Thesis (PhD)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The fractional quantum Hall effect represents a true many-body phenomenon in which the collective behaviour of interacting electrons plays a central role. In contrast to its integral counterpart, the appearance of a mobility gap in the fractional quantum Hall regime is due entirely to the Coulomb interaction and is not the result of a perturbed single particle gap. The bulk of our theoretical understanding of the underlying many-body problem is based on Laughlin’s ansatz wave function and the composite fermion picture proposed by Jain. In the latter the fractional quantum Hall effect of interacting electrons is formulated as the integral quantum Hall effect of weakly interacting quasiparticles called composite fermions. The composite fermion picture provides a qualitative description of the interacting system’s low-energy spectrum and leads to a generalisation of Laughlin’s wave functions for the electron ground state. These predictions have been verified through extensive numerical tests. In this work we present an alternative formulation of the composite fermion picture within a more rigorous mathematical framework. Our goal is to establish the relation between the strongly interacting electron problem and its dual description in terms of weakly interacting quasiparticles on the level of the microscopic Hamiltonian itself. This allows us to derive an analytic expression for the interaction induced excitation gap which agrees very well with existing numerical results. We also formulate a mapping between the states of the free particle and interacting descriptions in which the characteristic Jastrow-Slater structure of the composite fermion ansatz appears naturally. Our formalism also serves to clarify several aspects of the standard heuristic construction, particularly with regard to the emergence of the effective magnetic field and the role of higher Landau levels. We also resolve a long standing issue regarding the overlap of unprojected composite fermion trial wave functions with the lowest Landau level of the free particle Hamiltonian. / AFRIKAANSE OPSOMMING: Die fraksionele kwantum Hall-effek is ’n veeldeeltjie verskynsel waarin die kollektiewe gedrag van wisselwerkende elektrone ’n sentrale rol speel. In teenstelling met die heeltallige kwantum Hall-effek is die ontstaan van ’n energie gaping in die fraksionele geval nie ’n enkeldeeltjie effek nie, maar kan uitsluitlik aan die Coulomb wisselwerking toegeskryf word. Die teoretiese raamwerk waarbinne hierdie veeldeeltjie probleem verstaan word is grootliks gebaseer op Laughlin se proefgolffunksie en die komposiete-fermion beeld van Jain. In laasgenoemde word die fraksionele kwantum Hall-effek van wisselwerkende elektrone geformuleer as die heeltallige kwantum Hall-effek van swak-wisselwerkende kwasi-deeljies wat as komposiete-fermione bekend staan. Hierdie beeld lewer ’n kwalitatiewe beskrywing van die wisselwerkende sisteem se lae-energie spektrum en lei tot ’n veralgemening van Laughlin se golffunksies vir die elektron grondtoestand. Hierdie voorspellings is deur verskeie numeriese studies geverifieer. In hierdie tesis ontwikkel ons ’n alternatiewe formulering van die komposiete-fermion beeld binne ’n strenger wiskundige raamwerk. Ons doel is om die verband tussen die sterk-wisselwerkende elektron sisteem en sy duale beskrywing in terme van swak-wisselwerkende kwasi-deeltjies op die vlak van die mikroskopiese Hamilton-operator self te realiseer. Hierdie konstruksie lei tot ’n analitiese uitdrukking vir die opwekkingsenergie wat baie goed met bestaande numeriese resultate ooreenstem. Ons identifiseer ook ’n afbeelding tussen die vrye-deeltjie en wisselwerkende toestande waarbinne die Jastrow-Slater struktuur van die komposiete-fermion proefgolffunksies op ’n natuurlike wyse na vore kom. Verder werp ons formalisme nuwe lig op kwessies binne die standaard heuristiese konstruksie, veral met betrekking tot die oorsprong van die effektiewe magneetveld en die rol van ho¨er effektiewe Landau vlakke. Ons lewer ook uitspraak oor die vraagstuk van die oorvleueling van ongeprojekteerde komposiete-fermion golffunksies met die laagste Landau vlak van die vrye-deeltjie Landau probleem.