Available online at www.sciencedirect.com

NIM B
Beam Interactions
with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 266 (2008) 335–346
www.elsevier.com/locate/nimb

Pulsed source of ultra low energy positive muons
for near-surface lSR studies
Pavel Bakule a,*, Yasuyuki Matsuda a, Yasuhiro Miyake b, Kanetada Nagamine b,1,
Masahiko Iwasaki a, Yutaka Ikedo b,2, Koichiro Shimomura b,
Patrick Strasser b, Shunshuke Makimura bbaAdvanced Meson Science Laboratory, RIKEN Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan
Muon Science Laboratory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan

Received 5 July 2007; received in revised form 8 October 2007
Available online 21 November 2007

Abstract
We have produced a pulsed beam of low energy (ultra slow) polarized positive muons (LE-l+) and performed several demonstration
muon spin rotation/relaxation (lSR) experiments at ISIS RIKEN-RAL muon facility in UK. The energy of the muons implanted into asample is tuneable between 0.1 keV and 18 keV. This allows us to use muons as local magnetic microprobes on a nanometre scale. The
control over the implantation depth is from several nanometres to hundreds of nanometres depending on the sample density and muonenergy. The LE-l+ are produced by two-photon resonant laser ionization of thermal muonium atoms. Currently 15 LE-l+/s with 50%
spin polarization are transported to the lSR sample position, where they are focused to a small spot with a diameter of only 4 mm. The
overall LE-l+ generation eﬃciency of 3  105 is comparable to that obtained when moderating the muon beam to epithermal energies
in simple van der Waals bound solids. In contrast to other methods of LE-l+ generation, the implantation of the muons into the sample
can be externally triggered with the duration of the LE-l+ pulse being only 7.5 ns. This allows us to measure spin rotation frequencies of
up to 40 MHz.
Ó 2007 Elsevier B.V. All rights reserved.
PACS: 76.75.+i; 07.77.Ka; 36.10.Dr; 32.80.Rm; 41.75.–i; 42.65.Ky
Keywords: Low energy muons; Ultra slow muons; Muon spin rotation; Muonium generation; Muonium ionization; Vacuum-ultraviolet laser; Lyman-a;Thin ﬁlm

1. Introduction
Spin polarized LE-l+ are an important tool in condensed matter research for studying implantation-depthdependent properties of thin samples, nanomaterials,*

Corresponding author. Tel.: +44 1235445256; fax: +44 1235446881.
E-mail address: p.bakule@rl.ac.uk (P. Bakule).
1
Present address: (1) Atomic Physics Laboratory, RIKEN, Wako,
Saitama 351-0198, Japan. (2) Physics Department, University of California Riverside, Riverside, CA 92521, USA.
2
Present address: Toyota Central R&D Labs. Inc., 41-1 Yokomichi,
Nagakute, Aichi 480-1192, Japan.
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.nimb.2007.11.009

multilayered thin ﬁlms, or superconductors. The implantation depth can be easily controlled on a scale ranging fromseveral nanometres to hundreds of nanometres by re-accelerating LE-l+ from eV energies to tens of keV in an electrostatic ﬁeld. Using the technique of lSR (muon spinrotation and relaxation) [1,2] the beam of LE-l+ withwell-deﬁned initial spin polarization can be used as a depth
sensitive microscopic magnetic probe to measure local
magnetic ﬁelds or spin ﬂuctuations. Alternatively, in samples where it can bind to an electron to form muonium(Mu), the muonium can act as a light hydrogen-like probethat can be studied with the lSR technique.

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Over the past 10 years there has been a signiﬁcant eﬀort
to develop an eﬃcient method of LE-l+ generation fromthe surface muon beams with kinetic energies around
4 MeV available at various muon facilities [3–7].
A successful technique for generation of LE-l+ has beendeveloped using a continuous muon source at the Paul
Scherrer Institute (PSI) in Switzerland. This method, generating LE-l+ with epithermal energies down to 15 eV
without any loss of spin polarization, is based on themoderation of surface muons in wide band gap insulators.
Particularly suitable as moderators are van der Waals
bound solids, such as solid argon, neon or nitrogen. Most
reliable and eﬃcient so far has been moderation in a thinsolid nitrogen layer grown on a microstructured silver
substrate with large surface area. With such a target, theeﬃciency of converting incident muons to LE-l+ andtransporting them to the sample is as high as 3  105 [8].
We have been developing an alternative technique at the
RIKEN-RAL muon facility [9] located at the Rutherford
Appleton Laboratory (UK) using a pulsed surface muon
beam with intensity of 1.2  106 l+/s and pulse repetition
rate of 50 Hz. The basis of the technique has been
described in detail previously [10,11]. Brieﬂy, the surface
muon beam is thermalized in a hot tungsten foil of optimized thickness. The muons that diﬀuse to the surface
can be thermionically emitted to vacuum from the bulk
metal as neutral muonium atoms, as the work function
for muonium is much lower than that for the charged
Laser
power supplies

muon. The thermal muonium is then resonantly ionizedthrough a two-photon 1S?2P?unbound process by apulsed nanosecond laser to gain ‘‘free” muons with mean
kinetic energy of only 0.2 eV.
2. Details of the experimental setup
Fig. 1 shows the layout of the experiment as it is set up
at the RIKEN-RAL muon facility. The experimental setup
for performing lSR measurements with LE-l+ consists ofa laser system, an ultrahigh vacuum beamline (ion optics)
for eﬃcient transport of LE-l+ and a well shielded compact lSR spectrometer with all the necessary data acquisition electronics. Most of the laser parameters, as well as theparameters of the ion optics and tungsten target temperature can be remotely controlled and monitored from a dedicated control cabin.
2.1. Laser system
The binding energy of the electron in muonium is13.6 eV. We believe that the most eﬃcient laser ionization
can be achieved through two-photon resonant ionization
via the 2P state. This requires using two laser beams of different wavelengths. Firstly, for the strongly allowed electric-dipole transition from the 1S to 2P state, tuneableradiation around 122 nm (Lyman-a, 10.2 eV) is required.
The second laser beam, for the ionization from the 2P state,

RIKEN-RAL

T

Port 3 experimental area

T
T

HV

V
DAQ

T
TH

Air-conditioned
M&C

laser cabin

UHV(Figure 3)

Surface muon
beamline

Control cabin

Fig. 1. Layout of the experiment to generate the low energy positive muons at ISIS RIKEN-RAL muon facility. T mark the optical tables with the laser
system, UHV is the ultrahigh vacuum apparatus including the LE-l+ transport beamline (ion optics) and the lSR spectrometer, HV are the high voltage
power supplies for the ion optics, DAQ is the data acquisition electronics for the lSR spectrometer and the computer control of the ion optics, V is thecontrol rack for the ultrahigh vacuum system, TH is the high-current power supply for heating the tungsten foil, and M&C is the monitoring and remotecontrol electronics of the important components of the laser system.

