Setup and calibration of a position sensitive microchannel plate detector and analysis of a test run optimizing the WITCH experiment

The standard model of particle physics only implies vectorial and axial-vectorial currents. Symmetry considerations allow for additional, exotic currents, too. Experimentally these are ruled out only to a percent level. The so-called $\nu -\nu$ angular correlation coefficient $\textit{a}$ is a parameter who’s value strongly depends on the underlying interaction types. An indirect method for its determination is the measurement of the recoil energy spectrum of the daughter nuclei after $\beta$- decay. The shape of the spectrum is dependent on the value of $a$. The WITCH collaboration aims to determine $\textit{a}$ with a relative precision of $\frac{\Delta a}{a} \leq 0.005$ from a measurement of the recoil energy spectrum of the $^{35}$Ar decay. For this purpose $^{35}$Ar$^{+}$ ions are stored in a Penning trap and the recoil energy of the daughter nuclei will be determined by means of a retardation spectrometer with magnetic adiabatic collimation (MAC-E filter). To detect the recoil ions a position sensitive microchannel plate detector (MCP detector) is used. In this thesis a new MCP detector with larger active surface has been set up and commissioned. A detailed weak point analysis of the old detector design lead to enhanced signal quality, a homogeneous detection efficiency and a stable mode of operation of the detector system. Additionally a method to measure the relative detection efficiency and determine the position resolution of the detector has been developed. In the second part of this thesis, the data from a commissioning run in Oct. 2011 was used to establish an analysis routine to extract $\textit{a}$ and look for experimental deficiencies. By means of this analysis we could locate an unintentional Penning trap in the spectrometer, showed that measurements at very low retardation potentials are unsuited, discovered a synchronization problem between the data acquisition and the retardation voltage supply and found that two independent data acquisition branches produced inconsistent data. Altogether this lead to $s$ an optimized measurement cycle and improved data taking applied in a later measurement in Nov. 2012. Additionally on the basis of this analysis we were able to rate two important systematic effects with are of concern for a precision measurement of $\textit{a}$. As result of this analysis a value of $\textit{a}$= 0.45 (+0.48 −0.39)$_{stat}\pm$0.29$_{syst}$ was determined.