Measuring the α-particle charge radius with muonic helium-4 ions.

The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S-2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering1, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle2-5, in line with recent determinations of the proton charge radius6-9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

The size of the proton.

The proton is the primary building block of the visible Universe, but many of its properties-such as its charge radius and its anomalous magnetic moment-are not well understood. The root-mean-square charge radius, r(p), has been determined with an accuracy of 2 per cent (at best) by electron-proton scattering experiments. The present most accurate value of r(p) (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of r(p) as deduced from electron-proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant). An attractive means to improve the accuracy in the measurement of r(p) is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift (the energy difference between the 2S(1/2) and 2P(1/2) states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find r(p) = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by -110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

Thin-disk laser pump schemes for large number of passes and moderate pump source quality.

Thin-disk laser pump layouts yielding an increased number of passes for a given pump module size and pump source quality are proposed. These layouts result from a general scheme based on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard, commercially available pump optics with an additional mirror pair. More pump passes yield better efficiency, opening the way for the usage of active materials with low absorption. In a standard multipass pump design, scaling of the number of beam passes brings about an increase in the overall size of the optical arrangement or an increase in the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications.

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.

Muon cooling: longitudinal compression.

A 10 MeV/c positive muon beam was stopped in helium gas of a few mbar in a magnetic field of 5 T. The muon "swarm" has been efficiently compressed from a length of 16 cm down to a few mm along the magnetic field axis (longitudinal compression) using electrostatic fields. The simulation reproduces the low energy interactions of slow muons in helium gas. Phase space compression occurs on the order of microseconds, compatible with the muon lifetime of 2 µs. This paves the way for the preparation of a high-quality low-energy muon beam, with an increase in phase space density relative to a standard surface muon beam of 10^{7}. The achievable phase space compression by using only the longitudinal stage presented here is of the order of 10^{4}.

Laser spectroscopy of muonic deuterium.

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 r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The µd value is also 3.5σ smaller than the r(d) value from electronic deuterium spectroscopy. The smaller r(d), when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

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.

Proton structure from the measurement of 2S-2P transition frequencies of muonic hydrogen.

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 2S(1/2)(F=0)-2P(3/2)(F=1) transition frequency in µp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S(1/2)(F=1)-2P(3/2)(F=2) transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, r(Z) = 1.082(37) femtometers, and the magnetic radius, r(M) = 0.87(6) femtometer, of the proton. We also extracted the charge radius, r(E) = 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.

Observation of long-lived muonic hydrogen in the 2S state.

The kinetic energy distribution of ground state muonic hydrogen atoms mup(1S) is determined from time-of-flight spectra measured at 4, 16, and 64 hPa H2 room-temperature gas. A 0.9 keV component is discovered and attributed to radiationless deexcitation of long-lived mu p(2S) atoms in collisions with H2 molecules. The analysis reveals a relative population of about 1%, and a pressure-dependent lifetime (e.g., 30.4 +21.4/-9.7 ns at 64 hPa) of the long-lived mu p(2S) population, equivalent to a 2S quench rate in mu p(2S)+H2 collisions of 4.4 +2.1/-1.8 x 10(11) s(-1) at liquid-hydrogen density.