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The availability of laser systems capable of generating ultrashort optical pulses in the visible spectral range have made it possible to study molecular species with a temporal resolution in the order of intra-molecular dynamics which previously were not accessible. Henceforth, in this study a popular pump-probe technique called ultrafast transient absorption spectroscopy (UTAS) is employed to study the initial photochromic reaction of metal complex, dithizonatophenylmercury (II) (DPM) under various conditions. These conditions include the use of different solvents and electronically altering DPM by the addition of substituents with specific electron affinity properties. For this study the photochromic behaviour of DPM dissolved in methanol is used as standard. Using this standard, the initial photochromic reaction after ultrafast excitation within less than 100 fs caused a radiationless photoreaction with a time constant of about 2 ps, which is interpreted as C=N isomerization along the twist coordinate. It is found that during this isomerization reaction an orthogonally twisted intermediate state was formed and observed through its excited-state absorption, which funnels through a conical intersection onto the ground state potential. Once here, bifurcation along pathways towards the ground states of the reactant and product configurations occurs. This was the first observation of photochromism for DPM in a strong polar solvent such as methanol. From the results of the test compound in methanol, comparisons to the photo-behaviour of DPM dissolved in deuterated methanol and dichloromethane are made. What is established is that changing the solvent resulted in slightly different decay times as well as spectral shifts in the absorption profile which suggested that the potential energy surface of the excited state is modified. This is similar to the results found from the electronically altered DPM species. Here the entire photoreaction is found to either be sped up (1 ps) or slowed down (4 ps) depending on the sample investigated. Previous studies on the photochromicity of DPM like systems concluded that apart from the photo-activated forward reaction, a back reaction occurs in the absence of light. Therefore a detailed look at the back reaction of DPM and its derivatives are also studied. This is done by temporally monitoring the absorption change of the photo-product as it converts back to the reactant. In doing so the lifetime of the photo-product is determined and found to differ greatly depending on the solvent and substituent used. Lastly, in assuming that the back reaction follows first order kinetics, an Arrhenius type measurement on the photo-product of DPM is conducted. The result of this measurement is that a potential energy barrier of 64.8 kJ/mol is overcome in the back reaction. The measurements performed and the results obtained from the photochromicity of DPM contribute to the understanding of photo-induced cis-trans isomerization reactions about a C=N double bond. / AFRIKAANSE OPSOMMING: Die beskikbaarheid van laser sisteme in staat om ultrakort optiese pulse te genereer in die sigbare spektrale gebied, het die studie van molekulˆere spesies met ’n tydresolusie in die orde van intra-molekulˆere dinamika wat voorheen nie toeganklik was nie. Voortaan, in hierdie studie word ’n populˆere aktiveer-interogeer tegniek genaamd ultravinnige tydafhanklike absorpsie spektroskopie (UTAS) aangewend om die aanvanklike fotochromiese reaksie van die metaal kompleks, ditisoonfenielkwik (II) (DFK) onder verskillende kondisies te bestudeer. Hierdie kondisies sluit in die gebruik van verskillende oplosmiddels en die elektroniese verstelling van DFK deur die toevoeging van substituente met spesifieke elektron affiniteit eienskappe. Vir hierdie studie word die fotochromiese gedrag van DFK, opgelos in metanol, as standaard gebruik. Met hierdie standaard, word gevind dat die aanvanklike fotochroom reaksie na ultravinnige opwekking binne minder as 100 fs, ’n stralingslose fotoreaksie met ’n tydkonstante van 2 ps veroorsaak. Hierdie fotoreaksie word verklaar as die C=N isomerisasie met betrekking tot die draai ko¨ordinaat. Daar is ook gevind dat gedurende hierdie isomerisasie reaksie, ’n ortogonaal verdraaide oorgangstoestand gevorm word wat waargeneem is deur sy absorpsie in