Electron-Nuclear Correlation in Laser-Driven Diatomic Molecules

The interaction of short intense laser pulses with atoms/molecules produces a multitude of highly nonlinear processes requiring a non-perturbative treatment. Detailed study of these highly nonlinear processes by numerically solving the time-dependent Schrodinger equation becomes a daunting task when the number of degrees of freedom is large. Also the coupling between the electronic and nuclear degrees of freedom further aggravates the computational problems. In the present work we show that the time-dependent Hartree (TDH) approximation, which neglects the correlation effects, gives unreliable description of the system dynamics both in the absence and presence of an external field. A theoretical framework is required that treats the electrons and nuclei on equal footing and fully quantum mechanically. To address this issue we discuss two approaches, namely the multicomponent density functional theory (MCDFT) and the multiconfiguration time-dependent Hartree (MCTDH) method, that go beyond the TDH approximation and describe the correlated electron-nuclear dynamics accurately. In the MCDFT framework, where the time-dependent electronic and nuclear densities are the basic variables, we discuss an algorithm to calculate the exact Kohn-Sham (KS) potentials for small model systems. By simulating the photodissociation process in a model hydrogen molecular ion, we show that the exact KS potentials contain all the many-body effects and give an insight into the system dynamics. In the MCTDH approach, the wave function is expanded as a sum of products of single-particle functions (SPFs). The MCTDH method is able to describe the electron-nuclear correlation effects as the SPFs and the expansion coefficients evolve in time and give an accurate description of the system dynamics. We show that the MCTDH method is suitable to study a variety of processes such as the fragmentation of molecules, high-order harmonic generation, the two-center interference effect, and the lochfrass effect. We discuss these phenomena in a model hydrogen molecular ion and a model hydrogen molecule. Inclusion of absorbing boundaries in the mean-field approximation and its consequences are discussed using the model hydrogen molecular ion. To this end, two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full many-particle Hamiltonian and (ii) an approach in the spirit of time-dependent density functional theory (TDDFT), including complex absorbing potentials in the single-particle equations. It is elucidated that for small grids the TDDFT approach is superior to the variational approach.

Tomographic imaging of molecular orbitals in length and velocity form

Recently Itatani et al. [Nature 432, 876 (2004)] introduced the new concept of molecular orbital tomography, where high harmonic generation (HHG) is used to image electronic wave functions. We describe an alternative reconstruction form, using momentum instead of dipole matrix elements for the electron recombination step in HHG. We show that using this velocity-form reconstruction, one obtains better results than using the original length-form reconstruction. We provide numerical evidence for our claim that one has to resort to extremely short pulses to perform the reconstruction for an orbital with arbitrary symmetry. The numerical evidence is based on the exact solution of the time-dependent Schrödinger equation for 2D model systems to simulate the experiment. Furthermore we show that in the case of cylindrically symmetric orbitals, such as the N2 orbital that was reconstructed in the original work, one can obtain the full 3D wave function and not only a 2D projection of it. Vor kurzem führten Itatani et al. [Nature 432, 876 (2004)] das Konzept der Molelkülorbital-Tomographie ein. Hierbei wird die Erzeugung hoher Harmonischer verwendet, um Bilder von elektronischen Wellenfunktionen zu gewinnen. Wir beschreiben eine alternative Form der Rekonstruktion, die auf Impuls- statt Dipol-Matrixelementen für den Rekombinationsschritt bei der Erzeugung der Harmonischen basiert. Wir zeigen, dass diese "Geschwindigkeitsform" der Rekonstruktion bessere Ergebnisse als die ursprüngliche "Längenform" liefert. Wir zeigen numerische Beweise für unsere Behauptung, dass man zu extrem kurzen Laserpulsen gehen muss, um Orbitale mit beliebiger Symmetrie zu rekonstruieren. Diese Ergebnisse basieren auf der exakten Lösung der zeitabhängigen Schrödingergleichung für 2D-Modellsysteme. Wir zeigen ferner, dass für zylindersymmetrische Orbitale wie das N2-Orbital, welches in der oben zitierten Arbeit rekonstruiert wurde, das volle 3D-Orbital rekonstruiert werden kann, nicht nur seine 2D-Projektion.

Molecular effects on the cross section for pair production and their importance in the evaluation of the total photonuclear cross section of {^16}O in the {\delta-resonance} region

The screening correction to the coherent pair-production cross section on the oxygen molecule has been calculated using self-consistent relativistic wave functions for the one-center and two-center Coulomb potentials. It is shown that the modification of the wave function due to molecular binding and the interference between contributions from the two atoms have both sizeable effects on the screening correction. The so-obtained coherent pair-production cross section which makes up the largest part of the total atomic cross section was used to evaluate the total nuclear absorption cross section from photon attenuation measurements on liquid oxygen. The result agrees with cross sections for other nuclei if A-scaling is assumed. The molecular effect on the pair cross section amounts to 15 % of the nuclear cross section in the {\delta-resonance} region.

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.

