Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized. Hg_n clusters, we determine the size dependence of the bond character and the ionization potential I_p(n). For neutral Hg_n clusters we obtain a transition from van del Waals to covalent behaviour at the critical size n_c ~ 10-20 atoms. Results for I_p(Hg_n) with n \le 20 are in good agreement with experiments, and suggest that small Hg_n^+ clusters can be viewed as consisting of a positive trimer core Hg_3^+ surrounded by n - 3 polarized neutral atoms.

On the correlation between electric polarizabilities and the ionization potential of atoms

It is found that the electric dipole polarizabilities of neutral atoms correlate very strongly with their first ionization potential within the groups of elements with the same angular momenta of the outermost electrons. As the latter values are known very accurately, this allows a very good (<30%) prediction of various atomic polarizabilities.

Delocalization of a hole in van der Waals clusters: Ionization potential of rare-gas and small Hg_n clusters

The size dependence of the ionization potential I_p(n) of van der Waals (vdW) bound clusters has been calculated by using a model Hamiltonian, which includes electron hopping, vdW interactions, and charge-dipole interactions. The charge-density and dipole-density distributions for both neutral and ionized n-atom clusters are determined self-consistently. The competition between the polarization energy of the neutral atoms surrounding a partially localized hole and the tendency toward hole delocalization in the ionized clusters is found to dominate the size dependence of I_p(n). To test our theory, we culculate I_p(Xe_n) and I_p(Kr_n) for n \le 300. Good quantitative agreement with experiment is obtained. The theory is also applied to calculate I_p(Hg_n). Comparison with experiments suggests that in Hg_n^+ clusters with n \le 20 the positive charge is mainly distributed within a trimer which is situated at the center of the cluster and which polarizes the n - 3 surrounding neutral atoms.

Time-resolved studies of neutral and ionized Na_n clusters with femtosecond light pulses

The real-time dynamics of Na_n (n=3-21) cluster multiphoton ionization and fragmentation has been studied in beam experiments applying femtosecond pump-probe techniques in combination with ion and electron spectroscopy. Three dimensional wave packet motions in the trimer Na_3 ground state X and excited state B have been observed. We report the first study of cluster properties (energy, bandwidth and lifetime of intermediate resonances Na_n^*) with femtosecond laser pulses. The observation of four absorption resonances for the cluster Na_8 with different energy widths and different decay patterns is more difficult to interpret by surface plasmon like resonances than by molecular structure and dynamics. Timeresolved fragmentation of cluster ions Na_n^+ indicates that direct photo-induced fragmentation processes are more important at short times than the statistical unimolecular decay.

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.

Two-muonic atoms

X-ray transition energies for two-muonic atoms are calculated. The basis are relativistic self-consistent-field calculations including the corrections normally known in muonic atoms plus the vacuum polarization, magnetic interaction and retardation in the \mu-\mu-interaction, the specific mass correction and the configuration interaction.

Contribution of the exact Breit operator plus the electron state-dependent screening to the multiplet and fine structure of muon-electron atoms

We investigate for very general cases the multiplet and fine structure splitting of muonelectron atoms arising from the coupling of the electron and muon angular momenta, including the effect of the Breit operator plus the electron state-dependent screening. Although many conditions have to be fulfilled simultaneously to observe these effeets, it should be possible to measure them in the 6h- 5g muonic transition in the Sn region.

Shifts of electronic KX-rays in muonic atoms

Energies of electronic K X-rays in muonic atoms were calculated for muons in various outer orbitals and for different numbers of electrons. Energy shifts were obtained with respect to characteristic X-rays belonging to nuclear charge (Z - 1) and their possible observation is discussed. The shifts in muonic Sn as an example amount to 19, 37, and 59 eV for the muon in 5g, 6h, and 7i states respectively. However, shifts due to the number of electrons present and the electron vacancy distribution in the L-shell are significantly larger. Accurate measurements of the K X-ray energies would therefore enable us to learn more about the electronic structure during the muonic cascade.

Electronic structure calculations of small AI_n (n = 2 - 8) clusters

The electronic states of small AI_n (n = 2 - 8) clusters have been calculated with a relativistic ab-initio MOLCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photoelectron spectra.

Self-energy corrections in heavy muonic atoms

Self-energy corrections for ls_1/2 levels of heavy muonic atoms are calculated to all orders in the external field using numerical techniques to evaluate the bound-muon propagator. The resulting values of the selfenergy are about 10% larger than previous estimates.

Nuclear charge radii from X-ray transitions in muonic atoms of carbon, nitrogen and oxygen

Energies of muonic X-rays of the K-series of carbon, nitrogen and oxygen have been measured with an accuracy of about 15 eV. Root mean square radii of the nuclear charge distributions were deduced. The results 2.49±0.05 fm for carbon, 2.55 ±0.03 fm for nitrogen and 2.71 ±0.02 fm for oxygen are in good agreement at comparable accuracy with recent electron scattering data.

Values for the electron screening in muonic atoms for all Z

The electron screening correction in the X-ray transitions in muonic atoms is calculated within a relativistic SCF Hartree-Fock procedure for many transitions and all Z.

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Spin-polarized Hartree-Fock-Slater calculations in atoms and diatomic molecules with the finite element method

We present spin-polarized Hartree-Fock-Slater calculations performed with the highly accurate numerical finite element method for the atoms N and 0 and the diatomic radical OH as examples.