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A comprehensive theory of the Lamb shift in light muonic atoms such as $\mu$H, $\mu$D, $\mu^3$He$^+$, and $\mu^4$He$^+$ is presented, with all quantum electrodynamic corrections included at the precision level constrained by the uncertainty of nuclear structure effects. This analysis can be used in the global adjustment of fundamental constants and in the determination of nuclear charge radii. Further improvements in the understanding of electromagnetic interactions of light nuclei will allow for a promising test of fundamental interactions by comparison with ``normal" atomic spectroscopy, in particular, with H-D and $^3$He-$^4$He isotope shifts., Comment: 21 pages, 4 figures, matched the published version

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the $\mu$p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after this cycle modifies the $\mu$p atom diffusion in the hydrogen gas and the arrival time of the $\mu$p atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the $\mu$p diffusion in the H$_2$ gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H$_2$ molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment., Comment: Submission to SciPost

Muonic atom spectroscopy -- the measurement of the x rays emitted during the formation process of a muonic atom -- has a long standing history in probing the shape and size of nuclei. In fact, almost all stable elements have been subject to muonic atom spectroscopy measurements and the absolute charge radii extracted from these measurements typically offer the highest accuracy available. However, so far only targets of at least a few hundred milligram could be used as it required to stop a muon beam directly in the target to form the muonic atom. We have developed a new method relying on repeated transfer reactions taking place inside a 100-bar hydrogen gas cell with an admixture of 0.25% deuterium that allows us to drastically reduce the amount of target material needed while still offering an adequate efficiency. Detailed simulations of the transfer reactions match the measured data, suggesting good understanding of the processes taking place inside the gas mixture. As a proof of principle we demonstrate the method with a measurement of the 2p-1s muonic x rays from a 5-{\mu}g gold target., Comment: 16 pages, 14 figures

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $\mu$p atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a $\mu$p atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by {the laser bandwidth and }collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where $\mu$p is formed and the laser spectroscopy will occur., Comment: 21 pages, 4 figures

The hyperfine splitting of the 5g -> 4f transitions in muonic 185,187-Re has been measured using high resolution HPGe detectors and compared to state-of-the-art atomic theoretical predictions. The spectroscopic quadrupole moment has been extracted using modern fitting procedures and compared to the values available in literature obtained from muonic X rays of natural rhenium. The extracted values of the nuclear spectroscopic quadrupole moment are 2.07(5) barn and 1.94(5) barn, respectively for 185-Re and 187-Re. This work is part of a larger effort at the Paul Scherrer Institut towards the measurement of the nuclear charge radii of radioactive elements., Comment: 15 pages, 8 figures, 8 tables; accepted for publication in Phys. Rev. C

We present a multi-pass amplifier which passively compensates for distortions of the spherical phase front occurring in the active medium. The design is based on the Fourier transform propagation which makes the output beam parameters insensitive to variation of thermal lens effects in the active medium. The realized system allows for 20 reflections on the active medium and delivers a small signal gain of 30 with M$^2$ = 1.16. Its novel geometry combining Fourier transform propagations with 4f-imaging stages as well as a compact array of adjustable mirrors allows for a layout with a footprint of 400 mm x 1000 mm., Comment: 7 pages, 6 figures

Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S$\,$-$\,$2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with $Z \geq 3$. In addition, our approaches towards a precise measurement of the Zemach radii in muonic hydrogen ($\mu$p) and helium ($\mu$$^{3}$He$^{+}$) are discussed. These results will provide new tests of bound-state quantum-electrodynamics in hydrogen-like systems and can be used as benchmarks for nuclear structure theories., Comment: 17 pages, 8 figures

High-precision measurements of the proton radius from laser spectroscopy of muonic hydrogen demonstrated up to six standard deviations smaller values than obtained from electron-proton scattering and hydrogen spectroscopy. The status of this discrepancy, which is known as the proton radius puzzle will be discussed in this paper, complemented with the new insights obtained from spectroscopy of muonic deuterium., Comment: Moriond 2017 conference, 8 pages, 4 figures

