fock (MCDF) method we calculate with 9 configuration state functions the correlation energy as well as the total energy of the lowest J = 0 ground state of all two-electron systems from H- to Thorium (Z = 90). A comparison with experimental data, which are available only in the low Z region, shows a very good agreement.

Ionization potentials and radii of atoms and ions of element 104 (unnilquadium) and of hafnium (2+) derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values have been computed for the first four ionization potentials (IPs) of element 104 (unnilquadium) and of the other group 4 elements (Ti, Zr, and Hf). Factors were calculated that allowed correction of the systematic errors between the MCDF IPs and the experimental IPs. Single "experimental" IPs evaluated in eV (to ± 0.1 eV) for element 104 are: [104(0),6.5]; [104( 1 + ),14.8]; [104(2 + ),23.8]; [104(3 + ),31.9]. Multiple experimental IPs evaluated in eV for element 104 are: [(0-2+ ),21.2±0.2]; [(0-3+ ),45.1 ±0.2]; [(0-4+ ),76.8±0.3].Our MCDF results track 11 of the 12 experimental single IPs studied for group 4 atoms and ions. The exception is Hf( 2 + ). We submit our calculated IP of 22.4 ± 0.2 eV as much more accurate than the value of 23.3 eV derived from experiment.

Transitions between quintet states of doubly excited four-electron ions

Following an earlier observation in F VI we identified the line pair 1s2s2p^2 {^5P}-1s2s2p3d {^5P^0} , {^5D^0} for the elements N, O, Mg, and tentatively for A1 and Si in beam-foil spectra. Assignment was established by comparison with Multi-Configuration Dirac-Fock calculations along the isoelectronic sequence. Using this method we also identified some quartet lines of lithium-like ions with Z > 10.

Ionization potentials and radii of atoms and ions of element 105 (unnilpentium) and ions of tantalum derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values were calculated for the first five ionization potentials of element 105 (unnilpentium) and of the other group 5b elements (V, Nb, and Ta). Some of these ionization potentials in electron volts (eV) with uncertainties are: 105(0), 7.4±0.4; 105(1 +), 16.3 ±0.2; 105(2 +), 24.3 ± 0.2; 105(3 + ), 34.9 ± 0.5; and 105(4 + ), 44.9 ± 0.1. Ionization potentials for Ta(1+), Ta(2 +), and Ta(3 + ) were also calculated. Accurate experimental values for these ionization potentials are not available. Ionic radii are presented for the 2+, 3+, 4 +, and 5+ ions of element 105 and for the + 2 ions of vanadium and niobium. These radii for vanadium and niobium are not available elsewhere. The ionization potentials and ionic radii obtained are used to determine some standard electrode potentials for element 105. Born-Haber cycles and a form of the Born equation for the Gibbs free energy of hydration of ions were used to calculate the standard electrode potentials.