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

Abstract

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.

Implementation of Local Chiral Interactions in the Hyperspherical Harmonics Formalism

“…Overall, we confirm the chiral order-by-order convergence patter, already discussed in references [19,20], but there shown only for the binding energy and the point-proton radius, which does not include the single nucleon input. Interestingly, when comparing the 4 He theoretical charge radius with the newest muonic atom measurement from reference [61], we see that the µ − r c results are still consistent with the experiment, leaving, however, space for meson exchange currents to help improve the theoretical precision, which is by far lower than the experimental one.…”

“…As expected, at 3 He, 3 H, and 4 He systems at N2LO computed using either the single-nucleon CODATA-2014 values (columns e-r c ) or the more precise muonic atoms data (columns µ-r c ). The theoretical results are compared to data from the electron-nucleus system [56,58] and, when available, to data obtained from the muon-nucleus system [61].…”

“…The uncertainty bars include the numerical uncertainty of the EIHH method as well as the uncertainties coming from the truncation of the chiral expansion. The horizontal lines are the experimental values from electron scattering (solid line) [56] and from muonic atoms (dashed line) [61].…”

Laser spectroscopy of light muonic atoms and the nuclear charge radii

“…In total, ten transition frequencies in µp [23,24], µd [25], µ 4 He [26] and µ 3 He were measured (manuscript on µ 3 He is in preparation). A low background rate of 1 event/h was observed in all these measurements as due to the use of a continuous muon beam.…”

The muX project

“…In the past, the absolute nuclear charge radii < r 2 > 1/2 of almost all stable nuclei have been determined with a typical accuracy of 10 −4 -10 −3 by measuring the 2p − 1s transition energy [2]. More recently, the radii of the lightest nuclei were measured by the CREMA collaboration (Section 21 [3]) using laser spectroscopy on muonic atoms [4][5][6][7].…”