Double-autoionization decay of resonantly excited single-electron states

Perturbation theory in the lowest non-vanishing order in interelectron interaction has been applied to the theoretical investigation of double-ionization decays of resonantly excited single-electron states. The formulae for the transition probabilities were derived in the LS coupling scheme, and the orbital angular momentum and spin selection rules were obtained. In addition to the formulae, which are exact in this order, three approximate expressions, which correspond to illustrative model mechanisms of the transition, were derived as limiting cases of the exact ones. Numerical results were obtained for the decay of the resonantly excited Kr 1 3d^{-1}5p[^1P] state which demonstrated quite clearly the important role of the interelectron interaction in double-ionization processes. On the other hand, the results obtained show that low-energy electrons can appear in the photoelectron spectrum below the ionization threshold of the 3d shell. As a function of the photon frequency, the yield of these low-energy electrons is strongly amplified by the resonant transition of the 3d electron to 5p (or to other discrete levels), acting as an intermediate state, when the photon frequency approaches that of the transition.

Two-photon decay of the 1s2s ^1S_0 state in _36Kr^34+ produced by resonant transfer and excitation

The doubly excited 2s2p ^1P_1 level of Kr^{34+} populated via resonant transfer and excitation (RTE) feeds selectively the metastable ls2s ^1 S_0 state which can only decay via simultaneous emission of two photons to the ground state 1s^2 ^1 S_0. X-ray/X-ray coincidence measurements in heavy ionatom collisions enable the direct measurement of the spectral distribution of the two-photon decay in He-like ions. In addition, we observe strong photon cascades indueed by radiative electron capture.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Photoionization of Kr near the 4s threshold: IV. Photoionization through the autoionization of doubly-excited states

The photoionization cross sections for the production of the Kr II 4s state and Kr II satellite states were studied in the 4s ionization threshold region. The interference of direct photoionization and ionization through the autoionization decay of doubly-excited states was considered. In the calculations of doubly-excited state energies, performed by a configuration interaction technique, the 4p spin-orbit interaction and the (Kr II core)-(excited electron) Coulomb interaction were included. The theoretical cross sections are in many cases in good agreement with the measured values. Strong resonant features in the satellite spectra with threshold energies greater than 30 eV are predicted.

Femtosecond dynamics of molecules and clusters

The real-time dynamics of multiphoton ionization and fragmentation of molecules - Na_2 , Na_3 - and clusters - Na_n, Hg_n - has been studied in molecular beam experiments employing ion and electron spectroscopy together with femtosecond pump-probe techniques. Experiments with Na_2 and Na_3 reveal unexpected features of the dynamics of the absorption of several photons as seen in the one- and three dimensional vibrational wave packet motion in different potential surfaces and in high laser fields. Cluster size dependent studies of physical properties such as absorption resonances, lifetimes and decay channels have been performed using tunable femtosecond light pulses in resonance enhanced multiphoton ionization (REMPI) of the cluster size under investigation. This method failed in ns-laser experiments due to the ultrafast decay of the studied cluster. For Na_n, cluster we find that for cluster sizes n \le 21 molecular excitations and properties prevail over collective excitations of plasmon-like resonances. In the case of Hg_n cluster prompt formation of singly and doubly charged cluster are observed up to n \approx 60. The transient multiphoton ionization spectra show a 'short' time wave packet dynamics, which is identical for singly and doubly charged mercury clusters while the 'long' time fragmentation dynamics is different.

Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity

Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. The artificial boundary conditions involve the Steklov-Poincare operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R^{-N}), where N can be arbitrarily large.

Auger transitions in Li-like and Be-like ions

Measurements of the Auger decay of beam-foil excited Be II and Be I levels are reported along with a proposed assignment of the experimental spectra. The Li I, Be II and Be III (1s 2s^2) ^2 S \rightarrow (1s^2 2s)^2 S Auger transitions as presented in this letter represents the first observation of such states in positive ions with Z \le 5.