die opgewekte toestand wat tregter deur ’n koniese kruispunt na die potensiaal van die grondtoestand. By hierdie punt vurk die proses na die grondtoestande van die reaktant en die produk vorme. Di´e was die eerste waarneming van fotochromisme van DFK opgelos in ’n sterk polˆere oplosmiddel soos metanol. Vanuit die resultate vir die toets mengsel in metanol word vergelykings getrek tot die fotogedrag van DFK opgelos in gedeureriese metanol en dichlorometaan. Wat hieruit vasgestel is, is dat die verandering in oplosmiddel wel die fotoreaksie be¨ınvloed deurdat verskillende vervaltye en spekrale verskuiwings in die apsorpsie profiel waargeneem word. Hierdie verskille dui aan dat die potensie¨ele energie oppervlakte van die opgewekte toestand wel gemodifiseer word. Dit is ook soortgelyk aan die resultate vir die elektronies verstelde BFK spesies. Hier is gevind dat die tempo van die totale fotoreaksie `of toeneem (1 ps) `of afneem (4 ps) afhanklik van die spesifieke spesie wat bestudeer word. Vorige studies van die fotochromiese gedrag van sisteme soortgelyk aan DFK het gevind dat behalwe vir die fotogeaktiveerde voorwaartse reaksie, daar ook ’n keersy reaksie plaasvind in die afwesigheid van lig. Dus word die keersy reaksie vir DFK en sy derivate ook in detial bestudeer. In hierdie studie word die absorpsie verskille van die fotoproduk tydelik waargeneem soos dit terugkeer na die reaktant. Op hierdie manier word die leeftyd van die fotoproduk bepaal en gevind dat dit grootliks afhang van die tipe oplosmiddel en tipe substituent wat gebruik word. Ten slote, wanneer daar aanvaar word dat di´e keersy reaksie eerste orde kinetika volg, word ’n Arrhenius tipe meting op die fotoproduk uitgevoer. Die resultaat van hierdie meting is dat ’n potensie¨ele enrgie versperring van 64.8 kJ/mol oorkom word in die keersy reaksie. Die metings wat uitgevoer is en die resultate wat verkry is van die fotochromiese gedrag van DFK dra by tot die verstandhouding van lig-ge¨ınduseerde cis-trans isomerisasie reaksies rondom ’n C=N dubbelbinding.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The study of α clustering is a well-established topic of research in nuclear physics. Recent experimental evidence has revealed the first 2+ excitation of the Hoyle state in 12C, which is known to have a strong α cluster structure. The idea of multi-particle α cluster structures in light nuclear matter has received much attention from theoretical investigations of late. This research has profound implications in the fields of both nuclear structure and nuclear astrophysics. The 20Ne nucleus is a good example for α clustering, since many of its states are known to have α clustering structures. Few low spin states are known at high excitation energies of this nucleus. It is predicted that this nucleus contains a 0+ 5-α cluster state, a so-called ‘Hoyle analogue state’, above its 5-α break-up threshold at Ex = 19.17 MeV. This thesis presents a study of the 20Ne nucleus with the 22Ne(p,t)20Ne reaction at laboratory angles θlab =(0◦, 7◦, 16◦, 27◦). The iThemba LABS K600 magnetic spectrometer was employed with a beam of energy Elab = 60 MeV, incident upon a 22Ne gas target held intact by Aramid foils. The aim was to search for low spin states in 20Ne at excitation energies above Ex = 15 MeV, and, possibly, to find an indication of the 5-α cluster state. Three narrow states were discovered at energies of Ex = 20.59 MeV, Ex = 21.16 MeV and Ex = 21.80 MeV. Calculations performed with the isobaric multiplet mass equation indicate that these states may be T = 2 isobaric analogue states of three known states in 20O. However, shell-model calculations indicate that these states may also have T = 0 or T = 1 isospin values. There is also evidence of a new state at Ex = 17.67 MeV and, possibly, of a collection of new states which could not be resolved at Ex = 18.84 MeV. A tentative candidate for the desired 5-α cluster state was observed, but this will require another measurement with cleaner background to be confirmed. / AFRIKAANSE OPSOMMING: Alfa bondelvorming is ’n gevestigde navorsingsonderwerp in kernfisika. Daar is onlangse bewyse vir die ontdekking van die 2+ opwekking van die Hoyle toestand in 12C, wat ’n erkende alfa bondelstruktuur het. Die idee van multi-alfa bondelstrukture in ligte kerne het