Academic literature on the topic 'Plane wave Born approximation'

This thesis concerns the use of nuclear reactions to study the structure of neutron-rich light nuclei. Emphasis is placed on 11Be which has been identified as a nucleus with a single neutron halo and which offers a simple 2-body case for detailed analysis. Comparisons are made with experimental data for the break-up of 11Be on gold, titanium and beryllium targets. As a prelude to more detailed work a simple elastic break-up model calculation, using the Distorted Wave Born Approximation (DWBA), is attempted. The resulting theoretical cross-sections show good agreement with the shape of the experimental data but cannot predict the absolute magnitude. A major part of the break-up work is a more accurate model using the post-form DWBA. The formulation is built up from basic scattering theory and includes details of employing the Zero Range Approximation and the Vincent and Fortune method of integration. A Finite Range Correction is also applied. Cross-section calculations for a gold target agree closely with experiment but a problem arises for lighter targets. Here the Coulomb potential must be excluded from the calculation to obtain a result that matches the experimental data. A method for the calculation of inelastic break-up is presented which only requires a small modification to the methods used for elastic break-up. As it suffers from the same light target problem only calculations for a gold target give an inclusive cross-section, produced from the elastic and inelastic contributions, which matches the experimental data satisfactorily. To overcome the light target problem a full recoil calculation is introduced. Arguments and analysis are produced to show that this method is too demanding of both computing time and storage for practicable implementation. Future calculations are proposed using an analytical method for Coulomb break-up.

The differential scattering cross section for diffuse scattering of X-rays from thinfilm structures is discussed within the framework of the distorted wave Born ap-proximation (DWBA). In contrast to the standard Born approximation (BA), thedistorted wave approach succeeds in calculating scattering from surfaces near thecritical angle of reflection. The method is particularly useful for studying averagesurface properties.Compromises made in the derivation of the model substantially simplify thefinal expression, but also limit its range of validity, which depends on the surfaceroot mean square roughness &#963; and the momentum transfer between the incidentand scattered X-rays perpendicular to the surface, Qz . The approximation is validso long as (Qz x &#963;) << 1.However, this is also the only regime where it is necessary togo beyond the simpler Born approximation.A computer simulation software based on the DWBA is implemented in Python.The implemented DWBA depends on the fractal dimension of the surface featuresthrough a parameter h (D = 3 &#8722; h) and an in-plane correlation cut off length &#950;.The various effects of changing key model parameters, among them &#950; and h, isdemonstrated. Comparison between experimental data and the DWBA modellooks promising although there are some challenges in relation to determiningthe fractal dimension.Finally, the feasibility of implementing the DWBA model in a multi-parameterfitting algorithm is discussed.

This thesis presents a series of electron impact ionization measurements on the gas phase targets of argon and krypton. The (e,2e) coincidence technique has been employed to measure the triple differential cross section (TDCS) using a new coincidence spectrometer designed to operate in the low energy regime (2 to 5 times the ionization energy) and in the coplanar geometry. The spectrometer is a conventional device utilizing a non-energy selected electron gun and two 1800 hemispherical electron analysers fitted with channel electron multipliers for detection of the outgoing electrons. A series of TDCS measurements were performed on the 3s inner-valence and 3p valence orbitals of argon employing coplanar asymmetric kinematics. Measurements for both orbitals were performed at an incident energy of 113.5 eV, ejected energies of 10, 7.5, 5 and 2 eV and a scattering angle of -15°. The energy of the scattered electron in each case was chosen to satis~' energy conservation and is dependent on the ionization energies of the different orbitals. The experimental cross sections are compared to theoretical TDCS calculations using the distorted wave Born approximation (DWBA) and variations of the DWBA in an attempt to investigate the role that post collisional interaction (PCI), polarization and electron exchange play in describing the TDCS in the low energy regime. To further extend this analysis, a series of TDCS measurements were performed on the 3s and 4s. orbitals of argon and krypton, respectively, employing coplanar symmetric kinematics. Measurements were performed for the 3s orbital at outgoing energies of 50, 20, 10 and 4eV and for the 4s orbital at outgoing energies of 85, 50, 20 and 10 eV. The kinematics were chosen to coincide with several of the (e,2e) measurements made in the same geometry on the 3p orbital of argon by Rouvellou et al (1998). The experimental results were again compared to a DWBA calculation and similar variations to those employed for the asymmetric measurements.

