Journal of Nuclear and Radiochemical Sciences, Vol. 18, pp. 5-8, 2018

ArticlesMuon Transfer Rates from Muonic Hydrogen Atoms to Gaseous Benzene and Cyclohexane
Makoto Inagakia,*, Kazuhiko Ninomiyaa, Go Yoshidaa,b, Wataru Higemotoc,
Naritoshi Kawamurad, Yasuhiro Miyaked, Taichi Miurab and Atsushi Shinoharaa
Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
Radiation Science Center, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki
305-0801, Japanc
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata-Shirane, Tokai, Naka, Ibaraki
319-1195, Japand
Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), 1-1 Oho,
Tsukuba, Ibaraki 305-0801, Japanab

Received January 25, 2018; Accepted February 2, 2018: Published online February 22, 2018
The chemical effect of the muon transfer process from muonic hydrogen atom was examined for benzene andcyclohexane under low pressure gaseous conditions. The muon transfer rates were investigated by measuring theresulting muonic X-rays resulting from muon irradiation of hydrogen and neon gas mixtures. The muon transfer
rates to benzene and cyclohexane carbon atoms were very similar in the gaseous state. The results differed fromprevious results obtained for muon and pion transfer rates to benzene and cyclohexane under high density liquidconditions. It was concluded that the difference originated from the atomic muon state of the muonic hydrogenatoms with a large radius.

1. Introduction
A muonic atom is an atomic system in which one atomic
electron is replaced with a negatively charged muon. The
mass of a muon is 207 times larger than that of an electron andthe lifetime of a muon is 2.2 μs. Muonic atoms are formed
when a muon is captured in the Coulomb field of a nucleus.
Because a muon has a different mass from that of an electron,
the size and energy of atomic orbitals of the muonic atom arecompletely different from those of electrons. The binding
energy of the atomic muon is very large and the radius of themuon atomic orbital is very small and the muon is close to the
nucleus. Usually in the first step of the muon capture andmuonic atom formation processes, the muon can be found at ahighly excited atomic muon level, and the muon immediately
de-excites to the muonic 1s state by emitting Auger electrons
or characteristic muonic X-rays. When a muon is captured bya hydrogen atom, a muonic hydrogen atom that consists onlyof a muon and a nucleus (a proton) is formed. Because amuonic hydrogen atom has no electrons, the radius of themuonic hydrogen atom is approximately 200 times smaller
than that of an electronic hydrogen atom. Therefore, thecharge of the muonic hydrogen nucleus is strongly shielded by
the compact muon orbital and muonic hydrogen atom canbehave like a neutron. As a result, muonic hydrogen atom candiffuse freely, it can even pass through the electron clouds ofother atoms. When the muonic hydrogen atom approaches thenucleus of another Z≥2 atom, the muon moves from themuonic hydrogen atom to a deeper atomic muon level of the
Z>2 atom and forms a new Z>2 muonic atom. This process incompounds and mixtures is called muon transfer.1
To investigate the muonic atom formation process, determination of the muon capture probability by each atom in a substance is important. Multiple models have been proposed to
explain the muon capture probability.2-4 In these studies, the*Corresponding author. E-mail: inagakim12@chem.sci.osaka-u.
ac.jp, Fax: +81-6-6850-6999

chemical environmental effects in the muon capture process
have been singled out and named the “chemical effect.” Themuon capture probability strongly depends on the molecularchemical structure of the muon-capturing atom.5-7 For example, muon capture ratios per atom of carbon compared to thoseof oxygen are different between CO2 molecule and CO molecule.8 Similar studies have also been intensively carried out
with a negative pion; and because the negative pion has a similar mass to that of the negative muon, the formation processes
for pionic atoms and muonic atoms are thought to be very similar.9-11
The chemical effects of muonic (or pionic) atom formation
in a hydrogen-containing system have also been reported.12-14
The capture probability of hydrogen atoms is dependent on themolecular structure of the capturing molecule, and is strongly
influenced by the strength of the hydrogen bond.13,14 Changes
in the formation process originate from the difference in theinitial state of the captured muon in the hydrogen atom. On
the other hand, all of the chemical effects from the transfer
processes have not been fully examined. Muon transfer processes for hydrogen gas mixtures and other gaseous compounds under various pressure conditions were observed andthe following muon de-excitation processes were examined.15
The pressure dependence on muonic X-ray intensity patterns(X-ray structures) has already been reported, however, it is notclear whether such a dependence is due to a chemical effectfrom the muon transfer process or the difference in the muoncascading process after muon transfer by electron refilling. In
condensed substances, Shinohara et al.12 reported a chemical
effect for the pion transfer process between benzene and cyclohexane with carbon tetrachloride mixture. They reported thatthe pion transfer rate from pionic hydrogen atoms to the carbon atoms of benzene was about twice that of the carbon
atoms of cyclohexane. They concluded the difference originated from the difference between benzene and cyclohexanein steric hindrance around the carbon atoms.12 Inagaki et al.16
examined the chemical effect for muon transfer process in thesame system and found a small difference in muon transfer© 2018 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 02/22/2018

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InagakiFigure 1. Schematic view of the experimental setup.