Femtosecond pump-probe study of the spreading and recurrence of a vibrational wave packet in Na_2

The motion of a vibrational wave packet in the bound A(^1 \summe^+_u) electronic state of the sodium dimer is detected in a femtosecond pump/probe molecular beam experiment. For short times harmonic motion is seen in the total ion yield of Na^+_2 as a function of delay time between the two laser pulses. The spreading of the wave packet results in the loss of the periodic variation of the ion signal. For longer delay times (47 ps) the wave packet regains its initial form which is reflected in the revival structure of the Na^+_2 signal. Time-dependent quantum calculations reproduce the measured effects.

Evaluation of water retention capacity and flood control function of the forest catchment

This research quantitatively evaluates the water retention capacity and flood control function of the forest catchments by using hydrological data of the large flood events which happened after the serious droughts. The objective sites are the Oodo Dam and the Sameura Dam catchments in Japan. The kinematic wave model, which considers saturated and unsaturated sub-surface soil zones, is used for the rainfall-runoff analysis. The result shows that possible storage volume of the Oodo Dam catchment is 162.26 MCM in 2005, while that of Samerua is 102.83 MCM in 2005 and 102.64 MCM in 2007. Flood control function of the Oodo Dam catchment is 173 mm in water depth in 2005, while the Sameura Dam catchment 114 mm in 2005 and 126 mm in 2007. This indicates that the Oodo Dam catchment has more than twice as big water capacity as its capacity (78.4 mm), while the Sameura Dam catchment has about one-fifth of the its storage capacity (693 mm).

The function of SIFamide, PDF, and further neuropeptides in the circadian system of Rhyparobia maderae

Der täglich Wechsel von Hell- und Dunkelphasen führte während der Evolution zur Entwicklung innerer Uhren in nahezu allen Organismen. In der Schabe Rhyparobia maderae lokalisierten Läsions- und Transplantationsexperimente die innere Uhr in der akzessorischen Medulla (AME). Dieses kleine birnenförmige Neuropil am ventromedianen Rand der Medulla ist mit etwa 240 Neuronen assoziiert, die eine hohe Anzahl an zum Teil kolokalisierten Neuropeptiden und Neurotransmittern exprimieren. Diese Signalstoffe scheinen essentiell zu sein für die Synchronisation der inneren Uhr mit der Umwelt, der Kopplung der beiden bilateralen AME, der Aufrechterhaltung des circadianen Rhythmus sowie der zeitlichen Steuerung bestimmter Verhaltensweisen. Während die Funktion einiger dieser neuronalen Botenstoffe bereits gut untersucht ist, fehlt sie für andere. Zudem ist noch ungeklärt, wann einzelne Botenstoffe im circadianen Netzwerk agieren. Im Fokus dieser Studie lag daher die Erforschung der Funktion von SIFamide und Corazonin im circadianen Netzwerk sowie die weitere Untersuchung der Funktionen der Neuropeptide MIP und PDF. Es konnte gezeigt werden, dass SIFamide auch in R. maderae in vier großen neurosekretorischen Zellen in der pars intercerebralis exprimiert wird. Varikosenreiche SIFamide-immureaktive (-ir) Fasern innervieren eine Vielzahl an Neuropilen und finden sich auch in der Hüllregion der AME. Injektionsexperimente resultierten in einer monophasischen Phasen-Antwort-Kurve (PRC) mit einer Verzögerung zur frühen subjektiven Nacht. SIFamide ist also ein Eingangssignal für das circadiane Netzwerk und könnte in der Kontrolle der Schalf/Wach-Homöostase involviert sein. Auch Corazonin fungiert als Eingangssignal. Da die Injektionsexperimente in einer monophasischen PRC mit einem Phasenvorschub zur späten subjektiven Nacht resultierten, ist davon auszugehen, dass die Corazonin-ir AME-Zelle Bestandteil des Morning-Oszillator-Netzwerkes in R. maderae ist. Darüber hinaus zeigten Backfill-Experimente, dass MIP an der Kopplung beider AMAE beteiligt ist. ELISA-Quantifizierungen der PDF-Level im Tagesverlauf ergaben Schwankungen in der Konzentration, die auf eine Ausschüttung des Peptids während des Tages hindeuten – ähnlich wie es in Drosophila melanogaster der Fall ist. Dies spiegelt sich in der vervollständigten bimodalen PDF-PRC wieder. Hier führen Injektionen zu einem Phasenvorschub, bevor maximale Peptidlevel erreicht werden, sowie zu einer Phasenverzögerung, sobald die Peptidlevel wieder zu sinken beginnen. Die PRCs erlauben somit Rückschlüsse auf den Zeitpunkt der maximalen Peptidfreisetzung. PDF-ir Neuriten findet sich zudem in sämtlichen Ganglien des ventralen Strickleiternervensystems, was eine Funktion in der Kontrolle der Prozesse impliziert, die durch die Mustergeneratoren in Thorakal- und Abdominalganglien gesteuert werden.