P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

is required to have a wavelength shorter than 366 nm(3.4 eV) and, conveniently, the 355 nm laser beam generated as the third harmonic of a Nd:YAG laser can be used.
The laser beam at 122 nm has not only to be tuneable, butalso has to have a large bandwidth of about 200 GHz inorder to cover the Doppler width of the thermal energy
range of the muonium generated from the tungsten foil
heated to 2000 K.
The 122 nm radiation is generated through a nonlinear
frequency conversion process in a gaseous medium.
Although this is inherently rather ineﬃcient, being proportional to the third order nonlinear susceptibility v(3) tensor,
there is no possibility to use birefringent nonlinear crystals,
since none of the known nonlinear crystals is transparent atwavelengths below 190 nm. We are using a two-photon resonant sum-diﬀerence frequency mixing scheme in a phasematched krypton gas [12]. This frequency conversion
scheme unfortunately adds to the complexity of the laser
system as it requires two laser beams, but it provides a large
degree of tuneability and a high conversion eﬃciency(104). The ﬁrst laser is operating at 212.5 nm and istuned to a two-photon resonance in Kr, while the second
laser operating in the range of 810–850 nm provides thetuneability of the Lyman-a output and is designed to have
suﬃcient bandwidth to cover the Doppler width of muonium. The wide tuneability of the output allows us to ionize
under the same conditions not only muonium, but alsohydrogen or deuterium. This provides a useful tool for testing the whole apparatus without need for the muon beam.
Fig. 2 shows a simpliﬁed schematic diagram of the laser
system. The major part of laser system (generating therequired beams at 355 nm, 212.5 nm and 810–850 nm
respectively) is housed in an air-conditioned cabin connected via a duct with the rest of the apparatus at Port 3
of RIKEN-RAL muon facility (radiation area). The restof the laser system is attached to the ultrahigh vacuum
beamline and consists of beam steering and focusing optics,
and a Kr–Ar cell for generating the Lyman-a radiation
around 122 nm.
The details of the laser system and its layout have been
described previously [13]. The main changes since this publication include a threefold increase of the output at
355 nm to 380 mJ/pulse by replacing the Spectra physics
GCR-160 laser with a Continuum Powerlite 9025. At thesame time we have also installed an image relay telescopein the path of the 355 nm beam to image the laser output
to a distance of 12 m at the Port 3 experimental area
and thus ensure a more uniform intensity proﬁle insidethe ultrahigh vacuum beamline. Furthermore, an increasein the output pulse energy at 850 nm has been gained byadding a new 2-pass Ti:sapphire ampliﬁcation stage at
the output of the Continuum Mirage 800 laser and by
introducing image relay telescopes in the path of the pump
beams of the 4-pass Ti:sapphire ampliﬁer. The resulting
increase of the output pulse energy at 850 nm to 250 mJ/
pulse and the signiﬁcant improvement in the beam quality
has lead to an increase in the available pulse energy at the

337

SLM

Nd:YAG laser

Nd:YAG laser

Continuum
Powerlite 9025

Continuum
Powerlite 9025

532 nmSLM OPO +Ti:Sapphire amp .
Continuum Mirage 800

532 nm2-passTi:sapphire
amplifier532 nm4-pass 850 nm
Ti:sapphire
amplifier
SHG

Nd:YAG laser
Continuum
Powerlite 7025

OPO + OPA
laser
Continuum Mirage 3000

FHG

FHG

532 nm212.55 nm

815-855 nm

Nd:YAG laser
Continuum
Powerlite 9025

355 nmAir-conditioned laser cabin

0 eV
2P

355 nm355 nm Kr A-r
gas cellUHV
3 x10-8 hPa

122.09 nm(Lyman- α)1S-13.6 eV

Muonium

Tuneable
VUV
116-123 nm

Mu
atoms

RIKEN-RAL Port 3 Experimental area

Fig. 2. Schematic diagram of the laser system used for resonant ionizationof muonium. The image relay telescopes, beam focusing optics as well as
the laser beam diagnostics are not shown in this diagram. SHG is 7 mmlong BBO crystal (12  12  7 mm) for second harmonic conversion to
425 nm; FHG are temperature stabilised, 5 mm long, s-BBO crystals(12  12  5 mm) for conversion to 212.5 nm; SLM denotes single
longitudinal mode operation. An inset shows a simpliﬁed energy level
diagram of muonium to demonstrate the two-photon resonant ionization
scheme used to gain l+ with mean energy of just 0.2 eV.

generated second harmonic at 425 nm by a factor of two(to 140 mJ/pulse). The 425 nm beam is then split into two
beams and converted to 212.5 nm using two 5 mm long sBBO crystals with conversion eﬃciency of approximately
15%. Although the s-BBO crystals are superior to BBO
crystals at this wavelength, they still exhibit a signiﬁcantnonlinear absorption at 212.5 nm, resulting in a temperature gradient between the input and exit faces of the crystal. This introduces a phase mismatch for the generated
212.5 nm beam that reduces the conversion eﬃciency.
For this reason we have chosen to generate two separate
212.5 nm beams using two temperature stabilised s-BBO
crystals and to cool the centre of the output face of the sBBO by blowing nitrogen gas from a 1 mm diameter nozzle
onto the crystal.
The current output parameters of the laser system aresummarized in Table 1. The laser system has excellent long

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P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

Table 1
Summary of the laser output parameters
Wavelength
Pulse duration [FWHM]
Pulse energy
Bandwidth