onlangs baie aandag geniet in teoretiese ondersoeke. Hierdie navorsing het besondere implikasies vir kernstruktuur, sowel as vir kernastrofisika. Die 20Ne kern bied ‘n ideale voorbeeld vir alfa bondelvorming aangesien dit bekend is dat baie van die kern se toestande alfa bondelstrukture het. Min lae-spin toestande is by ho¨e opwekenergie¨e bekend in hierdie kern. Daar word voorspel dat ’n 0+ 5-alfa bondeltoestand, ’n sogenaamde ‘Hoyle analoogtoestand’, bo die drumpel vir 5-alfa verval by Ex = 19.17 MeV bestaan. Hierdie tesis beskryf ‘n studie van die 20Ne kern met die 22Ne(p,t)20Ne reaksie by laboratorium hoeke van θlab =(0◦, 7◦, 16◦, 27◦). Die K600 magnetiese spektrometer van iThemba LABS is gebruik met ‘n proton bundel, by ‘n energie van Elab = 60 MeV, wat op ‘n 22Ne gas teiken omhul met aramid foelies gerig is. Die doel was om lae-spin toestande in 20Ne by opwekenergie¨e bo Ex = 15 MeV op te spoor, en om moontlik ook ‘n aanduiding van die 5-alfa bondeltoestand te vind. Drie smal toestande is by energie¨e van Ex = 20.59 MeV, Ex = 21.16 MeV en Ex = 21.80 MeV opgespoor. Berekeninge wat met die isobariese multiplet massa vergelyking uitgevoer is, dui daarop dat hierdie toestande T = 2 isobariese analoogtoestande van drie bekende toestande in 20O kan wees, hoewel skilmodel berekeninge ook T = 0 en T = 1 kandidate aandui. Daar is ook bewyse van ’n nuwe toestand by Ex = 17.67 MeV, en moontlik van ’n versameling nuwe toestande rondom Ex = 18.84 MeV wat nie uitmekaar geken kon word nie. ‘n Tentatiewe kandidaat vir die gesogte 5-alfa bondel toestand is waargeneem, maar nog ‘n meting met ’n skoner agtergrond word vir bevestiging benodig.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this dissertation we address the conservation of topological states in polymer knots. Topological constraints are frequently included into theoretical descriptions of polymer systems through invariants such as winding numbers and linking numbers of polynomial invariants. In contrast, our approach is based on sequences of manipulations of knots that maintain a given knot's topology; these are known as Reidemeister moves. We begin by discussing basic properties of knots and their representations. In particular, we show how the Reidemeister moves may be viewed as rules for dynamics of crossings in planar projections of knots. Thereafter we consider various combinatoric enumeration procedures for knot configurations that are equivalent under chosen topological constraints. Firstly, we study a reduced system where only the zeroth and first Reidemeister moves are allowed, and present a diagrammatic summation of all contributions to the associated partition function. The partition function is then calculated under basic simplifying assumptions for the Boltzmann weights associated with various configurations. Secondly, we present a combinatoric scheme for enumerating all topologically equivalent configurations of a polymer strand that is wound around a rod and closed. This system has the constraint of a fixed winding number, which may be viewed in terms of manipulations that obey a Reidemeister move of the second kind of the polymer relative to the rod. Again configurations are coupled to relevant statistical weights, and the partition function is approximated. This result is used to calculate various physical quantities for confined geometries. The work in that chapter is based on a recent publication, "Conservation of polymer winding states: a combinatoric approach", C.M. Rohwer, K.K. Müller-Nedebock, and F.-E. Mpiana Mulamba, J. Phys. A: Math. Theor. 47 (2014) 065001. The remainder of the dissertation is concerned with a dynamical description of the Reidemeister moves. We show how the rules for crossing dynamics may be addressed in an operator formalism for stochastic dynamics. Differential equations for densities and correlators for crossings on strands are calculated for some of the Reidemeister moves. These quantities are shown to encode the relevant dynamical constraints. Lastly we sketch some suggestions for the incorporation of themes in this dissertation into an algorithm for the simulated annealing of knots. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die behoud van topologiese toestande in knope. Topologiese dwangvoorwaardes word dikwels d.m.v. invariante soos windingsgetalle, skakelgetalle en polinomiese invariante in die teoretiese beskrywings van polimere ingebou. In teenstelling hiermee is ons benadering gebaseer op reekse knoopmanipulasies wat die topologie van 'n gegewe knoop behou - die sogenaamde Reidemeisterskuiwe. Ons begin met 'n bespreking van die basiese eienskappe van knope en hul daarstellings. Spesi ek toon ons dat die Reidemeisterskuiwe beskryf kan word i.t.v. reëls vir die dinamika van kruisings in planêre knoopprojeksies. Daarna beskou ons verskeie kombinatoriese prosedures om ekwivalente knoopkon gurasies te genereer onderhewig aan gegewe topologiese dwangvoorwaardes. Eerstens bestudeer ons 'n vereenvoudigde sisteem waar slegs die nulde en eerste Reidemeisterskuiwe toegelaat word, en lei dan 'n diagrammatiese sommasie van alle bydraes tot die geassosieerde toestandsfunksie af. Die partisiefunksie word dan bereken onderhewig aan sekere vereenvoudigende aannames vir die Boltzmanngewigte wat met die verskeie kon- gurasies geassosieer is. Tweedens stel ons 'n kombinatoriese skema voor om ekwivalente kon gurasies te genereer vir 'n polimeer wat om 'n staaf gedraai word. Die beperking tot 'n vaste windingsgetal in hierdie sisteem kan daargestel word i.t.v. 'n Reidemeister skuif van die polimeer t.o.v. die staaf. Weereens word kon gurasies gekoppel aan relevante statistiese gewigte en die partisiefunksie word benader. Verskeie siese hoeveelhede word dan bereken vir beperkte geometrie e. Die werk in di e hoofstuk is gebaseer op 'n onlangse publikasie, "Conservation of polymer winding states: a combinatoric approach", C.M. Rohwer, K.K. Müller-Nedebock, and F.-E. Mpiana Mulamba, J. Phys. A: Math. Theor. 47 (2014) 065001. Die res van die tesis handel oor 'n dinamiese beskrywing van die Reidemeisterskuiwe. Ons toon hoe die re els vir kruisingsdinamika beskryf kan word i.t.v. 'n operatorformalisme vir stochastiese dinamika. Di erensiaalvergelykings vir digthede en korrelatore vir kruisings op stringe word bereken vir sekere Reidemeisterskuiwe. Daar word getoon dat hierdie hoeveelhede die relevante dinamiese beperkings respekteer. Laastens maak ons 'n paar voorstelle vir hoe idees uit hierdie tesis geï nkorporeer kan word in 'n algoritme vir die gesimuleerde vereenvoudiging van knope.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The facilities for radionuclide production at iThemba LABS have undergone a number of significant upgrades over the last decade in order to increase the production capacity and to diversify the product portfolio. Central to this effort is a new vertical beam target station (VBTS) and its associated targetry, designed and built to operate at higher proton beam intensities for the large-scale production of relatively long-lived, high-value radionuclides such as 22Na, 68Ge and 82Sr. Along with the VBTS, an existing smaller horizontal beam target station was adapted to accommodate targetry for 18F production, mainly to supply 18F-FDG for use in positron emission tomography (PET). The production capacity was further enhanced by means of a beam splitter to enable bombardments in two target stations simultaneously. This required new developments on several systems, e.g. beam diagnostics, control, interlocking and cooling. This project brings together a number of different aspects of the upgraded facilities as well as the associated research and development that enable the production of radionuclides in the medium energy region, up to approximately 70 MeV. Investigations were performed on the cooling of the interfacial windows between the cyclotron vacuum and the targets as well as the direct cooling of the targets themselves during intense proton bombardments. For this purpose, empirical as well as computational fluid dynamics (CFD) calculations were performed. In addition, the local radiation shield of the VBTS as well as the beam transport in some of the targetry was investigated by means of Monte Carlo radiation transport calculations. Excitation functions for the production of various radionuclides in the 66 MeV proton bombardment of 192Os, 159Tb, natGd, 155Gd, 152Gd, 93Nb, natZr and 89Y were measured and compared with theoretical predictions by means of statistical nuclear model calculations as well as the TENDL-2012 library. In particular, the production of 186Re, selected radioterbiums (149;152;155Tb) and radiozirconiums (88;89Zr) is of interest in existing and emerging diagnostic and therapeutic applications in nuclear medicine. A study on 28Mg production in the proton bombardment of natCl using stacked chloride targets was also performed at 200 MeV. This radionuclide is of interest as 28Mg is the only practical radiotracer of Mg. Finally, new targetry for the production of 18F was developed, modelled and optimized for the non-standard degraded beam employed in this particular case. / AFRIKAANSE OPSOMMING: Die fasiliteite vir die produksie van radionukliede by iThemba LABS is gedurende die afgelope dekade aansienlik opgegradeer om die produksiekapasiteit te verhoog en om die portfolio van produkte te diversifiseer. Sentraal tot hierdie poging is ’n vertikale-bundel skyfstasie (VBTS) wat gebou is om skywe met hoër intensiteit protonbundels te bombardeer ten einde relatief langlewende, hoë-waarde radionukliede op grootmaat te produseer, insluitende 22Na, 68Ge en 82Sr. Terselfdetyd is ’n bestaande, kleiner horisontale-bundel skyfstasie aangepas om skywe vir die produksie van 18F te huisves, meestal om 18FFDG vir positronemissietomografie (PET) te lewer. Die produksiekapasiteit is verder verhoog d.m.v. ’n bundeldeler sodat bundel gelyktyding aan twee skyfstasies gelewer kan word. Dit het ontwikkelingswerk vereis aan verskeie stelsels, insluitende diagnostiek, beheer, vergrendeling en verkoeling. Hierdie projek bring verskeie aspekte bymekaar t.o.v. die opgegradeerde produksiefasiliteite sowel as die geassosieerde navorsing en ontwikkeling benodig vir radionukliedproduksie in die middelenergiegebied tot ongeveer 70 MeV. Die verkoeling van die foelievensters tussen die vakuum van die siklotron en die skyfgerei is ondersoek sowel as die direkte verkoeling van skywe onder intense protonbombardement. Hierdie studie sluit beide empiriese sowel as numeriese vloeidinamika berekeninge in. Verder is die afskerming van die VBTS asook die bundeltransport in verskeie skywe ondersoek m.b.v. Monte Carlo stralingstransport berekeninge. Opwekkrommes vir die produksie van verskeie radionukliede met protongeïnduseerde reaksies tot en met 66 MeV op 192Os, 159Tb, natGd, 155Gd, 152Gd, 93Nb, natZr en 89Y is gemeet en vergelyk met statistiese kernmodel berekeninge sowel as die TENDL-2012 biblioteek. Die produksie van 186Re, verskeie radioterbiums (149;152;155Tb) en radiozirkoniums (88;89Zr) is van spesifieke belang vir bestaande en toekomstige diagnostiese en terapeutiese toepassings in die kerngeneeskunde. ’n Studie op die produksie van 28Mg in die bombardement van natCl met 200 MeV protone is ook onderneem. In hierdie ondersoek is ’n stapel chloriedskywe gebruik. Die 28Mg is van belang omdat dit die enigste Mg radioisotoop is wat geskik is as ’n radiospoorder van dié element. Laastens is nuwe skyfgerei vir die produksie van 18F ontwikkel, gemodelleer en geoptimiseer vir die nie-standaard afgeremde bundel wat benut word in hierdie geval.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: See fulltext for abstract. / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming.

Thesis (MSc (Physics))--University of Stellenbosch, 2008. / Experimental double differential cross sections and analyzing powers for the inclusive 93 Nb(p,α) r and 93 Nb(p, 3He) r reactions have been measured at an incident energy of 160 MeV. The results of this experiment, for emission angles ranging from 15º to 60º as well as previously measured data for 93 Nb(p,α) r at 100 MeV and 59Co(p,α) r at 100 and 160 MeV, have been compared with theoretical calculations based on a direct quasi-free α- cluster knockout mechanism. A computer code has been employed which calculates triple differential cross section and analysing power values using the distorted wave impulse approximation (DWIA). Inclusive double differential cross sections and analysing powers were calculated by integrating over the solid angle of the unobserved proton. It was found that the DWIA is limited in its ability to reproduce the experimental data. Some slight agreements have been observed in the region of large emission energies and small angles. This is consistent with the findings of previous studies based on a direct multi-step analysis which indicated that the first step knock-out reaction dominates in this region.

