The Lamb Shift Experiment in Muonic Hydrogen

The subject of this thesis is the muonic hydrogen (µp) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S-2P energy difference in µp atoms by laser spectroscopy and to deduce the proton root ­mean­ square (rms) charge radius with 10-3 precision, an order of magnitude better than presently known. This would make it possible to test bound-state quantum electrodynamics (QED) in hydrogen at the relative accuracy level of 10-7, and will lead to an improvement in the determination of the Rydberg constant by more than a factor of seven. Moreover it will represent a benchmark for QCD theories. The experiment is based on the measurement of the energy difference between the 2S(F=1) and 2P(F=2) levels in µp atoms to a precision of 30 ppm, using a pulsed laser tunable at wavelengths around 6 µm. Negative muons from a unique low energy muon beam are stopped at a rate of 70 s-1 in 0.6 hPa of hydrogen gas. Highly excited µp atoms are formed, and most of them promptly deexcite to the ground state within 100 ns. However, there is a roughly 1% probability that long­live µp(2S) atoms with a lifetime of 1.3 µs are formed. An incoming muon triggers a pulsed, multi­stage laser system which delivers 0.2 mJ per pulse at 6 µm with 55 s-1 repetition rate. It consists of two XeCl excimer lasers followed by dye lasers which pump an oscillator ­amplifier frequency ­controlled Ti:Sa laser. Its 6 ns long pulse at 708 nm is then frequency shifted to 6 µm via third Stokes production in a Raman cell filled with hydrogen. The laser pulse has a delay of about 1.5 µs with respect to the prompt muon cascade. If the laser is on resonance, it induces 2S-2P transitions. The subsequent deexcitation to the 1S state emits a 1.9 keV Lyman-alpha x ray which is detected by large area avalanche photo diodes. The resonance frequency, and hence the Lamb shift and the proton radius, are determined by measuring the intensity of these x rays as a function of the laser wavelength. A search for the 2S-2P resonance line was performed in November 2003 when a broad range of laser frequencies was scanned (49.7409 - 49.8757 THz), corresponding to proton radii between 0.844 and 0.905 fm. The result of the data analysis is that no significant 2S-2P resonance was observed. The negative result is with high probability due to the low statistics and not to an incorrect search region. The first part of this thesis reports on the present status of the Lamb shift theory in µp. Following, there is a detailed description of the apparatus and analysis of the data. An estimate of the present and future laser-­induced event rates are given, together with a study of the present and future background. In the Appendices are discussed: the energy levels in hydrogen, the proton radius definition, the relevance of this experiment, the 2S state population and lifetime, and the spectroscopic properties of the 2S-2P transition

Thin-disk laser scaling limit due to thermal-lens induced misalignment instability

We present an obstacle in power scaling of thin-disk lasers related with self-driven growth of misalignment due to thermal lens effects. This self-driven growth arises from the changes of the optical phase difference at the disk caused by the excursion of the laser eigen-mode from the optical axis. We found a criterion based on a simplified model of this phenomenon which can be applied to design laser resonators insensitive to this effect. Moreover, we propose several resonator architectures which are not affected by this effect.Comment: 19 pages, 13 figure

Spatial hole burning in thin-disk lasers and twisted-mode operation

Spatial hole burning prevents single-frequency operation of thin-disk lasers when the thin disk is used as a folding mirror. We present an evaluation of the saturation effects in the disk for disks acting as end-mirrors and as folding-mirrors explaining one of the main obstacles towards single-frequency operation. It is shown that a twisted-mode scheme based on a multi-order quarter-wave plate combined with a polarizer provides an almost complete suppression of spatial hole burning and creates an additional wavelength selectivity that enforces efficient single-frequency operation.Comment: 14 pages, 16 figure

Theory of the n=2 levels in muonic deuterium

The present knowledge of Lamb shift, fine- and hyperfine structure of the $\mathrm{2S}$ and $\mathrm{2P}$ states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S-2P}$ transition frequencies in muonic deuterium ($\mu\mathrm{d}$). A term-by-term comparison of all available sources reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift, which are essential for a determination of the deuteron rms charge radius from $\mu\mathrm{d}$. Apparent discrepancies between different sources are resolved, in particular for the difficult two-photon exchange contributions. Problematic single-sourced terms are identified which require independent recalculation.Comment: 26 pages, add missing feynman diagrams (Fig. 3), renumber items (Tab. IV), correct a sum (column 5, Tab. IV

Statistical Uncertainty in Quantitative Neutron Radiography

We demonstrate a novel procedure to calibrate neutron detection systems commonly used in standard neutron radiography. This calibration allows determining the uncertainties due to Poisson-like neutron counting statistics for each individual pixel of a radiographic image. The obtained statistical errors are necessary in order to perform a correct quantitative analysis. This fast and convenient method is applied to data measured at the cold neutron radiography facility ICON at the Paul Scherrer Institute. Moreover, from the results the effective neutron flux at the beam line is determined

Passive alignment stability and auto-alignment of multipass amplifiers based on Fourier transforms

The stability properties of Fourier-based multipass amplifier to misalignments (tilts) of its optical components has been investigated. For this purpose, a method to quantify the sensitivity to tilts based on the amplifier small signal gain has been elaborated and compared with measurements. To improve on the tilt stability by more than an order of magnitude a simple auto-alignment system has been proposed and tested. This study, combined with other investigations devoted to the stability of the output beam to variations of aperture and thermal lens effects of the active medium, qualifies the Fourier-based amplifier for the high-energy and the high-power sector.Comment: 10 pages, 11 figure

A compact 20-pass thin-disk multipass amplifier stable against thermal lensing effects and delivering 330 mJ pulses with M2<1.17\bf{M^2 < 1.17}

We report on an Yb:YAG thin-disk multipass amplifier delivering 50 ns long pulses at a central wavelength of 1030 nm with an energy of 330 mJ at a repetition rate of 100 Hz. The beam quality factor at the maximum energy was measured to be $\text{M}^2 = 1.17$. The small signal gain is 20, and the gain at 330 mJ was measured to be 6.9. The 20-pass amplifier is designed as a concatenation of stable resonator segments in which the beam is alternately Fourier transformed and relay-imaged back to the disk by a 4f-imaging optical scheme stage. The Fourier transform propagation makes the output beam robust against spherical phase front distortions, while the 4f-stage is used to compensate the thermal lens of the thin-disk and to reduce the footprint of the amplifier