The electron antineutrino angular correlation coefficient a in free neutron decay: Testing the standard model with the aSPECT-spectrometer

The beta-decay of free neutrons is a strongly over-determined process in the Standard Model (SM) of Particle Physics and is described by a multitude of observables. Some of those observables are sensitive to physics beyond the SM. For example, the correlation coefficients of the involved particles belong to them. The spectrometer aSPECT was designed to measure precisely the shape of the proton energy spectrum and to extract from it the electron anti-neutrino angular correlation coefficient "a". A first test period (2005/ 2006) showed the “proof-of-principles”. The limiting influence of uncontrollable background conditions in the spectrometer made it impossible to extract a reliable value for the coefficient "a" (publication: Baessler et al., 2008, Europhys. Journ. A, 38, p.17-26). A second measurement cycle (2007/ 2008) aimed to under-run the relative accuracy of previous experiments (Stratowa et al. (1978), Byrne et al. (2002)) da/a =5%. I performed the analysis of the data taken there which is the emphasis of this doctoral thesis. A central point are background studies. The systematic impact of background on a was reduced to da/a(syst.)=0.61 %. The statistical accuracy of the analyzed measurements is da/a(stat.)=1.4 %. Besides, saturation effects of the detector electronics were investigated which were initially observed. These turned out not to be correctable on a sufficient level. An applicable idea how to avoid the saturation effects will be discussed in the last chapter.

Numerical studies of colloidal systems

The interplay of hydrodynamic and electrostatic forces is of great importance for the understanding of colloidal dispersions. Theoretical descriptions are often based on the so called standard electrokinetic model. This Mean Field approach combines the Stokes equation for the hydrodynamic flow field, the Poisson equation for electrostatics and a continuity equation describing the evolution of the ion concentration fields. In the first part of this thesis a new lattice method is presented in order to efficiently solve the set of non-linear equations for a charge-stabilized colloidal dispersion in the presence of an external electric field. Within this framework, the research is mainly focused on the calculation of the electrophoretic mobility. Since this transport coefficient is independent of the electric field only for small driving, the algorithm is based upon a linearization of the governing equations. The zeroth order is the well known Poisson-Boltzmann theory and the first order is a coupled set of linear equations. Furthermore, this set of equations is divided into several subproblems. A specialized solver for each subproblem is developed, and various tests and applications are discussed for every particular method. Finally, all solvers are combined in an iterative procedure and applied to several interesting questions, for example, the effect of the screening mechanism on the electrophoretic mobility or the charge dependence of the field-induced dipole moment and ion clouds surrounding a weakly charged sphere. In the second part a quantitative data analysis method is developed for a new experimental approach, known as "Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy" (TIR-FCCS). The TIR-FCCS setup is an optical method using fluorescent colloidal particles to analyze the flow field close to a solid-fluid interface. The interpretation of the experimental results requires a theoretical model, which is usually the solution of a convection-diffusion equation. Since an analytic solution is not available due to the form of the flow field and the boundary conditions, an alternative numerical approach is presented. It is based on stochastic methods, i. e. a combination of a Brownian Dynamics algorithm and Monte Carlo techniques. Finally, experimental measurements for a hydrophilic surface are analyzed using this new numerical approach.

Total internal reflection fluorescence cross-correlation spectroscopy: theory and application for studying boundary slip phenomenon

I present a new experimental method called Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy (TIR-FCCS). It is a method that can probe hydrodynamic flows near solid surfaces, on length scales of tens of nanometres. Fluorescent tracers flowing with the liquid are excited by evanescent light, produced by epi-illumination through the periphery of a high NA oil-immersion objective. Due to the fast decay of the evanescent wave, fluorescence only occurs for tracers in the ~100 nm proximity of the surface, thus resulting in very high normal resolution. The time-resolved fluorescence intensity signals from two laterally shifted (in flow direction) observation volumes, created by two confocal pinholes are independently measured and recorded. The cross-correlation of these signals provides important information for the tracers’ motion and thus their flow velocity. Due to the high sensitivity of the method, fluorescent species with different size, down to single dye molecules can be used as tracers. The aim of my work was to build an experimental setup for TIR-FCCS and use it to experimentally measure the shear rate and slip length of water flowing on hydrophilic and hydrophobic surfaces. However, in order to extract these parameters from the measured correlation curves a quantitative data analysis is needed. This is not straightforward task due to the complexity of the problem, which makes the derivation of analytical expressions for the correlation functions needed to fit the experimental data, impossible. Therefore in order to process and interpret the experimental results I also describe a new numerical method of data analysis of the acquired auto- and cross-correlation curves – Brownian Dynamics techniques are used to produce simulated auto- and cross-correlation functions and to fit the corresponding experimental data. I show how to combine detailed and fairly realistic theoretical modelling of the phenomena with accurate measurements of the correlation functions, in order to establish a fully quantitative method to retrieve the flow properties from the experiments. An importance-sampling Monte Carlo procedure is employed in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for both modern desktop PC machines and massively parallel computers. The latter allows making the data analysis within short computing times. I applied this method to study flow of aqueous electrolyte solution near smooth hydrophilic and hydrophobic surfaces. Generally on hydrophilic surface slip is not expected, while on hydrophobic surface some slippage may exists. Our results show that on both hydrophilic and moderately hydrophobic (contact angle ~85°) surfaces the slip length is ~10-15nm or lower, and within the limitations of the experiments and the model, indistinguishable from zero.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.