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

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Measurement of muon spin rotation in muonic hydrogen atom
S. Kanda∗1 and K. Ishida∗2
A muonic atom is a bound-state consisting of a negative muon and a nucleus. The charge radius of thenucleus can be obtained by measuring the Lamb shift
in a muonic atom. In 2010, the Lamb shift of muonichydrogen (µp) measured at the Paul Scherrer Instituteindicated a significantly smaller proton charge radiusthan previously known from hydrogen spectroscopy
and electron-proton scattering.1)
In addition to the charge radius, the proton’s size isexpressed by the Zemach radius, which is defined byconvolving the charge and magnetic moment distribution. The Zemach radius is derived from the hyperfine
splitting (HFS), in contrast to the charge radius derived from the Lamb shift. For the Zemach radius, theconsistency between muonic and electronic measurements has not been fully discussed due to muonic measurements’ limited precision. To tackle this problem,
we are preparing for laser spectroscopy of the groundstate HFS in µp atoms.2)
In the experiment, a circularly polarized laser beam
excites µp atoms in the spin-singlet state to the spintriplet one. However, excited µp atoms are quenchedby spin-exchange collisions with protons.3) There is noexperimental result of this hyperfine quenching rate forµp atoms; therefore, we performed a muon spin rotation (µSR) measurement using a low-density gaseoushydrogen target. Only µp atoms in the spin-triplet
state show muon spin precession.
Figure 1 illustrates an experimental setup at Port 4of the RIKEN-RAL muon facility. A pulsed negative
muon beam irradiates hydrogen gas filled in an alu-Fig. 1. Experimental setup: (a) cross-sectional view; (b)view from upstream. The numbers in the parentheses
denote (1) hydrogen gas contained in an aluminum vessel, (2-5) electron detectors, (6) Helmholtz coils. Notethat the electron detectors are not shown in (b).
∗1∗2Institute of Materials Structure Science, KEK
RIKEN Nishina Center

Fig. 2. Decay electron time spectrum with protium gas target at 0.1 atm. A transverse magnetic field of 66.7 mT
was applied. Each line corresponds to the respective
fitting result. The vertical axis is normalized by thenumber of beam pulses.

minum vessel. The momentum of the beam was set
to 20 MeV/c. The gas pressure was 0.1 atm at room
temperature. A transverse magnetic field of 66.7 mT
was applied using a Helmholtz coil. Under these conditions, the quenching time of the triplet state andthe spin precession period are expected to be 500 nsand 320 ns, respectively. The electrons from the muon
decay were counted by a detector consisting of scintillating fibers and silicon photomultipliers (SiPMs).
Kalliope front-end electronics4) processed the signal
from the SiPM, and a multi-hit time-to-digital converter (TDC) recorded the time.
Figure 2 shows a decay electron time spectrum. Thespectrum has components corresponding to hydrogen,aluminum, silver, and constant background events.
The beam has a double-pulse structure with a 320 nsinterval. The first two peaks of the spectrum correspond to prompt electrons. Detailed analysis to extract the µSR asymmetry is in progress.
This experiment was conducted under the user program RB1970003 at the RIKEN-RAL muon facility.
This work was supported by Japanese JSPS KAKENHI Grant Numbers 18K13572 and 19H04618.
References

1) R. Pohl et al., Nature 466, 213 (2010).
2) S. Kanda et al., J. Phys. Conf. Ser. 1138, 012009 (2018).
3) J. S. Cohen, Phys. Rev. A 43, 466 (1991).
4) K. M. Kojima et al., J. Phys. Conf. Ser. 551, 012063(2014).

- 139 -1