355 nm
10 ns
380 mJ
30 GHz212.5 nm
4 ns
10–12 mJ (2 beams)<2 GHzterm reliability. Stable 24 h/day operation can be sustained
for up to 20 days, limited primarily by the lifetime of ﬂashlamps used in the Nd:YAG lasers.
It is important to note that the laser system is operating
at a repetition rate of only 25 Hz which means that only
half of the muon pulses are used for LE-l+ generation.
This limitation is due to strong thermal eﬀects associatedwith operating high power solid state laser systems that

810–850 nm
12 ns
12 mJ (2 beams)
180 GHz

116–123 nm (Lyman-a)
4 ns>0.5 lJ (2 beams)
180 GHzmake it diﬃcult to build 50 Hz system with same pulse
energy as achieved with the 25 Hz system.
2.2. LE-l+ transport beamline
Fig. 3 shows the layout of the LE-l+ beamline with thelSR spectrometer. The pulse of surface muons with
momentum of 28 MeV/c enters the apparatus through a

Fig. 3. Layout of the ultrahigh vacuum apparatus used to generate low energy positive muons (LE-l+) and to implant them in a sample. The sample ismounted on a cryostat inside a compact lSR spectrometer. Kr–Ar is the gas cell used to generate Lyman-a laser pulse by nonlinear frequency conversion,
CL is the cylindrical lens window of the Kr–Ar gas cell, M is a remotely controlled, retractable retro-reﬂection mirror for the Lyman-a beams, HR is aremotely controlled dielectric retro-reﬂection mirror for 355 nm beam, BS is a remotely controlled knife-edge beam stop to protect M from 212.5 nm and820 nm beams, NO is the ionization cell ﬁlled with NO gas for monitoring the Lyman-a pulse energy, T is the heated tungsten foil used to generatemuonium, G1 and G2 are vacuum gate valves, S1–S3 are electrodes of SOA immersion lens, and Q1–Q5 are electrostatic quadrupole focusing elements.
Section A-A shows the overlap of the laser beams in front of the tungsten foil.

P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

50 lm thick stainless steel window and is ﬁrst moderated
by 20 lm thick tungsten foil and then by a 45 lm thicktungsten foil heated by DC current up to 2100 K. The function of the ﬁrst foil is to shield the stainless steel window
from the heat of the 45 lm tungsten target. The area ofthe tungsten target foil exposed to the muon beam is
40 mm (W)  35 mm (H). The foils used were of 6 N purity(99.9999%W), manufactured by PLANSEE. The total
thickness of the foils is optimized to stop a signiﬁcant fraction of the incident beam near the rear surface of the hot
foil which results in eﬃcient emission of muonium atoms
from the hot tungsten target.
Two sets of laser beams at 212.5 nm and 820 nm areeach collinearly focused (with f = 500 mm plano-convex
spherical lenses) into the cell ﬁlled with mixture of krypton
and argon gas to generate two Lyman-a beams separated
vertically by 10–15 mm. These then enter the ultrahighvacuum chamber through a thin MgF2 cylindrical lens
(ROC = 78 mm; f = 120 mm @ 122 nm). The focusing
optics shapes each of the Lyman-a beams to have (in front
to the W foil) a width of only 1–2 mm (FWHM) in the horizontal plane and about 5–8 mm in the vertical plane. The
two Lyman-a beams pass through a 14 mm wide gap
between the tungsten target and the ﬁrst extraction grid
denoted as S1 and overlap the cloud of thermal muonium
atoms about 5 mm from the target surface. The 355 nm
beam is introduced to the beamline from the top at 30°
from the Lyman-a beam and is shaped similarly to havea width of 3 mm by 25 mm. All laser beams are retroreﬂected to maximize the ionization yield. Since the retroreﬂecting mirrors are placed at the distance of 0.5 m, thewidth of the ionizing pulse is eﬀectively broadened from
4 ns to 7 ns (FWHM). The overlap of the Lyman-a and355 nm beams deﬁnes an interaction region with a volume
of approximately 1 cm3.
In order to protect the Lyman-a retro-reﬂecting mirror(Acton Research; Al reﬂector coated with MgF2 protection
layer; reﬂectivity @ 122 nm 75%) from laser induced
damage, the laser beams were aligned slightly oﬀ-centre
on the cylindrical lens window. This dispersively separates
the laser beams, so that the 212.5 nm and 820 nm beams
can be blocked by a knife-edge beam stop placed in frontof the Lyman-a reﬂector.
The LE-l+ generated by the laser ionization are initiallyextracted by a low gradient electrical ﬁeld between thetungsten foil (held at 9.0 kV) and mesh electrode S1 (heldat 8.8 kV). S1 is the ﬁrst of three elements forming an
SOA immersion lens [14] which then re-accelerates theLE-l+ to 9.0 keV. Such arrangement is necessary in orderto minimize the energy variation of the re-accelerated
LE-l+ beam. The SOA lens also focuses the collected
LE-l+ to a tight spot of only 2.5 mm (FWHM) which isthen imaged to the sample surface with the ion transport
optics consisting of ﬁve electrostatic quadrupoles (Q1–
Q5), a bending magnet and an electrostatic deﬂector. In
this geometry the electrostatic deﬂector eﬀectively rotates
the muon spin polarization, which is originally anti-parallel339