Novel thin-disk laser pump layouts are proposed yielding an increased number of passes for a given pump module size and pump source quality. These novel layouts result from a general scheme which bases on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard commercially available pump optics simply by intro ducing an additional mirror-pair. More pump passes yield better efficiency, opening the way for usage of active materials with low absorption. In a standard multi-pass pump design, scaling of the number of beam passes brings ab out an increase of the overall size of the optical arrangement or an increase of the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications, Comment: 16 pages, 9 figures

In the context of the Lamb shift measurement in muonic helium we developed a thin-disk laser composed of a Q-switched oscillator and a multi-pass amplifier delivering pulses of 150 mJ at a pulse duration of 100 ns. Its peculiar requirements are stochastic trigger and short delay time (< 500 ns) between trigger and optical output. The concept of the thin-disk laser allows for energy and power scaling with high efficiency. However the single pass gain is small (about 1.2). Hence a multi-pass scheme with precise mode matching for large beam waists (w = 2 mm) is required. Instead of using the standard 4f design, we have developed a multi-pass amplifier with a beam propagation insensitive to thermal lens effects and misalignments. The beam propagation is equivalent to multiple roundtrips in an optically stable resonator. To support the propagation we used an array of 2 x 8 individually adjustable plane mirrors. Astigmatism has been minimized by a compact mirror placement. Precise alignment of the kinematic array was realized using our own mirror mount design. A small signal gain of 5 for 8 passes at a pump power of 400 W was reached. The laser was running for more than 3 months without the need of realignment. Pointing stability studies is also reported here., Comment: 11 pages, 14 figures

We review the status of the proton charge radius puzzle. Emphasis is given to the various experiments initiated to resolve the conflict between the muonic hydrogen results and the results from scattering and regular hydrogen spectroscopy., Comment: 9 pages, Few Body Systems FB21 conference

The present manuscript summarizes novel studies on the application of large area avalanche photodiodes (LAAPDs) to the detection of X-rays and vacuum ultraviolet (VUV) light. The operational characteristics of four different LAAPDs manufactured by Advanced Photonix Inc., with active areas of 80 and 200 mm^2 were investigated for X-ray detection at room temperature. The best energy resolution was found to be in the 10-18% range for 5.9 keV X-rays. The LAAPD, being compact, simple to operate and with high counting rate capability (up to about 10^5/s), proved to be useful in several applications, such as low-energy X-ray detection, where they can reach better performance than proportional counters. Since X-rays are used as reference in light measurements, the gain non-linearity between 5.9 keV X-rays and light pulses was investigated. The gain ratio between X-rays and VUV light decreases with gain, reaching 10 and 6% variations for VUV light produced in argon (~128 nm) and xenon (~172 nm), respectively, for a gain 200, while for visible light (~635 nm) the variation is lower than 1%. The effect of temperature on the LAAPD performance was investigated. Relative gain variations of about -5% per Celsius degree were observed for the highest gains. The excess noise factor was found to be independent on temperature, being between 1.8 and 2.3 for gains from 50 to 300. The energy resolution is better for decreasing temperatures due mainly to the dark current. LAAPDs were tested under intense magnetic fields up to 5 T, being insensitive when used in X-ray and visible-light detection, while for VUV light a significant amplitude reduction was observed at 5 T., Comment: 25 pages, 40 figures, submitted to JINST