HelF und sein Interaktionspartner Xrn1: zwei Regulatoren der RNA-Interferenz in D. discoideum

Hauptziel dieser Arbeit ist die Identifizierung, Verifizierung und Charakterisierung von Interaktionspartnern von HelF, einem Negativregulator der RNA-Interferenz in Dictyostelium discoideum (Popova et al. 2006). Es ist gelungen, die Interaktion von HelF und der 5‘ 3‘ Exonuklease Xrn1 nachzu-weisen, aber alle anderen Versuchen, bisher unbekannte Protein-Interaktionspartner zu identifizieren, schlugen fehl. Xrn1 ist in den Organismen D. melanogaster (Orban und Izaurralde 2005), C. elegans (Newbury und Woollard 2004) und A. thaliana (Gazzani et al. 2004) bereits als Regulator der RNA-Interferenz bekannt. Mit Aufreinigungen nach der TAP-Methode und mit dem Nanotrap wurde ebenfalls versucht, RNA-Interaktionspartner von HelF zu identifizieren. Es konnten in einigen Aufreinigungen putative, für HelF spezifische RNAs identifiziert werden, doch entweder es handelte sich nachweislich nicht um RNA oder die Reproduktion der Daten schlug trotz mehrfacher Versuche fehl. Bezüglich der zellulären Lokalisation von HelF und Xrn1 konnte gezeigt werden, dass HelF zusätzlich zur bekannten Lokalisation in Foci im Nukleus (Popova et al. 2006) vermutlich auch im Cytoplasma und dort angeordnet in mehreren Granula zu finden ist. Xrn1 ist nahezu ausschließlich im Cytoplasma lokalisiert, wo es in mehreren Foci organisiert ist. Es wird vermutet, dass es sich bei diesen Foci um Processing-Bodies (P-Bodies) handelt und dass möglicherweise Xrn1 und HelF in eben diesen P-Bodies co-lokalisieren. In der Entwicklung vom Einzeller zum mehrzelligen Organismus zeigen die Xrn1KO- und die HelFKO-Mutante jeweils einen eindeutigen Phänotyp, der vom Wildtyp abweicht. Die Phänotypen der beiden Mutanten unterscheiden sich deutlich voneinander. Beim Mischen von HelF-Knockout-Zellen mit grün fluoreszierenden Wildtyp-Zellen zeigt sich, dass beide Stämme innerhalb des sich entwickelnden Organismus an definierten Stellen lokalisieren. Entgegen den Erwartungen befinden sich die Zellen der Mutante in den Stadien „Finger“ und „Slug“ nicht hauptsächlich im vorderen Teil des Organismus, sondern sind auch im hinteren Teil, der später die Sporenmasse bildet, vertreten. Dies lässt vermuten, dass HelF-Knockout-Mutanten in gleichem Maße wie Wildtypzellen als Sporen in die nächste Generation übergehen. Weitere Mix-Experimente, in denen HelFKO-Zellen und Xrn1KO-Zellen mit grün fluoreszierenden Wildtypzellen gemischt wurden, belegen eindeutig, dass beide Knockoutmutanten in Konkurrenz zum Wildtyp bei der Generierung von Sporen und somit beim Übergang in die nächste Generation benachteiligt sind. Dies steht im Gegensatz zu den Ergebnissen der vorher beschriebenen Mix-Experimente, in denen der Organismus als Ganzes betrachtet wurde. Weiterhin konnte herausgefunden werden, dass Xrn1 ebenso wie HelF (Popova et al. 2006) eine Rolle als Negativregulator in der RNA-Interferenz innehat. Fraglich ist aber, ob HelF wie bisher angenommen auch Einfluss auf den Weg der Generierung von miRNAs nimmt, da in HelFKO für keinen der beiden miRNA-Kandidaten eine Hoch- bzw. Runterregulierung der reifen miRNAs im Vergleich zum Wildtyp beobachtet werden kann. Im Xrn1KO hingegen ist die reife miRNA ddi-mir-1176 im Vergleich zum Wildtyp hochreguliert. In Bezug auf die Generierung von siRNAs konnte herausgefunden werden, dass Xrn1 und HelF im Fall der Generierung von Skipper siRNAs regulierend eingreifen, dass aber nicht alle siRNAs von der negativen Regulierung durch HelF und Xrn1betroffen sind, was am Beispiel der DIRS-1-siRNAs belegt werden kann. Das von B. Popova entwickelte Modell (Popova 2005) bezüglich der Rolle von HelF in der RNA-Interferenz wurde basierend auf den neu gewonnenen Daten weiterentwickelt und um Xrn1 ergänzt, um die Funktionen von HelF und Xrn1 als Antagonisten der RNA-Interferenz näher zu beleuchten. Literatur: Gazzani, S., T. Lawrenson, et al. (2004). "A link between mRNA turnover and RNA interference in Arabidopsis." Science 306(5698): 1046-8. Newbury, S. and A. Woollard (2004). "The 5'-3' exoribonuclease xrn-1 is essential for ventral epithelial enclosure during C. elegans embryogenesis." Rna 10(1): 59-65. Orban, T. I. and E. Izaurralde (2005). "Decay of mRNAs targeted by RISC requires XRN1, the Ski complex, and the exosome." Rna 11(4): 459-69. Popova, B. (2005). HelF, a suppressor of RNAi mediated gene silencing in Dictyostelium discoideum. Genetik. Kassel, Universität Kassel. PhD: 200. Popova, B., M. Kuhlmann, et al. (2006). "HelF, a putative RNA helicase acts as a nuclear suppressor of RNAi but not antisense mediated gene silencing." Nucleic Acids Res 34(3): 773-84.