to the momentum, by 90°. The muons implanted into thestudied sample are therefore horizontally polarized withthe spin perpendicular to the muon momentum.
The section of the beamline between the bending magnet
and the electrostatic deﬂector houses a retractable positionsensitive microchannel plate detector (ROENTDEK DLD80). This is used either for checking the yield and proﬁle of
the LE-l+ beam or for measuring D+ yield when optimizing the performance of the apparatus by ionizing the residual deuterium dissociated by the hot tungsten target.
The total transmission eﬃciency of the beamline has notbeen measured, but it is worth noting that there is a significant loss of muons due to decay. The overall path lengthfrom the tungsten target to the focus at the sample chamber is 3.9 m and the time-of-ﬂight for 9.0 keV muons is1.15 ls, resulting in 40% loss of LE-l+ due to decay.
We are planning to increase the acceleration voltage to18 keV. This will extend the range of available implantation energies and reduce the loss through decay in ﬂight
to about 28%.
2.3. Sample chamber and lSR spectrometer
The sample chamber, which has a diameter of 100 mm
and a length of 540 mm, can be isolated from the rest of
the ultrahigh vacuum beamline to allow changing ofsamples. The vacuum level in the apparatus is typically3  108 hPa when measured in the vicinity of the heatedtungsten foil. The vacuum level in the sample chamber
can be as low as 8  1010 hPa several days after a sample
change. Experiments with LE-l+can be started approximately 6 h after the sample change when the vacuum level
reaches about 1  107 hPa. Samples for the lSR studies
can be mounted on a closed circuit two-stage helium cryostat (Iwatani HE-05 with cooling power of 0.5 W at 4 K)
capable of cooling samples to about 10 K. Alternatively,
the sample chamber can accommodate a position-sensitive
microchannel plate detector (ROENTDEK DLD-40) thatis used to check the focusing of the LE-l+ beam. Theenergy of the muons implanted into the sample can be continuously varied from zero to 18 keV by applying voltage inthe range of +9.0 kV to 9.0 kV directly onto the sample
holder, which is isolated from the cryostat ﬁnger by
10 mm thick disc of sapphire.
Around this small sample chamber we have built a compact lSR spectrometer designed with the aim of providinga very high signal-to-noise ratio. The sample chamber issurrounded by a close arrangement of eight telescope pairsof plastic scintillation counters covering a solid angle of
80% of 4p sr. These detectors are inserted inside a solenoid
type coil with a magnetic length of 260 mm providing magnetic ﬁeld with strength of up to 60 mT parallel to themuon momentum and perpendicular to the spin. The magnetic ﬁeld homogeneity at the ﬁeld value of 8 mT over a
distance of 40 mm along the magnet’s axis is below
500 ppm. The ﬁeld homogeneity measured at 3 mT in thetransverse direction over a 10 mm radius is below

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P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

100 ppm. In-built into the magnet are also coils for compensating external magnetic ﬁelds of up to 250 lT (2.5 G)in any direction. The spectrometer can be therefore used
for transverse ﬁeld TF-lSR measurements as well as
measurements in zero external magnetic ﬁeld (ZF-lSR).
During the ZF-lSR measurements the zero ﬁeld compensation can be monitored using three single axis ﬂuxgate
magnetometers (Bartington Instruments MAG01-H
F-probes). These are mounted on the sample holder immediately behind the sample. The zero ﬁeld condition can thus
be maintained at a level 0.1 lT (1 mG) over a period of several days.
To make meaningful lSR measurements with the relatively low LE-l+ rates currently achieved requires a very
low background. The combination of the bending magnet
and electrostatic deﬂector provides selection of thetransported ions by mass and energy, respectively. This,
together with lead shielding with thickness of 100–
200 mm around the scintillation detectors and the sample
chamber, provides excellent background suppression toless than 0.012 counts over the 15 ls period after eachmuon pulse. In our case, when the laser is operating at half
the repetition rate of the ISIS accelerator, the signal-tonoise ratio can be further increased by subtracting the ﬁxed
background of the laser-oﬀ spectrum from the laser-on
spectrum. This allows us to observe LE-l+ decay to at least
6 muon lifetimes after the implantation, see Fig. 4.
3. Experimental results
3.1. Dependence of LE-l+ yield on laser pulse energy
The high eﬃciency of thermal muonium production
from the surface muon beam makes this method potentially capable of cooling surface muons to eV energies with
eﬃciency as high as 102. However, it is currently limitedby the available laser pulse energy, especially at
the Lyman-a frequency. The relative measurement of theenergy of the Lyman-a pulse is made by passing the
Lyman-a beam through an NO gas cell at a pressure of

Decay counts [/200ns]

10 5

10 4

10 3

10 2

10 1

0

2

4

6

8

10

12

14

16

18

Time [μs]Fig. 4. Histogram of positron counts originating from LE-l+ decay in thesample chamber.

Fig. 5. Dependence of the overall eﬃciency of LE-l+ generation on thepulse energy of the Lyman-a at 122 nm. The eﬃciency is determined as aratio of the number of LE-l+ delivered at the sample position per laser
pulse NLE-l and the number of incident surface muons per pulse Nl.
Relative values of pulse energy at 122 nm are determined from photoionization signal in NO gas. A single 122 nm beam was generated by focusing
212.5 nm beam with energy of 12 mJ and 820 nm beam with pulse energyof 13 mJ into the Kr–Ar cell. In this measurement the 122 nm beam was
not retro-reﬂected and was instead absorbed in the NO gas cell. Theenergy of the 355 nm pulse measured at the output of the laser was 280 mJ.

6.5 hPa and measuring the photoionization current [15].
Fig. 5 shows the observed dependence of the LE-l+ yieldon the Lyman-a energy. It shows that even though the laser
beam overlaps just a small fraction of the muonium cloud(1 cm3), the Lyman-a intensity is still not suﬃcient to saturate the Doppler broadened 1S–2P transition. We do notcurrently have a detector in our setup to measure the absolute pulse energy of the generated Lyman-a and can only
make a rough estimate of 1 lJ/pulse (total of 2 beams)
based on the integrated ionization current of the NO gas
cell. Given the beam size in front of the tungsten foil we
can estimate the peak intensity to be in the region of several
kW/cm2, still below the expected saturation intensity (for
200 GHz Doppler broadening) of 5 kW/cm2.
Signiﬁcant improvement (beyond an order of magnitude) of the Lyman-a pulse energy with the existing laser
system is not currently envisaged. Our previous investigations have shown that process of Lyman-a generation in
krypton gas is saturated [13] and gains achieved by compensating for the phase mismatch in krypton gas withargon gas are not as high as originally anticipated. Our
measurements show that for the phase-matched Kr–Ar
mixture the conversion eﬃciency from the UV beam at
212.5 nm is ﬁxed at approximately the 104 level. For pulse
energy E of the 212.5 nm beam in the range of 2–14 mJ the
Lyman-a energy is increasing approximately as E0.8. Therefore, further increase of Lyman-a energy and consequently
a higher LE-l+ yield should be possible by increasing thepulse energy of the 212.5 nm beam. Further improvementof the LE-l+ yield can be also expected from an increaseof the pulse energy of the 355 nm beam judging from theenergy dependence of the LE-l+ yield shown in Fig. 6.
With the current laser parameters, the overall conversion eﬃciency including transport losses is 3  105 andabout 15 l+/s are observed at the sample chamber – asigniﬁcant improvement on our ﬁrst result in 2001 of

P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

Fig. 6. Dependence of the overall eﬃciency of LE-l+ generation on thelaser pulse energy at the wavelength of 355 nm. The laser pulse energy wasmeasured at the output of the laser; the actual pulse energy at 355 nm
delivered inside the ultrahigh vacuum system is about 35% lower due toabsorption in air and losses on mirrors and optical windows. Estimatedintensity of 355 nm beam inside the vacuum system is about 30 MW/cm2(at maximum laser output of 380 mJ) Compared to the measurement
shown in Fig. 5, the muonium excitation to the 2P state was increased byusing two 122 nm beams vertically separated by 15 mm that were retroreﬂected by VUV mirror with reﬂectivity R = 0.75. Each of the 122 nm
beams was generated from 9.0 mJ at 212.5 nm and 9.5 mJ at 820 nm.