Thesis (MSc (Physics))--University of Stellenbosch, 2005. / It was Wigner that in the 1950’s first introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of Random Matrix Theory has grown tremendously, with applications ranging from fluctuations on the economic markets to M-theory. It is the purpose of this thesis to discuss the basic concepts of Random Matrix Theory, using the ensembles of random matrices originally introduced by Wigner, the Gaussian ensembles, as a starting point. As Random Matrix Theory is classically concerned with the statistical properties of levels sequences, we start with a brief introduction to the statistical analysis of a level sequence before getting to the introduction of the Gaussian ensembles. With the ensembles defined, we move on to the statistical properties that they predict. In the light of these predictions, a few of the classical applications of Random Matrix Theory are discussed, and as an example of some of the important concepts, the Anderson model of localization is investigated in some detail.

Thesis (MSc)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: The efficient manipulation of various nonlinear optical processes frequently requires the shaping of the laser beams used for these processes. Three beam shaping techniques were investigated in this thesis. The focussing of Gaussian laser beams was investigated analytically, in order to efficiently manipulate the focussed beam characteristics. The beam-shaping characteristics of a diffractive optical element (DOE) was investigated numerically, which illustrates the beamshaping capability of the DOE, and identifies the critical parameters in experimental situations. The use of a waveguide as beam shaping device was investigated analytically and experimentally, and characterized for use with the available tunable laser sources. A Raman laser, or Raman shifter, employs stimulated vibrational Raman scattering to generate laser radiation at shifted frequencies. The waveguide was successfully applied as a beam shaping device in the Raman laser system, for optimisation of the process. The Raman laser system was investigated experimentally and characterized for use with the available tunable laser sources. The successful generation of laser radiation at shifted frequencies illustrates the usefulness of the system for generating tunable red-shifted frequencies. The results of this work allow the simple and efficient application of the Raman laser to generate laser radiation at shifted frequencies, in particular tunable infrared laser radiation which is desirable for molecular spectroscopy. / AFRIKAANSE OPSOMMING: Nie-liniêre optiese prosesse kan meer effektief benut word deur die vervorming van die laserbundels wat gebruik word in die prosesse. In hierdie tesis word drie laserbundel-vervormings tegnieke ondersoek. Die fokussering van Gaussiese laserbundels word analities ondersoek, om die gefokusseerde bundel se eienskappe effektief te manipuleer. Die bundel-vervormings eienskappe van ’n diffraktiewe optiese element word numeries ondersoek, wat die effektiwiteit van die bundelvervorming en die sensitiewe parameters in die sisteem uitwys. Die gebruik van ’n golfgeleier as ’n bundel-vervormings tegniek word ook analities en eksperimenteel ondersoek, en gekarakteriseer vir gebruik met die gegewe golflengte-verstelbare laser sisteme. ’n Raman laser, wat gestimuleerde vibrasionele Raman verstrooiing gebruik om laser lig te genereer by Stokes-verskuifde frekwensies, word ondersoek. Die golfgeleier word effektief gebruik as ’n bundel-vervormings tegniek in die Raman laser, om die bogenoemde nie-liniêre proses te optimeer. Die Raman laser was eksperimenteel ondersoek en gekarakteriseer vir gebruik met die gegewe golflengte-verstelbare lasers. Laser lig by verskuifde golflengtes is suksesvol gegenereer, wat die bruikbaarheid van die sisteem illustreer. Van belang is spesifiek verstelbare infrarooi laser lig, wat gebruik kan word in die laser-spektroskopie van molekules. Die resultate van hierdie werk lei tot die eenvoudige en effektiewe gebruik van die Raman laser, om langer golflengtes in die infrarooi gebied te genereer met ’n gegewe laser in die sigbare gebied.

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: static density and magnetic structure functions of a melt of flexible polymers whose monomers possess bond-directed dipoles which interact with each other. In order to observe the effect of screening of the dipolar interaction on the structure functions we obtain results for cases with and without steric interactions and also for cases with and without Debye-H¨uckel screening of the dipole moments. / AFRIKAANSE OPSOMMING: Approximation” RPA) om die statiese digtheids- en magnetiese struktuurfunksies te bereken vir ’n smelt van hoogsbuigsame polimere, waarvan die monomere dipole langs die verbindings besit wat met mekaar in wisselwerking tree. Om die effek van afskerming op die dipolare wisselwerking en die struktuurfunksies te kan waarneem, bepaal ons resultate vir die gevalle met en sonder steriese wisselwerkings en ook vir gevalle met en sonder die Debye-H¨uckel afskerming van die dipoolmomente.