Multielectron corrections in molecular high-order harmonic generation for different formulations of the strong-field approximation

We make a detailed assessment of which form of the dipole operator to use in calculating high order harmonic generation within the framework of the strong field approximation, and look specifically at the role the form plays in the inclusion of multielectron effects perturbatively with regard to the contributions of the highest occupied molecular orbital. We focus on how these corrections affect the high-order harmonic spectra from aligned homonuclear and heteronuclear molecules, exemplified by $\mathrm{N}_2$ and CO, respectively, which are isoelectronic. We find that the velocity form incorrectly finds zero static dipole moment in heteronuclear molecules. In contrast, the length form of the dipole operator leads to the physically expected non-vanishing expectation value for the dipole operator in this case. Furthermore, the so called "overlap" integrals, in which the dipole matrix element is computed using wavefunctions at different centers in the molecule, are prominent in the first-order multielectron corrections for the velocity form, and should not be ignored. Finally, inclusion of the multielectron corrections has very little effect on the spectrum. This suggests that relaxation, excitation and the dynamic motion of the core are important in order to describe multielectron effects in molecular high-order high harmonic generation.Comment: Figures 2 and 4 have been simplified in order to fulfil the size requirements of arXiv; in the new version references have been adde

Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules

The relation between high-harmonic spectra and the geometry of the molecular orbitals in position and momentum space is investigated. In particular we choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such that the highest occupied molecular orbital of the former exhibit at least one nodal plane. The imprint of such planes is a strong suppression in the harmonic spectra, for particular alignment angles. We are able to identify two distinct types of nodal planes. If the nodal planes are determined by the atomic wavefunctions only, the angle for which the yield is suppressed will remain the same for both types of molecules. In contrast, if they are determined by the linear combination of atomic orbitals at different centers in the molecule, there will be a shift in the angle at which the suppression occurs for the heteronuclear molecules, with regard to their homonuclear counterpart. This shows that, in principle, molecular imaging, which uses the homonuclear molecule as a reference and enables one to observe the wavefunction distortions in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order to comply with the arXiv size requirement

Excitation, two-center interference and the orbital geometry in laser-induced nonsequential double ionization of diatomic molecules

We address the influence of the molecular orbital geometry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules for different molecular species, namely $\mathrm{N}_2$ and $\mathrm{Li}_2$. We focus on the recollision excitation with subsequent tunneling ionization (RESI) mechanism, in which the first electron, upon return, promotes the second electron to an excited state, from where it subsequently tunnels. We show that the electron-momentum distributions exhibit interference maxima and minima due to the electron emission at spatially separated centers. We provide generalized analytical expressions for such maxima or minima, which take into account $s$ $p$ mixing and the orbital geometry. The patterns caused by the two-center interference are sharpest for vanishing alignment angle and get washed out as this parameter increases. Apart from that, there exist features due to the geometry of the lowest occupied molecular orbital (LUMO), which may be observed for a wide range of alignment angles. Such features manifest themselves as the suppression of probability density in specific momentum regions due to the shape of the LUMO wavefunction, or as an overall decrease in the RESI yield due to the presence of nodal planes.Comment: 11 pages revtex, 2 figure

Reading strategies and learning outcomes

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The project was concerned with action research aimed at improving the range and effectiveness of reading-to-learn. Students (Advanced Level and Undergraduates) report reading-to-learn problems but they are only vaguely aware of the cognitive organisation (intuitive tactics and strategy) which underlies and structures their reading behaviour. The research emphasis was therefore primarily learner oriented. 2. This approach clarified such issues as: (i) Learner interpretation of instructional directives to learn for specific tasks. (ii) Learner methods of translating the task definition into an operational plan for reading. (iii) The systematic relationship between the tactics and strategies of reading (the time-structure of reading behaviour), and the variety of reading outcomes, within sentence, paragraph and chapter sized texts. (iv) Training procedures (incorporating feedback of performance) by which a student can explore now tactics of reading-for-learning. 3. This approach has required the development of three now techniques: a) A method for recording reading behaviour. b) A method by which the ‘structure of a text’ can be systematically described. c) A system of training procedures for encouraging students to develop more effective methods of reading-for-learning. 4. The empirical data showed that there were two related aspects in developing more effective reading-for-learning; the first was to develop a clearer definition of instructional directives and the second was the ability to translate these into effective operational plans. As a result of individual differences in cognitive structure and skill, students differ in their operational task definition in relation to specific learning outcomes. The plans of a 'beginner' or an 'expert' may bring about the same outcome but they differ considerably. Students also differ in their training needs within a training procedure for reading-to-learn effectively. This emphasises the need to level a hierarchically organised learner-controlled programme of self-diagnosis and training. 5. The theoretical outcome of the research was a tentative model of the student learning by reading. This model is based on the concept of a dynamic interaction between the learner's cognitive structure and skill, the learner's task definition and how this becomes operational, and the syntactic and semantic structure of the text. The model can be considered as a hierarchically organised multi-level description of the reading process. The reading strategy formed of the tactics and the learning outcome, represent the observables of this interaction. The model was influenced by the theories of J. Bruner, G. Miller, N. Chomsky and R. Gagné. 6. The research was directed towards the identification of strategies and outcomes of reading-to-learn, with the double aim of investigating these areas and training students to increase their skill; both these aims were in line with endeavours to increase self-organisation and individual autonomy in learning. 7. Whilst the goals of the research were largely achieved, the results have illuminated a number of practical and theoretical issues that need further investigation.Social Science Research Counci

Auf dem Weg zur digitalen Stadt – Aufbau der digitalen Planungsinfrastruktur Hamburg

In dem „Zentralen Planungsinformationssystem Hamburg“ (PLIS-HH) werden rechtsgültige digitale georeferenzierte Planwerke des Bau- und Planungsrechtes (verbindliche und vorbereitende Bauleitpläne auf Basis des Baugesetzbuches (BauGB) / Bundesbaugesetzes (BBauG); Planwerke auf Basis alten Planrechts: Baustufenpläne, Durchführungspläne, Teilbebauungspläne; Erhaltungsverordnungen nach §172 BauGB und Gestaltungverordnungen nach §12 Hamburgische Bauordnung (HBauO)) erfasst und als Bestandteil der Geodateninfrastruktur der Freien und Hansestadt Hamburg (FHH) zentral in einer Geofachdatenhaltungskomponente in einer einheitlichen semantischen Struktur vorgehalten. Diese zentrale Datenhaltung erlaubt gleichzeitig eine dezentrale Fortführung und Pflege der Datenbestände durch den jeweiligen Sachbearbeiter an seinem Arbeitsplatz, setzt aber die Entwicklung und Einrichtung vereinheitlichter und abgestimmter Datenaustausch- und Aktualisierungsprozesse voraus. Damit ist gewährleistet, dass alle in der FHH vorgehaltenen Auskunfts- und Monitoringsysteme, Beteiligungs- und Baugenehmigungsverfahren, die Bauleitpläne und sonstigen Verordnungen als Informationsbasis benötigen, eine einheitliche Datenbasis zur Verfügung haben. Eine arbeitsaufwändige Recherche nach aktuellem Planrecht und die damit verbundene Aktualisierung der Datenhaltung für die unterschiedlichen Fachinformationssysteme können somit zukünftig entfallen