0.03 l+/s [13]. This has allowed us to perform simple lSR
experiments and demonstrate the feasibility of this method
for pulsed muon sources.
Of as much importance as the LE-l+ rate is the capability to focus the muons into a small spot at the sample, sincefor the lSR investigations with the LE-l+ only small samples may be available. While the full-width at half-maximum (FWHM) diameter of the incident surface muon
beam is 35 mm, the FWHM diameter of LE-l+ beam isabout 10 times smaller. The beam spot was measured witha position-sensitive MCP (ROENTDEK DLD-40) placedat the sample position. The spot-size measured at the focusof the LE-l+ beam accelerated to 9.0 keV is shown in
Fig. 7. Gaussian ﬁtting in the horizontal and vertical directions yields FWHM of 3.3 mm and 4.1 mm, respectively.
3.2. Pulse duration
A particularly important advantage of using the shortlaser pulse to ionize muonium is the improvement of themuon pulse structure and the capability of having an external control over the triggering of the LE-l+. The surface
muon beam at RIKEN-RAL has a double-pulse structure
consisting of 80 ns (FWHM) pulses separated by 320 ns.
The short laser pulses ionizing muonium atoms are triggered with an optimum delay of about 400 ns relative tothe surface muon pulse. This delay allows the muonium –having the mean thermal velocity of 20 mm/ls – to evaporate to a few millimetres away from the tungsten target andreach its maximum density in the laser beam volume. The
arrival time of the muons at the sample is determined by
the timing of the laser pulse plus a ﬁxed delay corresponding to a time-of-ﬂight (TOF) through the apparatus. As the341

Fig. 7. Plot of the 9 keV LE-l+ beam spot at the sample position
measured with a position-sensitive microchannel plate detector with aresolution of 0.5 mm.

muonium cloud is expanding relatively slowly, the laser
timing and consequently the LE-muon timing can be varied
around the optimum value by several hundred nanoseconds at the expense of the LE-l+ rate (the rate is approximately halved by delaying the muonium ionization by
400 ns relative to the optimum delay). As the laser itself
can be externally triggered with 1 ns accuracy, this feature
opens a possibility to perform new lSR measurements
requiring precise triggering of the muon implantation andsynchronization with pulsed sample excitation. The timeof muon implantation relative to an external laser trigger
is known to within the pulse width of the LE-l+ in the
TOF spectrum, which is below 10 ns. This pulse width of
the LE-l+ is completely independent of the complicatedpulse structure of the surface muon beam and is determined primarily by the duration of the laser pulse andpartly also by the acceleration voltage. The time-of-ﬂight(TOF) spectrum measured at sample position for 9.0 keV
muons is shown in Fig. 8.
3.3. Energy resolution
The generation of LE-l+ based on the laser ionization ofthermal muonium makes it possible to generate beams withextremely narrow energy resolution, as the LE-l+ havekinetic energy of only 0.2 eV after ionization. This is significantly lower than the intrinsic energy resolution of the
LE-l+ generated by moderation in van der Waals boundsolids, where the epithermal muons escape the moderator
with rms energy spread of about 15 eV. If the high energy
resolution of the order of several eV can be maintained
through re-acceleration, transport and deceleration up to
the sample, ultra-thin ﬁlms or surfaces could be studied
using the lSR technique with 1 nm resolution. The depth

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The eﬀect of the pulse-to-pulse pointing stability of thelaser beams is below 1 eV level. These contributions give an
estimate of the energy resolution of the extracted LE-l+ as
rE = 14 eV (33 eV at FWHM). The energy resolution canbe improved by reducing the extraction ﬁeld between thetungsten foil and S1 and possibly also by reducing the widthof the interaction region, though this would make alignmentof the retro-reﬂected Lyman-a beams more diﬃcult.
3.4. Test lSR experiments
Fig. 8. Time-of-ﬂight histogram of the 9.0 keV LE-l+ detected by
microchannel plate detector at the sample position. Time zero corresponds
to muonium ionization by the laser pulses. Gaussian ﬁt to this histogram
yields FWHM pulse duration of 7.5 ns.

resolution in the sample depends mainly on the density ofthe material and the muons’ struggling in it. To give an
example, for muons implanted in Al with a mean energy
of 20 eV and a standard deviation of 10 eV, the calculation
using the Monte Carlo code TRIM.SP [16,17] gives themean penetration depth to be just 0.7 nm with a spreadof 0.7 nm. Reducing the energy resolution below 10 eV,
however, does not signiﬁcantly reduce the width of themuon implantation proﬁle as it is determined by muons’
struggling in Al. In this respect the depth resolution of
the order of 1 nm should be achievable by either methodof LE-l+ generation but only using a pulsed muon beam.
For continuous muons beams, such as available at PSI, it
is necessary to determine the muon implantation time inorder to construct the lSR spectrum. This requires inserting a thin foil into the LE-l+ beam and thus broadening
the energy resolution at the sample to 400 eV [10].
In our experimental setup achieving the energy resolution of several eV at the sample is possible. The energy variation of the re-accelerated LE-l+ depends on thediﬀerences in the potential seen by the individual muonsat the point of laser ionization relative to the S1 electrode.
The diﬀerence in electrostatic potential over the 14 mm gap
between the tungsten foil and S1 is therefore kept low (atonly 200 V). The diﬀerences in electrostatic potential seenby the individual muons are mainly arising due to:(a) the width of the ionization region determined by theoverlap of the Lyman-a and 355 nm beams (including
the retro-reﬂected beams), which is of the order of
2 mm (FWHM), thus contributing to the standard
deviation of the muon energy with 13 eV;(b) the uneven distance between tungsten foil and S1
arising from bending of the heated tungsten foil into
the gap – this reduces the gap of 14 mm at the edgesof the foil to 12 mm at its centre – contributing to
the standard deviation of the muon energy with
4 eV;(c) any diﬀerences in aligning the two Lyman-a beams at
the same distance from S1 and parallel to S1 – also
contributing to the energy variation with 4 eV.

