Journal of Nuclear and Radiochemical Sciences, Vol. 19, pp. 8-13, 2019

ArticlesNon-destructive, position-selective, and multi-elemental analysis method involving negative
muons
Kazuhiko NINOMIYA*
Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
Received July 14, 2019; Accepted September 27, 2019; Published online October 4, 2019
Elemental analysis is of fundamental importance in several scientific domains. Many elemental analysis methods
have been developed till date, with particular importance having been given to non-destructive analysis methods.
In this paper, we review a novel non-destructive, position-selective, and multi-elemental analysis method for bulk
material that utilizes a new type of probe, a negative muon. When a muon is stopped by an atom in a material,
muonic X-rays are emitted. Due to the large mass of a muon, the energy of muonic X-rays is very high, and the“X-ray fluorescence analysis” method using a muon can solve the problem of self-absorption in an ordinary
method using an electron. Two studies involving quantitative and depth-profiling analysis of archeological artifacts by this method are reviewed in this work. We also discuss the scope for future research using this method.

1. Introduction
Many elemental analysis methods that utilize various
probes have been developed till date in several research fields.
Among them, non-destructive analysis methods are particularly useful, although these have proven to have accuracies
inferior to destructive analysis methods in most cases. The
usefulness of non-destructive methods stems from the fact thata sample can be utilized for further processes after a round of
non-destructive analysis. Therefore, non-destructive methods
are advantageous for the analysis of valuable samples. The
development of an elemental analysis method that enables theanalysis of all elements in a given sample, even bulk samples
with high positional sensitivity, is a major goal for analyticalscientists at present. Recently, a new elemental analysis
method that satisfies these conditions by utilizing a negative
muon (MIXE: muon induced x-ray emission) has been developed and applied in several studies1-6. A negative muon is anelementary particle, and intense muon beams generated in an
accelerator are used in many studies. With recent advancement in accelerator technology to produce intense muon
beams, it has become possible to use muons for practical elemental analyses7-10.
A muon’s mass is about 207 times that of an electron(105.658 MeV/c2). When a muon is injected into a substance, it
gradually loses its kinetic energy due to its interaction withelectrons and finally comes to a stop. Because a negative
muon has the same charge as an electron, it binds with nuclei.
An atom in which a negative muon has replaced an electron iscalled a muonic atom. The binding energies of a muon in theorbital states of a muonic atom are about 200 times higher thanthose of an electron with the corresponding principal quantum
number. Although much research has been conducted on themuon capture process in an atom11-13, the process is still notcompletely understood. During the initial stages of muonic
atom formation, the captured muons are highly excited.
However, then, because there is only one muon in a muonic
atom, and all other muon atomic orbits are vacant, the muon
immediately de-excites to the muonic 1s state. As a result,,
electrons by muon-electron Auger processes and characteristic
X-rays (muonic X-rays) are emitted. Since a muon is 200*Corresponding author. E-mail: ninokazu@chem.sci.osaka-u.ac.jp
Fax: +81-6-6850-6999*

times heavier than an electron, the muon atomic orbit is muchcloser to the nucleus than the electron atomic orbit and thebinding energy is much larger. Therefore, the energies ofmuonic X-rays are 200 times higher than those of the characteristic X-rays of electrons. After a muon reaches the 1s muon
atomic orbit, it either decays into an electron and two neutrinos within its lifetime14, or gets absorbed into the nucleus in
the case of heavy nuclei. The muon absorption reaction is very
similar to EC (electron capture) decay, leading to the formation of a Z-1 nucleus15.
Muonic X-rays can be applied to elemental analysis by
X-ray spectroscopy as well as X-ray fluorescence. As aforementioned, because muonic X-rays have higher energy thanthe characteristic X-rays from electrons, muonic X-rays canpenetrate samples easily. As a result, the impact of X-ray
absorption by the sample on the results can be ignored in a
muonic X-ray measurement; this is a significantly large problem in X-ray fluorescence analysis. Further, even light elements such as carbon, that are difficult to analyze using
conventional X-ray fluorescence analysis have large muonic
X-ray energies. For example, the energy of the Kα X-ray (2p1s transition) of a muonic carbon atom is 75 keV16, which is theenergy corresponding to the lead KX-ray line in the case ofordinary X-ray fluorescence. The probability of muonic X-ray
emission depends on the probability of muonic atom formation. One muonic atom is formed when a muon stops in it, andmultiple muonic X-rays are emitted during the muon de-excitation process17. Therefore, highly sensitive elemental analysis
is possible using muonic X-rays. However, it is difficult topredict muon capture probabilities in each element precisely
because the probabilities are slightly altered by the chemical
environment of the muon capturing atom18-20. It was revealedin our previous work1 that the muon capture probability for anelement is almost independent of the element concentration (inwt %) in a sample, implying that the analytical sensitivity ishardly be altered. When a muon beam is generated by anaccelerator, the incident energy into the sample can be selectedby the magnetic system in the beam transportation line. Since
the muon stopping depth in a sample depends on the incidence
energy of a muon, it is possible to control the position ofmuonic X-ray emissions, allowing the position of analysis tobe selected 2,3,21. For these reasons, we agree that muonic X-ray
measurement has superior features for elemental analysis: its© 2019 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 10/04/2019