La reflectivite des rayons x par des multicouches planaires et structurees est presentee en utilisant differentes approches theoriques. Les phenomenes de diffusion etudies sont : la reflectivite speculaire par des multicouches planaires ayant diverses sequences d'empilement (monocouche, periodique, quasiperiodique), la diffusion diffuse de multicouches rugueuses, et enfin la diffusion par des reseaux de surface et par des reseaux de multicouche. Les theories employees pour les calculs : la theorie cinematique, l'approximation de l'onde deformee de born, la theorie dynamique, et plusieurs approximations de la theorie dynamique (approximation a une reflexion unique, approximation a deux ondes et approximation a diffusion multiple), sont developpees dans un formularisme unique. Ce formalisme permet de discuter et de comparer toutes les theories d'une maniere solide et methodologique. Les calculs numeriques sont appliques pour l'ajustement des courbes experiementales pour mettre en evidence les parametres structuraux des divers systemes multicouches.

Diese Arbeit befasst sich mit der theoretischen Beschreibung nichtlinearer optischer Phänomene in Hinblick auf das (numerische) unstetige Galerkin-Zeitraumverfahren. Insbesondere werden zwei Materialmodelle behandelt: das hydrodynamische Modell für Metalle und das Modell für Raman-aktive Materialien. Im ersten Teil der Arbeit wird das hydordynamische Modell für Metalle unter Verwendung eines störungstheoretischen Ansatzes behandelt. Insbesondere wird dieser Ansatz genutzt, um die nichtlinearen optischen Effekte, Erzeugung zweiter Harmonischer und Summenfrequenzerzeugung, mit Hilfe des unstetigen Galerkin-Verfahrens zu studieren. In diesem Zusammenhang wird demonstriert, wie das optische Signal zweiter Ordnung von Nanoantennen optimiert werden kann. Hierzu wird ein hier erarbeitetes Schema für die Abstimmung des eingestrahten Lichtes angewandt. Zudem führt eine intelligente Wahl des Antennendesigns zu einem optimierten Signal. Im zweiten Teil dieser Arbeit wird das Modell für Raman-aktive Dielektrika behandelt. Genauer wird die nichtlineare Antwort dritter Ordnung für stimulierte Raman-Streuung hergeleitet. Diese wird dazu genutzt, um ein System aus Hilfsdifferentialgleichungen für das unstetige Galerkin-Verfahren zu konstruieren. Die Ergebnisse des erweiterten numerischen Verfahrens werden im Anschluss gezeigt und diskutiert.<br>This thesis is concerned with the theoretical description of nonlinear optical phenomena with regards to the (numerical) discontinuous Galerkin time-domain (DGTD) method. It deals with two different material models: the hydrodynamic model for metals and the model for Raman-active dielectrics. In the first part, we review the hydrodynamic model for metals, where we apply a perturbative approach to the model. We use this approach to calculate the second-order nonlinear optical effects of second-harmonic generation and sum-frequency generation using the DGTD method. In this context, we will see how to optimize the second-order response of plasmonic nanoantennas by applying a deliberate tuning scheme for the optical excitations as well as by choosing an intelligent nanoantenna design. In the second part, we examine the material model for Raman-active dielectrics. In particular, we see how to derive the third-order nonlinear response by which one can describe the process of stimulated Raman scattering. We show how to incorporate this third-order response into the DGTD scheme yielding a novel set of auxiliary differential equations. Finally, we demonstrate the workings of the modified numerical scheme.