To demonstrate the feasibility of using the pulsed beamof LE-l+ for lSR measurements we have measured some
simple muon spin precession spectra in transverse magnetic
ﬁeld. Despite the relatively low rate of 15 l+/s implanted
into the sample, up to 106 positrons originating from themuon decay in sample ðlþ ! eþ þ me þ ml Þ can be detected
per day by the scintillation counters of our lSR spectrometer. The number of detected positrons as a function oftime after the muon implantation in each of the detector
pairs was recorded in eight histograms Ni(t) (i = 1, . . ., 8).
Let us assume for simplicity of the explanation that themuons are implanted into a metal, where muonium can
not be formed, and subjected to a static magnetic ﬁeld oriented perpendicular to the initial muon spin direction. The
time dependence recorded in these histograms then corresponds to the exponential muon decay with the muon lifetime sl modulated by the free muon spin precession with
Larmor precession frequency xl, and by the spin relaxation function G(t) and can be expressed in the form
N i ðtÞ ¼ N 0i et=sl ½1 þ Al Gl ðtÞ cosðxl t þ ui Þþ N BGði ¼ 1; . . . ; 8Þ;
i ðtÞ

ð1Þ

where N0i is normalization constant for each of the detector pairs. The initial phases ui are ﬁxed by the geometry
to the initial phase u1 (ui = ui1 + p/4 for i = 2, . . ., 8).
The background contribution and N BG
i ðtÞ to the signal
can in our setup be determined from every second muon
pulse when laser is oﬀ and the low energy muons are notincident on the sample. The spin relaxation function depends on the distribution of the local magnetic ﬁelds seenby the implanted muons. For example, if local ﬁelds havea Lorentzian distribution then GLl ðtÞ ¼ ekt . Simultaneousﬁtting of all eight histograms then allows determining theparameters xl, k and the initial amplitude of the precession
signal Al, the so-called diamagnetic asymmetry. It follows
from the angular distribution of the positrons originatingfrom the muon decay that the maximum value of Al when
integrated over all positron energies is equal to 1/3 if theimplanted muons are initially 100% spin polarized. The
asymmetry values in the vicinity of 0.2–0.25 are typicalfor lSR instruments, depending on the setup.
The LE-l+ generated by the ionization of muonium,
however, are only 50% spin polarized and the asymmetryis therefore expected to be half of the value typical forother lSR instruments. This polarization loss is a result

P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

of the interaction with the electron spin in the muonium
atom. The muonium bound state is formed with equal
probabilities for the muon and electron spins to be either
parallel (ortho-muonium) or anti-parallel (para-muonium).
In the case of anti-parallel spins, the hyperﬁne interaction
causes rapid depolarization of the initial muon spin
[18,19] and hence only half of the low energy muonsobtained by the muonium ionization are spin polarized.
In our ﬁrst experiment we have implanted LE-l+ withenergy of 9 keV into a 20 mm diameter silver sample atroom temperature. The initial diamagnetic asymmetry Al
determined by ﬁtting the data from the eight detector pairs
was AAgl ¼ 10:11  0:23% with no observable spin depolarization (G(t) = 1).
In order to visualize the muon spin precession signal wehave divided the detectors into two opposing groups offour detectors and added the positron signals in each group
into one histogram and subtracted the background signal
determined from the ‘‘laser oﬀ” data. The lSR asymmetry
spectrum from these two histograms NG1(t) and NG2(t) is
plotted in Fig. 9 simply as
a0 ðtÞ ¼

N G1 ðtÞ  N G2 ðtÞ:
N G1 ðtÞ þ N G2 ðtÞð2ÞThe amplitude of the oscillations determined from these
two histograms is consistent with multiplying the initial
diamagnetic asymmetry Al by a geometrical factor of
0.653, reﬂecting the fact that positron signal is integrated
over an angle of p rather than p/4 radians.
In our next test experiment we have used the pulsed LEl+ beam for depth-resolved lSR measurement analogous
to the measurements of Morenzoni et al. [17] of a thinmetallic ﬁlm sample coated on an insulator. The purposeof the experiment was to demonstrate the control overthe implantation energy and the mean implantation depth.
The principle of the experiment is described in detail byMorenzoni et al. [17] and relies on the fact that the stopping site of muons can be determined from the amplitudeof the spin precession signal of the ‘‘free” diamagnetic
muon (diamagnetic asymmetry) in the sample. The muonsthat penetrate through the metallic layer and thermalize in343

the insulator substrate will mostly form muonium. For thehalf of the muons that form para-muonium the polarization will be rapidly lost due to the hyperﬁne interaction
and for the rest that forms ortho-muonium the transitions
between muonium triplet states in a weak transverse magnetic ﬁeld B will yield a single Larmor precession frequency
of xMu = 87.619 Mrad/mT * B, about 100 times fasterthan the muon precession of xl = 0.852 Mrad/mT * B.
By choosing the ﬁeld B suﬃciently large, so that 2p/xMu
is much shorter than the binning interval of the positron
decay histogram, the muonium spin precession signal can
be averaged out. The muons that formed muonium willthen show in the measured signal as a loss of the diamagnetic asymmetry, which will be reduced proportionally to
reﬂect the remaining number of diamagnetic muons inthe sample.
Our sample, placed at the focus of the LE-l+ beam(4 mm FWHM), was an optically ﬂat SiO2 substrate,
20 mm in diameter, coated by sputtering with a pure Al
layer with a nominal thickness of 40 nm. The experiment
was performed at the room temperature under UHV conditions at a pressure of 109 hPa in a 4 mT (40 G) external magnetic ﬁeld transverse to the muon spin.
The implantation proﬁle for muons – taking into
account the muon energy, the incidence angle and the sample density – can be accurately calculated using the Monte
Carlo code TRIM.SP. Fig. 10 shows the calculated implantation proﬁles in the sample for several implantationenergies.
Fig. 11 shows the measured initial amplitude of the diamagnetic muon precession (diamagnetic asymmetry) as afunction of the muon implantation energy. This measured
dependence is in a good agreement with the calculated fraction of diamagnetic muons using the TRIM.SP program.
The measured asymmetry is a sum of contributions fromdiamagnetic muons that have thermalized in the Al layer
and from the small fraction of muons in the SiO2 substratethat did not form muonium; there is also a small background contribution from muons that thermalized in any
metal parts outside the sample, e.g. in the metal ring holding the edges of the sample. For muons that penetrate theFig. 9. Muon spin precession signal measured in pure Ag sample with 9 keV LE-l+. The signal represents asymmetry in the positron decay spectrum
observed between two opposing groups of four detectors. Since the signals from four detectors in each group were added into one histogram the amplitudeof the oscillations reﬂecting the spin precession of l+ is eﬀectively reduced. The diamagnetic asymmetry Al as deﬁned in Eq. (1) for eight individual
detectors can be obtained by dividing the amplitude of the spin precession signal shown here by a factor of 0.653.

