Marc Diepold

Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen

Proton Still Too Small Despite a protons tiny size, it is possible to measure its radius based on its charge or magnetization distributions. Traditional measurements of proton radius were based on the scattering between protons and electrons. Recently, a precision measurement of a line in the spectrum of muonium—an atom consisting of a proton and a muon, instead of an electron—revealed a radius inconsistent with that deduced from scattering studies. Antognini et al. (p. 417; see the Perspective by Margolis) examined a different spectral line of muonium, with results less dependent on theoretical analyses, yet still inconsistent with the scattering result; in fact, the discrepancy increased. A precision spectroscopic measurement of the proton radius indicates a growing discrepancy with respect to scattering results. [Also see Perspective by Margolis] Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (μp, that is, a proton orbited by a muon). We measured the 2S1/2F=0-2P3/2F=1 transition frequency in μp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S1/2F=1-2P3/2F=2 transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, rZ = 1.082(37) femtometers, and the magnetic radius, rM = 0.87(6) femtometer, of the proton. We also extracted the charge radius, rE = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.

Laser spectroscopy of muonic deuterium

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science, this issue p. 669 The charge radius of the deuteron is several standard deviations smaller than the previously accepted value. The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ–. We measured three 2S-2P transitions in μd and obtain rd = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value rd = 2.1424(21) fm. The μd value is also 3.5σ smaller than the rd value from electronic deuterium spectroscopy. The smaller rd, when combined with the electronic isotope shift, yields a “small” proton radius rp, similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

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.

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.

Lifetime and population of the 2S state in muonic hydrogen and deuterium

Radiative deexcitation (RD) of the metastable 2S state of muonic protium and deuterium atoms has been observed. In muonic protium, we improve the precision on lifetime and population (formation probability) values for the short-lived {\mu}p(2S) component, and give an upper limit for RD of long-lived {\mu}p(2S) atoms. In muonic deuterium at 1 hPa, 3.1 +-0.3 % of all stopped muons form {\mu}d(2S) atoms. The short-lived 2S component has a population of 1.35 +0.57 -0.33 % and a lifetime of {\tau}_short({\mu}d) = 138 +32 -34 ns. We see evidence for RD of long-lived {\mu}d(2S) with a lifetime of {\tau}_long({\mu}d) = 1.15 +0.75 -0.53 {\mu}s. This is interpreted as formation and decay of excited muonic molecules.

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.