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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

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

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