Julian J. Krauth

Theory of the n=2 levels in muonic deuterium

Abstract The present knowledge of Lamb shift, fine- and hyperfine structure of the 2S and 2P states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several 2S −2P transition frequencies in muonic deuterium ( μ 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 μ 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.

Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius Rd from D spectroscopy alone of 2.1415(45) fm. This value is independent of the measurements that lead to the proton charge radius, and five times more accurate than the value found in the CODATA Adjustment 10. The improvement is due to the use of a value for the 1S->2S transition in atomic deuterium which can be inferred from published data or found in a PhD thesis.

Experiments towards resolving the proton charge radius puzzle

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.

Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy.

Multipass laser cavity for efficient transverse illumination of an elongated volume

A multipass laser cavity is presented which can be used to illuminate an elongated volume from a transverse direction. The illuminated volume can also have a very large transverse cross section. Convenient access to the illuminated volume is granted. The multipass cavity is very robust against misalignment, and no active stabilization is needed. The scheme is suitable for example in beam experiments, where the beam path must not be blocked by a laser mirror, or if the illuminated volume must be very large. This cavity was used for the muonic-hydrogen experiment in which 6 μm laser light illuminated a volume of 7 × 25 × 176 mm3, using mirrors that are only 12 mm in height. We present our measurement of the intensity distribution inside the multipass cavity and show that this is in good agreement with our simulation.

Theory of the n = 2 levels in muonic helium-3 ions

Abstract The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → 2P transition frequencies in the muonic helium-3 ion, μ3He+. This ion is the bound state of a single negative muon μ- and a bare helium-3 nucleus (helion), 3He++. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radius and the nuclear structure effects to the hyperfine splitting in μ3He+. With this review we continue our series of theory summaries in light muonic atoms [see A. Antognini et al., Ann. Phys. 331, 127 (2013); J.J. Krauth et al., Ann. Phys. 366, 168 (2016); and M. Diepold et al. arXiv:1606.05231 (2016)]. Graphical abstract

Improved x-ray detection and particle identification with avalanche photodiodes

Avalanche photodiodes are commonly used as detectors for low energy x-rays. In this work, we report on a fitting technique used to account for different detector responses resulting from photoabsorption in the various avalanche photodiode layers. The use of this technique results in an improvement of the energy resolution at 8.2 keV by up to a factor of 2 and corrects the timing information by up to 25 ns to account for space dependent electron drift time. In addition, this waveform analysis is used for particle identification, e.g., to distinguish between x-rays and MeV electrons in our experiment.

On the double peak structure of avalanche photodiode response to monoenergetic x-rays at various temperatures and bias voltages

The double response of a large area avalanche photodiode, a planar RMD model S1315, to 6-keV x-rays was investigated as a function of APD biasing voltage and for different operating temperatures. Our data are consistent with the interpretation that the dissimilar APD response is due to x-ray interactions in the different APD-layer structures; interactions in the APD entrance layer just below the front electrode, where the electric field intensity is very low lead to pulses with higher risetime and lower amplitudes, when compared with interactions in the deeper layers where the electric field is more intense. Average pulse risetime values of 14 and 7 ns have been measured in our setup, the slower pulses presenting average amplitudes which are around 20% lower than those of the faster pulses. While the fast risetime does not depend significantly on APD biasing voltage and on temperature, the slow risetime presents a slight decrease with increasing bias voltage and decreasing temperature, a behaviour that is consistent with the increase of the electric field as a result of the increase in the APD biasing voltage. The fraction of the slow pulses reduces from 60% to 40% as the APD biasing increases from about 1.58 to 1.64 kV, indicating a reduction in the thickness, from 25 to 15 μm, in the weak-electric-field entrance layer.

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He–4He Isotope Shift

Abstract 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 ( μ 4 He ) + . 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 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.