Line shape analysis of the Kβ transition in muonic hydrogen

Abstract

The Kβ 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 method.PACS. 36.10.-k, 07.85.Nc Exotic atoms, X-ray spectrometers a present address: Bosch Termotecnologia, S.A., EN 16 -Km 3,weak, or strong interactions but also collision-induced processes at quite distinctive conditions, because the distance scale in the case of exotic hydrogen is smaller by a factor m e /m X while the energy scale is larger by a factor m X /m e in comparison with usual atoms. Here, m e and m X denote the mass of electron and captured particle X, respectively.An exotic atom formed with hydrogen isotopes is exceptional, because it is electrically neutral. Hence, during its life time it is able to penetrate deeply into the atomic shells when colliding with other molecules. Various collisional processes strongly influence the development of the atomic de-excitation cascade, which manifests experimentally in a strong density dependence of the K X-ray yields [1,2,3,4]. Amongst others, in the Coulomb de-excitation process the energy released is transferred to kinetic energy [5] leading to a Doppler broadening for subsequently emitted X-rays.First evidence for such high-velocity exotic atoms was found in the charge-exchange reaction π − p → π 0 n with arXiv:1709.05950v2 [physics.atom-ph]

Pionic hydrogen and deuterium

“…For lower temperature, hydrogen and oxygen measurements were performed alternately. Figure 14.3: Spectra of the (3p − 1s) transitions in muonic [9] and pionic hydrogen [10] and pionic deuterium [7]. The narrow structures displayed inside the µH and πD lines demonstrate the resolution of the spectrometer equipped with a Si 111 crystal as measured by using an ECR source [19].…”

“…As the formation rate scales with collision probability, a density-dependent X-ray energy would demonstrate its appearance. No such effect was observed for either hydrogen and deuterium [7,9,10].…”

“…The possibility of performing high-statistics experiments of exotic hydrogen even in dilute targets with high-resolution devices like crystal spectrometers became possible by using the cyclotron trap (Section 13 [8]). Figure 14.1 shows the set-up of cyclotron trap and crystal spectrometer for the studies described here [7,[9][10][11]. With a massive specially tailored concrete shielding an improvement in the beam-induced background of up to a factor of 50 is achieved compared to previous experiments.…”

Cyclotron trap

“…This led to a successful series of measurements in muonic hydrogen and in both pionic hydrogen and deuterium, reducing typical measuring times to a month (Section 14 [14]). The line shape of the muonic hydrogen Kβ transition was determined with high precision as a prerequisite for later experiments in pionic hydrogen [15]. A method was developed to extract muons from the centre of the trap to form a low-energy muon beam.…”

Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm

“…At present, Bayesian methods are routinely used in many fields: astrophysics and cosmology [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ], particle physics [ 9 ], plasma physics [ 10 , 11 ], machine learning [ 12 ] and many others [ 13 , 14 ]. In the past few years, they were also applied to nuclear [ 15 , 16 ] and atomic physics [ 17 , 18 , 19 , 20 , 21 ]. On one hand, one of the reasons for this success is related to the possibility of assigning a probability value to models (hypotheses) from the analysis of the same set of data in a very defined framework.…”