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.

Semi-empirical analysis of leptons in gases in crossed electric and magnetic fields. I. Electrons in helium.

In this series, we outline a strategy for analyzing electrons and muons in gases in crossed electric and magnetic fields using the straightforward transport equations of momentum-transfer theory, plus empirical arguments. The method, which can be carried through from first principles to provide numerical estimates of quantities of experimental interest, offers a straightforward, physically transparent alternative to "off-the-shelf" simulation packages, such as Magboltz and GEANT. In this first article, we show how swarm data for electrons in helium gas subject to an electric field only can be incorporated into the analysis to generate electron swarm properties in helium gas in crossed electric and magnetic fields and to estimate the Lorentz angle in particular. The subsequent articles in the series analyze muons in crossed fields using similar transport theory, though the absence of muon swarm data requires empiricism of quite a different nature.

Semi-empirical analysis of leptons in gases in crossed electric and magnetic fields. Part II. Transverse compression of muon beams.

This article employs fluid equations to analyze muon beams in gases subject to crossed electric and magnetic fields, focusing, in particular, on a scheme proposed by Taqqu [Phys. Rev. Lett. 97, 194801 (2006)], whereby transverse compression of the beam is achieved by creating a density gradient in the gas. A general criterion for maximizing beam compression, derived from first principles, is then applied to determine optimal experimental conditions for µ+ in helium gas. Although the calculations require the input of transport data for (µ+, He), which are generally unavailable, this issue is circumvented by "aliasing" (µ+, He) with (H+, He), for which transport coefficient data are available.

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}.

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.