Metastable ${2S}$ muonic-hydrogen atoms undergo collisional ${2S}$-quenching, with rates which depend strongly on whether the $\mu p$ kinetic energy is above or below the ${2S}\to {2P}$ energy threshold. Above threshold, collisional ${2S} \to {2P}$ excitation followed by fast radiative ${2P} \to {1S}$ deexcitation is allowed. The corresponding short-lived $\mu p ({2S})$ component was measured at 0.6 hPa $\mathrm{H}_2$ room temperature gas pressure, with lifetime $\tau_{2S}^\mathrm{short} = 165 ^{+38}_{-29}$ ns (i.e., $\lambda_{2S}^\mathrm{quench} = 7.9 ^{+1.8}_{-1.6} \times 10^{12} \mathrm{s}^{-1}$ at liquid-hydrogen density) and population $\epsilon_{2S}^\mathrm{short} = 1.70^{+0.80}_{-0.56}$ % (per $\mu p$ atom). In addition, a value of the $\mu p$ cascade time, $T_\mathrm{cas}^{\mu p} = (37\pm5)$ ns, was found., Comment: 4 pages, 3 figures

An experiment measuring the 2S Lamb shift in muonic hydrogen mup is being performed at the Paul Scherrer Institute, Switzerland. It requires small and compact detectors for 1.9 keV x rays (2P-1S transition) with an energy resolution around 25% at 2 keV, a time resolution better than 100 ns, a large solid angle coverage, and insensitivity to a 5 T magnetic field. We have chosen Large Area Avalanche Photodiodes (LAAPDs) from Radiation Monitoring Devices as x-ray detectors, and they were used during the last data taking period in 2003. For x-ray spectroscopy applications, these LAAPDs have to be cooled in order to suppress the dark current noise, hence, a series of tests were performed to choose the optimal operation temperature. Specifically, the temperature dependence of gain, energy resolution, dark current, excess noise factor, and detector response linearity was studied. Finally, details of the LAAPDs application in the muonic hydrogen experiment as well as their response to alpha particles are presented., Comment: 20 pages, 19 figures, submitted to Nucl. Instr. and Methods A

We have measured the heat conduction between 0.05 K and 1.0 K of high purity silicon wafers carrying on their polished faces a variety of thin dielectric films and polycrystalline thin metallic films. Using a Monte Carlo simulation to analyze the conduction measurements, we have determined the phonon mean free path within the films, and found all of them to be much shorter even than in typical bulk amorphous solids, with no exceptions. We have also measured the internal friction of these films below 10 K and found, however, their internal friction at low temperatures strikingly close to that of amorphous solids, both in magnitude and in their temperature independence, with the exception of the MBE Si and alloy Al 5056, whose internal friction is even much smaller than that of amorphous solids. The internal friction results indicate the phonon scattering in these thin films is the same as, or even much less stronger than, in other amorphous solids, according to the Tunneling Model. Thus, we conclude that the heat conduction measurements do not support the picture that the lattice vibrations of these films are glasslike, as had been surmised earlier for thin metallic films, on the basis of low temperature internal friction measurements alone [Phys. Rev. B 59, 11767 (1999)]. At the least, the films must contain additional scattering centers which lead to the very small phonon mean free path. Most remarkably, the MBE Si shows the same strong scattering of thermal phonons as do the other films, while having the negligible internal friction expected for a perfect film. The disorder causing the strong scattering of the thermal phonons in this film is completely unknown. The non-glasslike phonon scattering phenomena observed here in thin dielectric and metallic films deserve further investigations., Comment: 11 pages, 12 figures in REVTeX. Submitted to PRB

Internal friction and speed of sound of a-SiO(2) was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark the transition between the linear and non-linear regime. In the linear regime, excellent agreement with the Tunneling Model was observed for both the internal friction and speed of sound, with a cut-off energy of E(min) = 6.6 mK. In the non-linear regime, two different behaviors were observed. Above 10 mK the behavior was typical for non-linear harmonic oscillators, while below 10 mK a different behavior was found. Its origin is not understood., Comment: 1 tex file, 6 figures

The internal friction of e-beam amorphous silicon was measured in a magnetic field between 0 and 6 T, from 1.5-20 K, and was found to be independent of the field to better than 8%. It is concluded that the low energy excitations observed in this experiment are predominantly atomic in nature., Comment: 4 pages, 4 figures, REVTeX