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J. Nucl. Radiochem. Sci., Vol. 19, 2019

Ninomiya

PXRQ

Beam ductpolyimide foil
Germanium
detector~360 mm

Sample445 mm

417 mm
422 mmGermanium detector

Germanium detector

Figure 1. Schematic view of the experimental setup and photograph of the samples. The muon beam entered the air layer and irradiated on thesample. The sample was set at 45° with the beam direction. Muonic X-rays were measured by three high-purity germanium detectors. Two
Tempo-Tsuho coins were subjected to the muon-irradiation experiment; the left one is authentic, called Edo-Seiji, and the right one is an imitation, called Mito-Seiji.
muonic Sn (5-4) X-ray
muonic Cu (4-3) X-ray

muonic Cu (5-3) X-ray
muonic Pb (6-5) X-ray
muonic Cu (3-2) X-ray

103

muonic Sn (4-3) X-ray

Countsmuonic Pb (5-4) X-ray
muonic Cu (4-2) X-ray

102
Edo-Seiji

101

100

Mito-Seiji(Intensity × 0.1)

0

100

200

300

400

500

600

Energy /keV
Figure 2. Muonic X-ray spectrum for two Tempo-Tsuho coins: Edo-Seiji and Mito-Seiji. Muonic X-rays originating from muon capture on Cu,
Sn, and Pb are clearly observed. The numbers in parentheses indicate the change of the principal quantum number with the transition of theatomic muon.

use makes the method non-destructive, multi-elemental,
including light elements, and position selective.
The possibility of element analysis using muons waspointed out over 40 years ago22 , following which some pioneering studies have been conducted in this field23-26. However,previous works largely performed qualitative analyses due to alack of understanding of the muonic atom formation process
and difficulty in obtaining good quality data from low-intensity muon beams. In recent years, fundamental research on
muonic atom formation has been performed using an intense
muon beam source in the Japan Proton Accelerator ResearchComplex (J-PARC)27-31. The use of such intense muon beamsources has made elemental analysis using muonic X-rays
increasingly possible and significant progress has been madein applying this method to various samples, such as archeological artifacts, extraterrestrial materials, etc.1-3,32,33. In thispaper, we review two elemental analysis methods for archeological material, which were developed and verified at
J-PARC.
2. Quantitative elemental analysis of the interior of a bronze
artifact
To determine the elemental composition of old bronze coins
non-destructively1, muonic X-ray measurements were performed in the D2 experimental area of the MUon Science

