Relativistic wave and Green's functions for hydrogen--like ions

The \textsc{Greens} library is presented which provides a set of C++ procedures for the computation of the (radial) Coulomb wave and Green's functions. Both, the nonrelativistic as well as relativistic representations of these functions are supported by the library. However, while the wave functions are implemented for all, the bound and free--electron states, the Green's functions are provided only for bound--state energies $(E < 0$). Apart from the Coulomb functions, moreover, the implementation of several special functions, such as the Kummer and Whittaker functions of the first and second kind, as well as a few utility procedures may help the user with the set--up and evaluation of matrix elements.Comment: 21 page

Relativistic central--field Green's functions for the RATIP package

From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green's functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green's functions also for atoms and ions other than the hydrogen--like ions, here we provide an extension to the Ratip program which supports the computation of relativistic (one--electron) Green's functions in an -- arbitrarily given -- central--field potential \rV(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green's functions for all bound--state energies $E < 0$. In addition, care has been taken to provide a user--friendly component of the Ratip package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module--oriented design.Comment: 20 pages, 1 figur

Angular distribution studies on the two-photon ionization of hydrogen-like ions: Relativistic description

The angular distribution of the emitted electrons, following the two-photon ionization of the hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium- and high-Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with the electric-dipole approximation. This includes a strong forward emission while, in dipole approxmation, the electron emission always occurs symmetric with respect to the plane which is perpendicular to the photon beam. Detailed computations for the dependence of the photoelectron angular distributions on the polarization of the incident light are carried out for the ionization of H, Xe$^{53+}$, and U$^{91+}$ (hydrogen-like) ions.Comment: 16 pages, 4 figures, published in J Phys

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen--like ions

Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen--like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb--field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen--like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion--atom and ion--photon collisions.Comment: 23 pages, 1 figur

Kupfer als Pflanzenschutzmittel unter besonderer Berücksichtigung des Ökologischen Landbaus

In den vergangenen 15 bis 20 Jahren hat der Öko-Landbau erhebliche Anstrengungen sowohl bei der Suche nach Kupferalternativen im Pflanzenschutz als auch bei der Minimierung der eingesetzten Kupfermengen unternommen. Allerdings sind bislang und in naher Zukunft keine Präparate oder Verfahren in Sicht, die einen annährend gleichwertigen Ersatz für Kupfer darstellen könnten. Dabei ist darauf hinzuweisen, dass ein gleichwertiger Ersatz nicht durch einen einzelnen Wirkstoff zu schaffen ist, wenn nicht ausgeschlossen werden kann, dass die betreffenden Schaderreger innerhalb kurzer Zeit Resistenzen gegenüber einem solchen Wirkstoff bilden. Unbenommen von allen Schwierigkeiten muss aber die Erforschung von Kupferersatzstoffen und -verfahren forciert werden. In der Vergangenheit hat der Öko-Landbau gezeigt, dass neue Möglichkeiten zur Reduktion von Kupfer im Pflanzenschutz wie der Anbau pilzwiderstandsfähiger Sorten, der Einsatz von verbesserten Prognosemodellen, das Vorkeimen der Saatkartoffeln, die Sortenwahl, neue Applikationstechniken sowie der kombinierte Einsatz von Tonerdenpräparaten schnell und erfolgreich im Sinne einer Einsatzminimierung von der Öko-Praxis übernommen wurden. Die in den Untersuchungen und Modellen ermittelte akute und chronische Toxizität auf Bodenorganismen oder auf Vögel und Kleinsäuger deckt sich häufig nicht mit wissenschaftlichen Untersuchungen und Beobachtungen in der Praxis. Auch wird beispielsweise im Öko-Hopfenanbau, aber nicht nur dort, beobachtet, dass eine Anreicherung bei den im Öko-Anbau üblichen Kupferaufwandmengen und begleitenden Maßnahmen wie die Kompostierung und Verteilung von Hopfenhäcksel auf anderen Flächen sich häufig nicht zeigt. Daraus leiten sich Fragen ab, die es unbedingt wissenschaftlich zu untersuchen gilt. Bei einem Verzicht auf Kupfer als Pflanzenschutzmittel im Öko-Anbau beim derzeitigen Stand der Technik und des Wissens sowie unter den hiesigen klimatischen Bedingungen wären, abhängig von der Kultur, hohe Ertragsund Qualitätsausfälle bis hin zum Totalausfall unvermeidbar. Beispielsweise würden die nachgewiesenen Ausfälle im ökologischen Gemüse- und Zierpflanzenbau bei 10 bis 15 %, bei Öko-Kartoffeln im Schnitt bei etwa 15 bis 20 % und im ökologischen Hopfen-, Wein- und Obstbau bei ca. 50 bis 100 % liegen. Damit kommt der Möglichkeit, Kupfer als Pflanzenschutzmittel im Öko-Anbau einzusetzen, eine ernorm große wirtschaftliche Bedeutung zu. Aber auch im konventionellen Anbau, ist die Bedeutung von Kupfer als Mittel zur Resistenzvermeidung sehr hoch