Optical Antennas for Biosensing Applications

The aim of the thesis is to theoretically investigate optical/plasmonic antennas for biosensing applications. The full 3-D numerical electromagnetic simulations have been performed by using finite integration technique (FIT). The electromagnetic properties of surface plasmon polaritons (SPPs) and the localized surface plasmons (LSPs) based devices are studied for sensing purpose. The surface plasmon resonance (SPR) biosensors offer high refractive index sensitivity at a fixed wavelength but are not enough for the detection of low concentrations of molecules. It has been demonstrated that the sensitivity of SPR sensors can be increased by employing the transverse magneto-optic Kerr effect (TMOKE) in combination with SPPs. The sensor based on the phenomena of TMOKE and SPPs are known as magneto-optic SPR (MOSPR) sensors. The optimized MOSPR sensor is analyzed which provides 8 times higher sensitivity than the SPR sensor, which will be able to detect lower concentration of molecules. But, the range of the refractive index detection is limited, due to the rapid decay of the amplitude of the MOSPR-signal with the increase of the refractive indices. Whereas, LSPs based sensors can detect lower concentrations of molecules, but their sensitivity is small at a fixed wavelength. Therefore, another device configuration known as perfect plasmonic absorber (PPA) is investigated which is based on the phenomena of metal-insulator-metal (MIM) waveguide. The PPA consists of a periodic array of gold nanoparticles and a thick gold film separated by a dielectric spacer. The electromagnetic modes of the PPA system are analyzed for sensing purpose. The second order mode of the PPA at a fixed wavelength has been proposed for the first time for biosensing applications. The PPA based sensor combines the properties of the LSPR sensor and the SPR sensor, for example, it illustrates increment in sensitivity of the LSPR sensor comparable to the SPR and can detect lower concentration of molecules due to the presence of nanoparticles.

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL_3 über Funktionenkörpern

Harmonische Funktionen auf dem Bruhat-Tits-Gebäude der PGL(3) über Funktionenkörpern lassen sich als ein Analogon zu den auf der oberen Halbebene definierten klassischen Spitzenformen verstehen. An die Stelle des starken Abklingens der Spitzenformen tritt hier die Endlichkeit des Trägers modulo einer gewissen Untergruppe. Der erste Teil der vorliegenden Arbeit befaßt sich mit der Untersuchung und Charakterisierung dieses Trägers. Im weiteren Verlauf werden gewisse Konzepte der klassischen Theorie auf harmonische Funktionen übertragen. So wird gezeigt, daß diese sich ebenfalls als Fourierreihe darstellen lassen und es werden explizite Formeln für die Fourierkoeffizienten hergeleitet. Es stellt sich heraus, daß sich die Harmonizität in gewissen Relationen zwischen den Fourierkoeffizienten widerspiegelt und sich umgekehrt aus einem Satz passender Koeffizienten eine harmonische Funktion erzeugen läßt. Dies wird zur expliziten Konstruktion zweier quasi-harmonischer Funktionen genutzt, die ein Pendant zu klassischen Poincaré-Reihen darstellen. Abschließend werden Hecke-Operatoren definiert und Formeln für die Fourierkoeffizienten der Hecke-Transformierten einer harmonischen Funktion hergeleitet.