Establishment (MUSE) in the Materials and Life Science
Facility (MLF), the Japan Proton Accelerator ResearchComplex (J-PARC)9. The schematic of the experimental setup
is given in Figure 1. The muon beam from the D2 beamline
was passed through a polyimide foil, then air, and finally irradiated onto the sample. Three coaxial-type germanium semiconductor detectors (GMX20, ORTEC Inc. USA) were placedaround the sample to measure the muonic X-rays emitted fromthe muonic atoms generated after the muon stopped in thesample. To reduce the background events, the measurement of
the muonic X-rays was performed only at the times coincident
with muon beam pulses. The muon irradiation was conducted
for each bronze coin over approximately 10 h. These bronze
coins were similar in their appearance, as shown in Figure 1,
but were made in different places. The coin on the left (EdoSeiji) in Figure 1 is authentic while the one on the right (MitoSeiji) is an imitation with different elemental compositions.
Muon irradiation analyses were also conducted for standard
bronze samples whose elemental compositions were alreadydetermined by ICP-AES (Inductively Coupled Plasma Atomic
Emission Spectroscopy) were also conducted. The energy of
the incident muon was 35 MeV/c, which corresponds to a stopping depth of ~ 250 μm from the sample surface. The spreadin the distribution of the muon stopping depth was estimatedto be 10% at the stopping position, about 25 μm in this case.
Figure 2 shows the spectra obtained by muon irradiation of

J. Nucl. Radiochem. Sci., Vol. 19, 2019Non-destructive, position-selective, and multi-elemental analysis method

0.15

Germanium
detector

X-ray intensity ratio(Sn/Cu)Bronze-3
0.1Bronze-2

Aluminum foil

Bronze-1

FP

SampleBeam duct

0.05

92 mm

(a)
0
0

0.05

0.1

10

0.15

PXRQ
EHDP

92 mm

Elemental ratio of
Sn/Cu in wt.%
0.15

Vacuum chamber

X-ray intensity ratio(Pb/Cu)Bronze-3
Germanium
detector

0.1

Figure 4. Experimental setup for elemental depth profiling for the
Tempo-koban sample with 0.2, 0.27, 0.30, 0.49, and 1.0 MeV incident
muon energy conditions. The irradiations were conducted in thevacuum chamber. Muonic X-rays were measured by two germanium
detectors. The sample was set at 45° with the muon beam direction.
The experiment with 5.6 MeV irradiation condition was performed
without the vacuum chamber as described in a previous paper35.

0.05

(b)
0
0

0.05

0.1

0.15

Elemental ratio of
Pb/Cu in wt.%
Figure 3. The relationship between the elemental ratios in weightpercent and muonic X-ray intensity ratios for (a) Sn/Cu and (b) Pb/
Cu.

for the bronze coins. The muonic X-rays from copper, tin, andlead atoms, which are the constituent elements of bronze,
could be clearly observed. The muonic X-ray spectra of thebronze coins are very similar to each other, but have different
intensities in each line. Since the intensity of the muonic
X-rays correspond to the number of muons captured in eachelement, it is possible to determine the elemental composition
from the intensity of the muonic X-rays. By focusing on themuonic X-ray intensities for muonic copper (4-3), muonic tin(5-4) and muonic lead (6-5), which have the highest counting
statistics in the measured energy range for each element, theelemental compositions of the bronze coins were quantitatively
determined. The numbers in parentheses indicate the change
in the principal quantum number with the transition of themuonic atom; for example, (4-3) implies muonic Nα X-ray.
Figure 3 shows the relationship between the elemental compositions and muonic X-ray intensities of Sn/Cu and Pb/Cu
obtained via measurements of the standard bronze samples.
As shown in Figure 3(a), the X-ray intensity of the muonic tin
atom increases with increase in the elemental composition oftin in the sample. The linear relationship between the muonic
X-ray intensities (muon capture probabilities) and elemental
composition with various alloys34, can be determined from thecalibration line, as shown in Figure 3. Additionally, the slopeof the proportional relationship is approximately 1. The linearity implies that the relative weight percentages of these
metals mostly correspond to the muonic X-ray intensity ratios;that is, the sensitivity is almost the same for any element, as
discussed above1. From the muonic X-ray intensity of thebronze coin, the elemental compositions were determinedusing the relationship shown in Figure 3. They were found to
be Cu: 77.7±1.6%, Sn: 12.5±1.5%, and Pb: 9.8±1.5% for the
Edo-Sheiji sample and Cu: 69.0±1.9%, Sn: 9.9±1.3%, and Pb:
21.1±2.6% for the Mito-Seiji sample. This indicates thatthough two bronze coins seem to have the same appearance,
they have different elemental compositions. These results are
consistent with the results of surface elemental analysis using
X-ray florescence; Cu: 77.8%, Sn: 14.5%, and Pb: 7.8% for the
Edo-Seiji sample and Cu: 73.6%, Sn: 12.2%, and Pb: 14.2% for
the Mito-Seiji sample. It should be noted that conventional
X-ray fluorescence analysis determines only the surface elemental composition, while muonic X-ray analysis identifies
the deep interior of the sample. Thus, the bulk elemental composition of the bronze coins was successfully quantitatively
determined without destroying the samples.
3. Non-destructive depth-profiling of gold-silver alloy
The stopping depth of an incident muon can be controlled
by adjusting the current of the beamline magnets and selecting
the incident muon energy. Non-destructive elemental depthprofiling analysis was carried out by changing the incident
muon energy for an old Japanese gold coin of Tempo-koban,
made in the nineteenth century3, 35. The bulk gold componentof the Tempo-koban is about 57 wt%, and most of its residue issilver36. In addition, the Tempo-koban has a gold rich layer
near the surface that is several micrometers thick owing tochemical treatment to enhance the gold brilliance36. The
experiment was conducted at the MUSE D2 beamline in the
MLF J-PARC. The incident energies of muon were 0.20, 0.27,
0.30, 0.49, 1.0, and 5.6 MeV; the stopping depths of these incident muon energies in the Tempo-koban was calculated to be
1.6, 2.2, 2.4, 4.7, 15.0, and 210 μm, respectively. The details of
the calculation procedures are described in our previous
report 3. Figure 4 shows the schematics of the experimental
setup. Unlike the experiment with bronze coins, in this case11