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P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

SiO2

Al

Relative number implanted

0.3 keV

1 keV

energybackscatteredstopped in Al

0.3 keV

18.5%

81.5%

0.0%

1.0 keV

9.3%

90.7%

0.0%

3.0 keV

3.2%

96.8%

0.0%

5.0 keV

1.7%

58.2%

40.1%

stopped in SiO2

10.0 keV

0.7%

4.7%

94.6%

17.0 keV

0.3%

0.7%

99.0%

3 keV
5 keV

0

10 keV40

80

17 keV

120

160

Depth [nm]Fig. 10. The implantation proﬁles for LE-l+ in 40 nm thick Al layer on SiO2 substrate calculated for diﬀerent implantation energies using TRIM.SP code.
Calculation assumes narrow Gaussian energy distribution of the incident muons with a standard deviation of rE = 14 eV and the incidence angle being
perpendicular to the sample surface with ra = 5.

12

40 nm Al layer on SiO 2
10

Aμ [%]

8
6
4
2
0
0

5

10

15

20

Muon energy [keV]
Fig. 11. Energy dependence of the asymmetry of the diamagnetic muon
Al measured in SiO2 sample coated with 40 nm thick Al layer. For muon
implantation energies below 4 keV the muons are mostly stopped in Al
layer and remain as free muons and consequently the measured asymmetry approaches the maximum observable asymmetry Amax of the lSR
spectrometer. With increasing implantation energy, the muons penetrate
into SiO2 substrate (see Fig. 10) where most of the stopped muons form
muonium. This results in proportional loss of the measured diamagnetic
asymmetry Al. The solid line is the expected energy dependence of Al
derived from the muon stopping proﬁles calculated using the TRIM.SP
code.

SiO2 with residual energy below 5 keV there remains a relatively large fraction that does not form muonium and the
diamagnetic asymmetry contribution from the SiO2 substrate is therefore energy dependent. We have used thisenergy dependence ASiO2 ðEÞ measured in [[17] (Fig. 8)] to
determine the contribution from free diamagnetic muonsin the SiO2 substrate to the measured asymmetry. The
mean residual energies of muons after passing throughthe 40 nm Al layer as well as the numbers of muons
implanted to SiO2 and Al layer were calculated using the

TRIM.SP code for 105 incident LE-l+. In the calculation
we have assumed standard deviation of the incident muonenergy to be rE = 14 eV and the standard deviation of theincidence angle from the normal incidence to be ra = 5°.
We have included in the calculation small thickness variation of the Al layer with a standard deviation of 2 nm. We
have not considered any Al2O3 oxide layer that might haveformed on the surface of the sample as we have seen no
reduction of the measured asymmetry for low implantationenergies. The TRIM.SP calculation predicts reﬂection of afraction of muons at low incident energies (about 9% of thetotal at 1 keV and as much as 30% at 0.1 keV). Upon reﬂection there is a high probability that the muon captures anelectron and forms muonium and this should result in acorresponding reduction of the measured diamagnetic
asymmetry. We have not, however, seen this reduction
for muons implanted at energy of 1 keV, given the low statistics we have accumulated for this data point.
The background contribution to the asymmetry fromthe muons stopping in metal parts outside the sample
was determined from the diamagnetic asymmetry of
1.5 ± 0.2% measured at 18 keV. At this energy all of theincident muons are implanted in SiO2, where about
0.09 ± 0.01 of them will remain as diamagnetic muons[17] contributing to the asymmetry with 1.0 ± 0.1%. The
background contribution to the measured asymmetry isthen estimated to be 0.5 ± 0.2%, corresponding to about
0.045 of the incident muons stopping outside of the
20 mm diameter of the sample.
It should be noted that at room temperature the muons
implanted in the Al layer will rapidly diﬀuse throughout
the metal layer, but not necessarily into the SiO2 substrate.
For the muon energies in the range of 1–4 keV, whenmost of the muons are implanted into the Al layer, wehave observed a small spin relaxation rate k = 0.10 ls1

P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

p2 s2p f 2Aðf Þ¼ expðÞ:
Að0Þ
4 ln 2

1.0
0.8
0.6
0.4
0.2
0.0
0.1

1.0

10.0

100.0

Frequency [MHz]Fig. 12. Frequency response plot of the LE-l+ lSR apparatus asmeasured using muonium spin precession signal in SiO2 sample. The
data points show the ratio of the measured muonium asymmetry to the
expected muonium asymmetry obtained for several precession frequencies
from 7 MHz up to 42 MHz. The solid line represents ﬁt to the data points
with frequency dependence according to Eq. (3) yielding
sp = 12.7 ± 2.0 ns. For comparison, the dotted line shows the frequency
response for sp = 82 ns, equivalent to FWHM duration of the ISIS surface
muon pulse.