KPNA2 protein expression in invasive breast carcinoma and matched peritumoral ductal carcinoma in situ

The aim of this study was to evaluate protein expression of Karyopherin alpha 2 (KPNA2) in invasive breast cancer and matched ductal carcinoma in situ (DCIS) and to correlate it with clinicopathological data, including patient survival. KPNA2 protein expression was assessed by immunohistochemistry in breast tissue samples, containing invasive carcinomas, DCIS, and adjacent histologically benign breast tissues. A polyclonal goat KPNA2 antibody was used for immunostaining of 83 clinicopathologically characterized cases. For statistical analysis, staining of at least 10% of nuclei was considered KPNA2 positive. Immunohistochemical detection of KPNA2 in invasive carcinoma showed a significant correlation with higher tumor stage, positive lymph node status, higher tumor grade, and negative ER status. Concordantly, KPNA2-positive tumors (31.3%) showed significantly shorter disease-free survival times (69months vs 118months; p = 0.007). KPNA2 protein expression was also detected in DCIS (21.3%) adjacent to invasive tumor and correlated with nuclear grade (p = 0.013). Expression of KPNA2 in invasive breast cancer correlates with conventional prognostic parameters and shorter disease-free survival. Additionally, KPNA2 is overexpressed in DCIS, particularly high grade lesions, which emphasizes its potential role in carcinogenesis of invasive breast carcinoma

Relativistic and retardation effects in the two--photon ionization of hydrogen--like ions

The non-resonant two-photon ionization of hydrogen-like ions is studied in second-order perturbation theory, based on the Dirac equation. To carry out the summation over the complete Coulomb spectrum, a Green function approach has been applied to the computation of the ionization cross sections. Exact second-order relativistic cross sections are compared with data as obtained from a relativistic long-wavelength approximation as well as from the scaling of non-relativistic results. For high-Z ions, the relativistic wavefunction contraction may lower the two-photon ionization cross sections by a factor of two or more, while retardation effects appear less pronounced but still give rise to non-negligible contributions.Comment: 6 pages, 2 figure

History as Trash: Reading Berlin 2000

The expectation that Berlin, at the cusp of the twenty-first century, should produce big-city novels that, like Döblin\u27s Berlin Alexanderplatz in its own time, would catch the encounters, juxtapositions, and historical layerings of the newly reunified capital is perhaps unfair, and certainly a high bar, but it reflects widespread interest in literary representations of this brazenly, even insolently transformed city..

What Do Human Rights Mean for Citizenship Education?

The article argues that citizenship education and human rights education can be understood as educational responses to specific social and political challenges in different national, regional and global contexts. It outlines four cases: (1) Nbsp; the early German response of civic education; (2) The late British response of citizenship education; (3) The response of EDC within the European framework of the Council of Europe; (4) The response of HRE within the global framework of the UN and the UNESCO. The main aim is to contribute to the necessary clarification of what is shared and what is different of EDC and HRE in this ongoing process of cooperation and integration between the two approaches in Europe