Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 52 (2019)

Negative muon spin rotation with low-density gas target undertransverse magnetic field to solve the proton radius puzzle
S. Kanda,∗1 K. Ishida,∗2 M. Iwasaki,∗1,∗2 Y. Ma,∗1,∗2 S. Okada,∗1 and M. Sato∗3
When a negative muon is captured by a nuclear
Coulomb potential, an electron around the nuclei iskicked out and the muon forms an exotic bound state
called muonic atom. Muonic atom provides a unique
opportunity to study the nuclear structure such as thecharge radius of the nuclei. In particular, the proton
charge radius attracts renewed interest since the measurement of the Lamb shift in muonic hydrogen.1) The
experiment derived a signiﬁcantly discrepant result compared to the results of electron-proton scattering andhydrogen spectroscopy. This discrepancy has been an
important unsolved problem in sub-atomic physics.
To obtain a new insight into the puzzle, a new measurement of the ground-state hyperﬁne splitting (HFS)in muonic hydrogen is planned. The experiment aims
to determine the proton Zemach radius, which is deﬁned as a convolution of the electric charge and magnetic
moment distributions. As a preliminary experiment toward the spectroscopy of HFS, a muon spin rotation(µSR) measurement with a gaseous hydrogen target wasproposed.2) The objective of the experiment was to understand the spin depolarization process involving themuonic hydrogen atom.
In a magnetic ﬁeld, muon spin rotates with the Larmor frequency, which depends on the hyperﬁne state ofmuonic atom. Therefore, we can quantify the population of the hyperﬁne states and the depolarization eﬀect
by measuring the angular asymmetry of decay electrons.
Figure 1 illustrates the experimental setup at Port4

Fig. 1. Experimental setup: (a) cross-sectional view; (b)view from downstream. The numbers in the parentheses
denote: (1) negative pulsed muon beam, (2) Helmholtz
coils, (3) aluminium gas chamber, (4) top electron detectors, and (5) bottom electron detectors.
∗1
∗2
∗3

RIKEN Cluster for Pioneering Research
RIKEN Nishina Center
High Energy Accelerator Research Organization (KEK)Fig. 2. Decay electron time spectrum with deuterium gas
target at 1 atm. No magnetic field was applied. Eachline corresponds to the respective fitting result.

in RIKEN-RAL muon facility. A transverse magnetic
ﬁeld was applied using the coils, which are parts of
the CHRONUS spectrometer. Decay electrons from themuonic atoms were detected by the segmented scintillation counters with silicon photomultiplier (SiPM) readout. The detectors were originally developed for themuonium production experiment at Port3.3) A study
conducted in 20164) revealed that a countermeasure forthe background arising from the duct-streaming neutrons is essential for suﬃcient signal-to-noise ratio. Accordingly, the detectors were placed away from the beamaxis. The inner walls of the target chamber were covered
with silver plates to reduce the lifetime of wall-stopped
muons via nuclear capture.
The experiment was conducted in 2018 with a gaseous
deuterium target to establish the measurement procedure. Deuterium was selected owing to its longerlifetime of polarization instead of protium. Figure 2
shows a measured time spectrum of electrons from themuon decays. The spectrum was analyzed using a ﬁtting function containing three exponential components
and a constant background. Each exponential component corresponded to the muon lifetime in silver (87 ns),aluminium (864 ns), and deuterium (2195 ns). The
beam momentum was optimized at several target densities considering the muonic hydrogen yield. The analysis
for the µSR measurement under the transverse magnetic
ﬁeld is in progress.
References

1) R. Pohl et al., Nature 466, 213 (2010).
2) S. Kanda et al., J. Phys. Conf. Ser. 1138, 012009 (2018).
3) S. Okada et al., RIKEN Accel. Prog. Rep. 50, 244 (2016).
4) M. Sato et al., RIKEN Accel. Prog. Rep. 51, 228 (2017).

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