ð3Þ

We have measured this frequency response using the orthomuonium spin precession signal in a transverse ﬁeld of up
to 3 mT (30 G). LE-l+ with energy of 15 keV were implanted into the Al (40 nm) coated SiO2 sample. If the positron decay time histograms are binned in intervals shorter
than 2p/xMu the ﬁtting function (Eq. (1)) has to include an
additional term describing the muonium spin precession
N i ðtÞ ¼ N 0i et=sl ½1 þ Al Gl ðtÞ cosðxl t þ ui Þ
AMu
GMu ðtÞ cosð-Mu t þ uMuþ
i Þ2
ði ¼ 1; . . . ; 8Þ;þ N BGi ðtÞ

1.2

A Mu(f)/A Mu (0)independent of the implantation energy (within our experimental error). It was found by measurements in bulk Al
that pure Al gives rise to no depolarization in the temperature range of 0.1–300 K [20]. Our own measurements with
18 keV muons implanted into a 500 nm thick pure Al sample at room temperature also show minimal relaxation rate
k = 0.03 ± 0.02 ls1. The small relaxation observed in our
40 nm thick Al layer is therefore most likely related to asmall fraction of muons diﬀusing across the Al/SiO2 interface. The structural disorder and imperfections at the layerinterface in samples prepared by sputtering signiﬁcantly
hinder the diﬀusion across the interface, as was observed
for the Cr/Au interface prepared by sputtering [21].
The short pulse duration of the LE-l+ generated by thelaser ionization of muonium allows us to measure very highprecession frequencies and extend the dynamic range forpulsed lSR to measure processes on a timescale ranging
from nearly 10 ns to more than 10 ls. For a Gaussian pulse
shape with FWHM width of sp the amplitude A of the harmonic component at frequency f will reduce by a factor

345

asymmetry reduced by 25% compared to the asymmetry
measured at low frequency. By ﬁtting the measured data
points with frequency dependence according to Eq. (3)the pulse width sp can be determined as sp = 12.7 ± 2.0 ns.
This value is somewhat higher than the LE-l+ pulse duration determined from the time-of-ﬂight spectrum (Fig. 8) as
it also includes various optical and electronics delays involved in detecting the positrons from the muon decay inthe lSR spectrometer.
4. Conclusions

ð4Þ

where the amplitude of the muonium precession signal iswritten in the usual convention as one half of the initial
muonium asymmetry AMu, since the other half of themuonium asymmetry is not observed due to fast depolarization. On implantation, the sum of Al and AMu must
equal the maximal experimentally observable asymmetry
Amax which we have determined from our measurementof diamagnetic asymmetry in pure metal sampleðAmax ¼ AAg
l ¼ 10:11  0:23%Þ. As we have determined in
the measurements shown in Fig. 11, the diamagnetic asymmetry from the free diamagnetic muons at 15 keV is1.56 ± 0.38%, the expected muonium asymmetry AMu isthen 8.55 ± 0.44%. The ratio of the observed muonium
asymmetry and the expected muonium asymmetry is thenplotted against the muonium precession frequency inFig. 12. As expected from the short duration of the LEl+ pulse, fast spin precession frequencies and fast
relaxation rates can be observed; although this is admittedly limited by the relatively low count rate. With about
106 muon decay events detected, the muonium spin precession at 28 MHz could be clearly observed with muonium

An experimental setup has been constructed at RIKENRAL muon facility to perform depth-resolved lSR measurements on nanometre scale with pulsed ultra low energymuons. Several lSR experiments have been carried out todemonstrate the characteristics of the apparatus. The
parameters of the pulsed low energy muon beam are summarised in Table 2. The eﬃciency of the surface muon beamcooling to eV level is comparable to the method using thecryogenic moderator (of 3  105). The eﬃciency of thermal muonium production is, however, of the order of 102.
As Figs. 5 and 6 demonstrate, the laser pulse energy is not
yet suﬃcient to ionize all muonium atoms, even though
the laser beams overlap only a small fraction of the generated thermal muonium cloud. Therefore, there is a clear
prospect that with development of a new and more intense
VUV laser source, the eﬃciency of LE-l+ production could
be increased by up to two orders of magnitude. The muonium ionization method of LE-l+ generation has distinct
advantages for pulsed operation. The LE-l+ implantationin the sample can be externally triggered with nanosecond
accuracy that makes it possible to perform lSR experiments
where the muon implantation is synchronised with a sample

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P. Bakule et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 335–346

Table 2Present characteristics of the pulsed LE-l+ beam and of the lSR
spectrometer
Low energy muon beam parameters
Intensity at sample
Beam spot diameter at sample
Energy at W target region
Energy after reacceleration
Energy uncertainty after reacceleration
Pulse repetition rate
Pulse duration in TOF spectrum at 9.0 keV
l+ spin polarizationlSR spectrometer parameters
Solid angle covered by detectors
Maximum instrumental asymmetry of lSR
spectrometer
Maximum measurable spin precession frequency
Sample cryostat temperature range
Transverse magnetic ﬁeld range
Zero ﬁeld compensation

15 l+/s
4 mm(FWHM)
0.2 eV
0.1–18 keV
rE  14 eV
25 Hz
7.5 ns(FWHM)
50%
80% of 4p sr
10.1%
40 MHz
10–300 K
0–60 mT0.1 lT

excitation. The LE-l+ pulse duration is reduced to only
7.5 ns (measured at FWHM), which is in fact as short as
the time resolution for the LE-l+ implantation at continuous muon source [22]. This short pulse duration is independent of the initial pulse structure of the incident surface
muon beam, which would be of particular advantage if thismethod of LE-l+ generation was used at the new J-PARC
Muon Science Facility where each muon pulse will consistof two bunches each of 100 ns duration and separated by
as much as 600 ns [23].
Acknowledgements
The authors would like to thank F. Pratt for his advice
on analysing the data from lSR measurements and his
keen interest in our experiments. We are also very gratefulto E. Morenzoni and W. Eckstein for kindly providing uswith the TRIM.SP code. We are also indebted to R. Scheuermann for his contribution to the construction of the ion
beamline. The construction of this low energy muon facility was possible due to large ﬁnancial support of KEKMSL and UT-MSL (for purchasing the high power lasers
and ion optics), and of RIKEN (for construction and operational costs). This research was partially supported by the
Grant-in-Aid for Scientiﬁc Research (A)16206005,(B)11559019, (C)11650052 and Grant-in-aid for Exploratory Research 16656295 by the Ministry of Education,
Culture, Sports, Science and Technology of Japan.
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