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Register a new userLine shape analysis of the K$beta$ transition in muonic hydrogen
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The K$beta$ transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding triplet-to-singlet ratio, and the kinetic energy distribution in the $3p$ state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian approach.
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The first measurement of the temperature dependence of the muon transfer rate from muonic hydrogen to oxygen was performed by the FAMU collaboration in 2016. The results provide evidence that the transfer rate rises with the temperature in the range 104-300 K. This paper presents the results of the experiment done in 2018 to extend the measurements towards lower (70 K) and higher (336 K) temperatures. The 2018 results confirm the temperature dependence of the muon transfer rate observed in 2016 and sets firm ground for comparison with the theoretical predictions.
We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.
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 ($mumathrm{d}$). 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 $mumathrm{d}$. 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.
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, $T_mathrm{cas}^{mu p} = (37pm5)$ ns, was found.
We provide an up to date summary of the theory contributions to the 2S-2P Lamb shift and the fine structure of the 2P state in the muonic helium ion $(mathrm{mu^4He})^+$. This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the $mathrm{^3He-^4He}$ isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of $n=2$ theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.
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