Figure 2. Time deviation spectrum between the accelerator operation signal and muonic X-ray detection signal. The two peak components (2830 ns and 3430 ns) correspond to the muon beam injection
timing in the sample.

rates.
The chemical effects in the transfer processes have only
been reported using condensed phase samples.12,16 In suchhigh-density conditions, muon transfer occurs in a very shorttime scale. This fact implies that the chemical effects in thetransfer processes are apparent only from the excited state of
the muonic hydrogen atoms that can exist immediately after
capturing a muon in a hydrogen atom. This is consistent withthe existence of a chemical effects in the pion transfer processes because the pionic hydrogen atoms in the 1s state areunstable and the pion transfer processes occur only fromexcited state.
In this study, an examination was made on the chemical
effect in the muon transfer in benzene and cyclohexane in a
low-density gaseous state and the obtained results were compared with these in high-density conditions.16 Under low pressure conditions, the muon transfer rate should be low and thus,
the muon transfer process component was separated from thatof direct muon capture. Additionally, under such conditions, it
was possible to extract the ground state muonic hydrogen atom
contribution.
2. Experimental
The muon irradiation experiment was performed at the
MUSE D1 beam line in the Materials and Life Science
Experimental Facility of J-PARC, Ibaraki Prefecture, Japan in
2014. The experimental equipment consisted of a gas cham-ber, a diaphragm-type pressure gauge, a sample vessel, and agas handling system. A schematic view of the experimental
setup is shown in Figure 1. A thin polyimide film of 50 μm
thickness was used for the muon entering window. The measured samples were: C6H6 (0.2 kPa) + Ne (3.0 kPa) + H2 (96.8kPa), labeled as the C6 H6 sample; C6 H12 (0.2 kPa) + Ne (3.0kPa) + H2 (96.8 kPa), labeled as the C6H12 sample; and Ne (3.0kPa) + H 2 (97.0 kPa), labeled as the blank sample. The measurement times for each sample were 9.5 h, 9.1 h, and 3.7 hrespectively. Each sample was prepared by introducing thegases into the chamber to the requisite target pressure in theorder of benzene or cyclohexane, neon, and hydrogen.
A pulsed muon beam with a momentum of 19 MeV/c wasirradiated on each sample gas, and the emitted muonic X-rays
were measured using three germanium semiconductor detectors (Canberra GL0515R, Ortec Loax 36300, and Ortec GLP16195). All muonic X-ray events were recorded for both
energy and timing information, which is the elapsed time fromthe frequency signal supplied from the accelerator facility to
the X-ray detection. The EGS5 Monte Carlo simulation code17
was used to determine the detection efficiencies of the germanium detectors based on a standard radiation source measurement.
3. Results
The time spectrum between the accelerator signal andmuonic X-ray detection for the C6H6 sample is shown Figure 2.

J. Nucl. Radiochem. Sci., Vol. 18, 2018

Muon Transfer Rates from Muonic Hydrogen Atoms to Gaseous Benzene

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Figure 3. Muonic X-ray spectra for the C6H6 and blank samples.

TABLE 1: Muonic X-ray intensity ratios of muonic carbon Lyman series to muonic neon Lyman series and Balmer series
for C6H6 and C6H12 samples. The intensities of muonic X-rays were determined from the sum of series X-rays. For example,
the μNe Balmer was obtained from the sum of Lα, Lβ and Lγ X-rays of muonic neon. The ratios correspond to the ratios ofmuon transfer rates.
C6H6 sample

C6H12 sample

C6H6 sample / C6H12 sample

μC Lyman / μNe Balmer

6.4 ± 0.7

5.7 ± 0.5

1.1 ± 0.2

μC Lyman / μNe Lyman

8.0 ± 1.3

8.8 ± 1.6

0.9 ± 0.2

Around 2830 ns and 3430 ns, a peak component derived fromthe muon direct capture process was observed just after themuon injection timing (prompt component) and a decreasing
signal over time was identified as the muon transfer process(delayed component). The prompt component consisted of adouble peak approximately 100 ns in width with a 600 ns
interval time that was coincident with the incident muon beam
cycle of J-PARC/MUSE. The events originating from themuon transfer process were obtained delayed from the muon
beam pulse because the muon transfer process occurs after
muonic hydrogen atom formation and collision with anothernucleus. Therefore, investigate the muon capture event wasinvestigated from the muon transfer process by extracting thedelayed component.
Figure 3 shows the energy spectra of the delayed components from 2980 ns to 3280 ns and from 3580 ns to 12230 ns of
the C6H6 and the blank samples. In the C6H6 sample, X-rays ofthe neon Balmer series (μNe Lα, μNe Lβ and μNe Lγ), carbon
Lyman series (μC Kα , μC K β and μC Kγ), and neon Lyman
series (μNe K α) were identified. A similar spectrum was
obtained from the C6H12 sample. Small signals from muonic
oxygen, nitrogen, and carbon atoms were observed in the spectrum of the blank sample. These signals were derived fromthe polyimide film used for the muon entrance window of thechamber. The X-ray intensity ratio of carbon and oxygen in
the blank sample spectrum was used, and the muonic carbon
X-rays contributed from the polyimide film were corrected in
the spectra of the C6H6 and C6H12 samples.
From the series of muonic X-ray intensities, the number of
captured muons in each element were determined. Table 1
shows the ratio of the muonic X-ray intensity of the delayedcomponent of carbon to that of neon in the C6 H6 and C6 H12samples. Since the muon transfer rates to neon is reasonably
assumed to be equal in both samples, the muonic X-ray intensity ratio shows the relative values of the muon transfer rates tocarbon based on the muon transfer rate to neon. The values
using the neon Lyman series were smaller than the values