J. Nucl. Radiochem. Sci., Vol. 19, 2019

Ninomiyamuonic Au (7-6) X-ray

10

3

gamma-raymuonic Ag (5-4) X-ray
muonic Au (6-5) X-ray

muonic Au (5-4) X-ray

Countsmuonic Ag (4-3) X-ray

102
0.20 MeV

1.0 MeV(Intensity × 0.1)

101
100

200

300

400

500

Energy /keV
Figure 5. Muonic X-ray spectra for the Tempo-koban with 0.20 and 1.0 MeV incident muon energies. Muonic X-rays of gold (5-4) and silver(4-3) were clearly identified. The X-ray intensity ratios of Au/Ag were found to be clearly different based on the incident muon energies.

4. Isotopic analysis by muonic KX-ray measurement
Since the muon atomic orbitals are very close to the nucleus,
the energies of these levels are strongly influenced by the proton distribution of the nucleus, i.e., isotope37. As a result, alarge isotopic shift on the muonic X-ray is observed, particularly for KX-rays, which involve the orbit closest to the nucleus
during the transition. Proton distributions have been studied
for various nuclei by measuring the muonic KX-ray energies38,39. In other words, it is possible to identify the isotopes
by muonic X-ray measurements; thus, in addition to elemental
analysis, isotopic analysis is also possible using the muonic
X-ray measurement owing to the isotopic shift of the muonic
X-rays. In a recent work, non-destructive isotopic analysis by
the muonic X-ray measurement was conducted for lead sam-

X-ray intensity ratio(Au/Ag)

5
4
3
2
1
0

0

1

2

3

4

5

Elemental ratio of
Au/Ag in wt.%
Figure 6. The relationship between the elemental ratio of Au/Ag inweight percent and X-ray intensity ratio obtained from muon irradiations for gold-silver alloys with gold contents of 50, 60, and 80 wt%.

