Tobias Nebel

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.

Thin-Disk Yb:YAG Oscillator-Amplifier Laser, ASE, and Effective Yb:YAG Lifetime

We report on a thin-disk Yb:YAG laser made from a Q-switched oscillator and a multipass amplifier delivering pulses of 48 mJ at 1030 nm. The peculiar requirements for this laser are the short delay time (< 500 ns) between electronic trigger and optical output pulse and the time randomness with which these triggers occur (with trigger to next trigger delay ges 1.5 ms). Details concerning the oscillator dynamics (-switching cycle, intensity stabilization), and the peculiar amplifier layout are given. Simulations of the beam propagation in the amplifier based on the Collins integral and the measured aspherical components of the disk reproduce well the measured beam intensity profiles (with higher order intensity moments) and gains. Measurements of the thermal lens and ASE effects of the disk are also presented. A novel method to deduce the effective Yb:YAG upper state lifetime (under real laser operation and including ASE effects) is presented. That knowledge is necessary to determine gain and stored energy in the active medium and to understand the limiting factors for energy scaling of thin-disk lasers.

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.

Status of the muonic hydrogen Lamb-shift experiment

The Lamb-shift experiment in muonic hydrogen (μ– p) aims to measure the energy difference between the atomic levels to a precision of 30 ppm. This would allow the r.m.s. proton charge radius rp to be deduced to a precision of 10–3 and open a way to check bound-state quantum electrodynamics (QED) to a level of 10–7. The poor knowledge of the proton charge radius restricts tests of bound-state QED to the precision level of about 6 × 10–6, although the experimental data themselves (Lamb-shift in hydrogen) have reached a precision of  × 10–6. Values for rp not depending on bound-state QED results from electron scattering experiments have a surprisingly large uncertainty of 2%. In our Lamb-shift experiment, low-energy negative muons are stopped in low-density hydrogen gas, where, following the μ– atomic capture and cascade, 1% of the muonic hydrogen atoms form the metastable 2S state with a lifetime of about 1 μs. A laser pulse at λ ≈ 6 μm is used to drive the 2S → 2P transition. Following the laser excitation...

The size of the proton and the deuteron

We have recently measured the 2S1/2F=1 − 2P3/2F = 2 energy splitting in the muonic hydrogen atom μp to be 49881.88 (76) GHz. Using recent QED calculations of the fine-, hyperfine, QED and finite size contributions we obtain a root-mean-square proton charge radius of rp = 0.84184 (67) fm. This value is ten times more precise, but 5 standard deviations smaller, than the 2006 CODATA value of rp = 0.8768 (69) fm. The source of this discrepancy is unknown. Using the precise measurements of the 1S-2S transition in regular hydrogen and deuterium and our value of rp we obtain improved values of the Rydberg constant, R∞ = 10973731.568160 (16) m−1and the rms charge radius of the deuteron rd = 2.12809 (31) fm.

The proton radius puzzle

By means of pulsed laser spectroscopy applied to muonic hydrogen (μ− p) we have measured the 2SF = 11/2 – 2PF = 23/2 transition frequency to be 49881.88(76) GHz [1]. By comparing this measurement with its theoretical prediction [2, 3, 4, 5, 6, 7] based on bound-state QED we have determined a proton radius value of rp = 0.84184(67) fm. This new value differs by 5.0 standard deviations from the COD ATA value of 0.8768(69) fm [8], and 3 standard deviation from the e-p scattering results of 0.897(18) fm [9]. The observed discrepancy may arise from a computational mistake of the energy levels in μp or H, or a fundamental problem in bound-state QED, an unknown effect related to the proton or the muon, or an experimental error.

Is the proton radius a player in the redefinition of the International System of Units

It is now recognized that the International System of Units (SI units) will be redefined in terms of fundamental constants, even if the date when this will occur is still under debate. Actually, the best estimate of fundamental constant values is given by a least-squares adjustment, carried out under the auspices of the Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants. This adjustment provides a significant measure of the correctness and overall consistency of the basic theories and experimental methods of physics using the values of the constants obtained from widely differing experiments. The physical theories that underlie this adjustment are assumed to be valid, such as quantum electrodynamics (QED). Testing QED, one of the most precise theories is the aim of many accurate experiments. The calculations and the corresponding experiments can be carried out either on a boundless system, such as the electron magnetic moment anomaly, or on a bound system, such as atomic hydrogen. The value of fundamental constants can be deduced from the comparison of theory and experiment. For example, using QED calculations, the value of the fine structure constant given by the CODATA is mainly inferred from the measurement of the electron magnetic moment anomaly carried out by Gabrielses group. (Hanneke et al. 2008 Phys. Rev. Lett. 100, 120801) The value of the Rydberg constant is known from two-photon spectroscopy of hydrogen combined with accurate theoretical quantities. The Rydberg constant, determined by the comparison of theory and experiment using atomic hydrogen, is known with a relative uncertainty of 6.6×10−12. It is one of the most accurate fundamental constants to date. A careful analysis shows that knowledge of the electrical size of the proton is nowadays a limitation in this comparison. The aim of muonic hydrogen spectroscopy was to obtain an accurate value of the proton charge radius. However, the value deduced from this experiment contradicts other less accurate determinations. This problem is known as the proton radius puzzle. This new determination of the proton radius may affect the value of the Rydberg constant . This constant is related to many fundamental constants; in particular, links the two possible ways proposed for the redefinition of the kilogram, the Avogadro constant NA and the Planck constant h. However, the current relative uncertainty on the experimental determinations of NA or h is three orders of magnitude larger than the ‘possible’ shift of the Rydberg constant, which may be shown by the new value of the size of the proton radius determined from muonic hydrogen. The proton radius puzzle will not interfere in the redefinition of the kilogram. After a short introduction to the properties of the proton, we will describe the muonic hydrogen experiment. There is intense theoretical activity as a result of our observation. A brief summary of possible theoretical explanations at the date of writing of the paper will be given. The contribution of the proton radius puzzle to the redefinition of SI-based units will then be examined.

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.

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.