using the neon Balmer series because Kβ and the subsequent
events on the neon Lyman series could not be observed due tothe low detection efficiency. The muon transfer rates to carbon in the C6H6 and C6H12 samples were within the experimental error derived from peak count statistics, as shown in Table
1. This indicated that no clear difference was found in on themuon capture for carbon in these two molecules.
4. Discussion
In this experimental system, no significant difference in themuon transfer rate to carbon atoms was observed between
benzene and cyclohexane. This result differed from thoseobtained in the liquid system previously.12 For pion transfer,the transfer rate to the carbon atom of benzene is two times
higher than that of cyclohexane.12 Such a difference would becaused by the difference in muonic hydrogen atom states
between the two systems. The sample densities of benzene
and cyclohexane in this experiment were 5 orders of magnitude lower than those in the corresponding liquid system. The
muon transfer rate to carbon in the present experimental system was estimated to be on the order of 105 s−1 from the decay
constant of the delayed component shown in Figure 2, and themuon transfer was completed with an average time on theorder of 10 −6 s. This time scale is slower than the muon cascading process in a hydrogen atom; de-excitation to the 1s or
2s state is completed within 10 −7 s, and most of the muons inhydrogen atom reach the 1s state while the muon transfer proceeds.12 On the other hand, considering the density ratio in gas
and liquid samples, the muon transfer rate in the liquid system
was estimated to be on the order of 1010 s−1, and the transfer
was finished with a mean time on the order of 10 −11 s. At 10−11s, most of the captured muons have not reached the muonic 1s
state and 70% of the captured muons remain in a state with aprincipal quantum number n ≥ 3.18 Therefore, in the liquid system, muon transfer was considered to mainly occur from theexcited state with a principal quantum number n ≥ 3.

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Likewise, in the case of pion transfer in a liquid system, thetransfer occurs only from the excited state, because in pionichydrogen atoms, due to the strong interaction between the pionand proton, the lifetime in the ground state is extremely short(~10 −15 s). On the other hand, in the case of muonic hydrogenatoms, a strong interaction does not exist between the muonand proton and the ground state lifetime is long (10 −6 s). In
this way, pion transfer in the liquid state occurs only from theexcited state of pionic hydrogen atoms, most of the muontransfer in the liquid state occurs from the muonic hydrogenatoms at the principal quantum number n ≥ 3, and muon transfer in the gas state occurs from the ground state muonic hydrogen atoms.
The difference in steric hindrance around the carbon atomof benzene and cyclohexane causes a chemical effect in thetransfer process, that is, a difference in the transfer rates tocarbon atoms.12 When a muonic hydrogen atom, or a pionichydrogen atom, approaches a cyclohexane carbon atom, thesteric hindrance is larger than in the case of benzene. In thecase of benzene, only one hydrogen atom is bound to eachbenzene carbon atom, whereas two hydrogen atoms are boundto the cyclohexane carbon atom. Such a steric hindrance maystrongly inf luence the transfer from the excited state ofmuonic or pionic hydrogen atoms. For example, a pionichydrogen atoms with the principal quantum number n = 3 hasa radius approximately 9 times larger than that of a muonichydrogen atoms in the ground state. As a result, a significant
chemical effect on the muon transfer process was not observedin the present experimental system, in which muon transfer
occurred only from the ground state muonic hydrogen atoms.
4. Conclusion
The muon transfer rates in gaseous benzene and cyclohexane were investigated from the relative muonic X-ray intensities of carbon to those of neon. Although a chemical effect on
the muon and pion transfer processes were reported between
benzene and cyclohexane in a liquid system, such a chemical
effect was not observed within the measurement accuracy ofthis experiment. In gaseous state muon transfer, most of themuon transfer occurred from the muonic hydrogen atoms in
the ground state. Ground state muonic hydrogen atom has asmall radius and the effect of steric hindrance was very small.
On the other hand, in a liquid system, most of the muon andpion transfer processes occur from the excited states. As aresult, steric hindrance during transfer is large and a difference in the transfer process between benzene and cyclohexane
is observed.

Inagaki
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