100

Au content in wt. %the muon irradiation was performed in vacuum, except at 5.6
MeV, because a low-energy muon is stopped by the air layer
before reaching the sample. The muonic X-rays emitted fromthe sample were measured using HPGe detectors. Muon irradiations on standard gold-silver alloys containing 50, 60, and80 wt% of gold were also performed.
Figure 5 shows the muonic X-ray spectra in the 100–500
keV region for the Tempo-koban sample with two incident
muon energies 0.20 and 1.0 MeV. The muonic X-rays originating from the muon captures by the gold (muonic gold (5-4)line) and silver (muonic silver (4-3) line) atoms can be clearly
identified. The intensity ratios of the X-rays emitted from thegold and silver atoms appear to be dependent on the incident
muon energies, implying that the elemental compositions of
the Tempo-koban are different owing to different stopping
depths of the muon. To conduct quantitative analysis, the calibration curve between the muonic X-ray intensity and the elemental composition ratio was obtained in the same manner asthat in the experiment with bronze: by analyzing the data of
the standard samples of Au/Ag alloy, and obtaining a linear
relationship (see Figure 6). From this relationship and theintensity of the muonic X-ray, the gold content corresponding
to each muon stopping depth was determined, as shown in
Figure 7. The content of gold was about 80% near the surface
and about 57% at depths greater than 2.4 μm from the surface
in Tempo-koban. The results for both the surface and interiorof the Tempo-koban were consistent with the values determined by destructive analysis. Thus, using this method, accurate elemental depth-profiling is possible by muon irradiation
using various muon incident energies.

80
60
40
20
0
0

10

20

210

 
Figure 7. Elemental depth profiling of the Tempo-koban in gold
contents. The gold concentration near the surface is higher than thatin deep regions. This depth profile is consistent with the analysis
results from the destructive approach36.

Non-destructive, position-selective, and multi-elemental analysis method

ples for the first time, and the results were consistent withthose from mass spectrometry40. Owing to the absence ofpractical methods for non-destructive isotopic analysis, amuon-based method has potential for application in various
scientific studies.
5. Three-dimensional elemental analysis
The elemental depth-profiling analysis by the muon has
already been achieved, as discussed using the example ofTempo-koban. In addition, further attempts to develop threedimensional (3D) elemental analyses have already been madeby combining the depth information from an incident muonenergy with two-dimensional muonic X-ray detectors41, 42. A
large solid-angle CdTe imaging detector was developed for aspace observation satellite 43. This detector was used by
Katsuragawa et al. in 3D imaging analysis with muons inmuon irradiation experiments for a patterned LiF sample
sealed within an aluminum box. By controlling the incident
muon energies, the muons were selectively stopped in LiF
inside the aluminum box, and the muonic X-rays of fluorine
atoms were measured. The pattern of LiF in the aluminumbox was clearly identified with a spherical resolution of a few
hundred microns. By further improving the detectors, it isexpected that clearer images can be obtained, and 3D elemental analysis by muons can be developed.
6. Measurement of gamma rays emitted after nuclear capture of muon
Similar to muonic X-rays, the gamma rays emitted after theformation of muonic atoms can also be used for the elemental
analysis. After reaching the 1s orbit, the muon is absorbed by
the nucleus through weak interactions. By this reaction, one
proton in the nucleus is converted to one neutron in the nucleus
and a Z-1 nucleus is formed. Because the mass of the muon isconverted to the excitation energy of the nucleus, the resulting
Z-1 nucleus is in a highly excited state. A part of this excitation energy is removed by the neutrino generated in the muon
absorption reaction. From the excited Z-1 nucleus, the gamma
rays and/or neutrons are emitted in the de-excitation process44.
If the residual Z-1 nucleus is unstable, it further leads to
gamma-ray emission and decay. The studies on the muon
nuclear absorption processes and nuclear structures have
employed gamma-ray measurements 45, 46. In addition to theelemental analysis 47, isotopic analyses 48 have also been conducted by gamma-ray measurements, with the results being
consistent with the values determined by other methods,
including muonic X-ray measurements.
7. Summary and future scope
In recent years, owing to the availability of high-intensity
muon beams, non-destructive elemental analysis methods
using muons have been developed and applied to samples invarious research fields. Recently, non-destructive isotopic
analysis for heavy elements and 3D analysis have also become
possible. Further development is expected in various directions, for example, development of high-resolution 3D elemental analysis by improving the imaging detector, high-precision
analysis by developing measurement systems with large solid
angles and high efficiency using multiple germanium detectors, and non-destructive isotopic analysis including light elements using high-energy resolution detectors. In the future,
this method of elemental analysis can be applied to diverse scientific disciplines such as archeology and geology.

J. Nucl. Radiochem. Sci., Vol. 19, 201912

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