Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

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Nuclear Instruments and Methods in Physics Research B
journal homepage: www.elsevier.com/locate/nimb

Development of spin-polarized slow positron beam using a 68Ge–68Ga
positron source
Masaki Maekawa ⇑, Yuki Fukaya, Atsushi Yabuuchi, Izumi Mochizuki, Atsuo Kawasuso
Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japana r t i c l e

i n f oArticle history:
Received 4 June 2012
Received in revised form 1 March 2013
Available online 19 April 2013
Keywords:
Slow positron beam
Spin polarized68
Ge
Ion irradiationa b s t r a c t
A 68Ge–68Ga positron source was produced from the 69Ga(p, 2n)68Ge nuclear reaction by irradiating a GaN
substrate with 20 MeV protons. Fast positrons from the source were converted to slow positrons usingtungsten meshes and foils and were then electrostatically transported to the sample chamber. The spinpolarization of the positron beam was determined as 47 ± 8% from the magnetic ﬁeld dependence of thepara-positronium intensity in fused silica. The Doppler broadening of the annihilation radiation spectra ofpolycrystalline Fe showed asymmetry upon ﬁeld reversal. The spin-polarized positron beam generated by
the 68Ge–68Ga source may be applicable to study the magnetic properties associated with surfaces, interfaces, and thin ﬁlms.
Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction

2. Preliminary evaluation

Positrons emitted from radioisotopes are longitudinally spinpolarized due to the parity non-conservation in the weak interaction. Positron annihilation studies have shown that the ferromagnetic band structure can be investigated using the angularcorrelation of annihilation radiation (ACAR) technique with spinpolarized positrons [1–3]. More recently, the Doppler broadeningof annihilation radiation (DBAR) technique, which in comparison
with ACAR has a much simpler experimental setup, may also be
suitable for spin-polarized positron annihilation spectroscopy(SP-PAS).
In 1980s, Gidley et al. demonstrated the spin polarization of aslow positron beam generated with a 22Na source. They used thespin-polarized positron beam to the study of surface magnetismof Ni [4]. Subsequently, only a limited number of works have been
performed. Considering the fact that various novel spin phenomena have recently been found to occur at surfaces/interfaces andin thin ﬁlms, spin-polarized positron beams may be useful in spintronics studies [4–12].
In this work, we developed a spin-polarized beam from a68
Ge–68Ga source based on electrostatic beam transport. We describe the numerical simulations used to determine the optimum
conditions for generating a spin-polarized positron beam. We thendiscuss the development of the 68Ge–68Ga source and the spinpolarized positron beam.

2.1. Spin polarization⇑ Corresponding author. Tel.: +81 27 346 9330.
E-mail address: maekawa.masaki@jaea.go.jp (M. Maekawa).
0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.nimb.2013.04.015

SP-PAS for surfaces, interfaces, and thin ﬁlms requires a highly
spin-polarized positron beam. The spin polarization of positrons
emitted from a positron source into an open angle, h, in a speciﬁc
direction is given byP¼

v 1 þ cos h
c

2

;

ð1Þ

where v is the positron speed and c is the speed of light [13]. The
speed term can be rewritten in terms of the kinetic energy, Ev
c¼

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
11
;½1 þ E=ðmc2 Þ2ð2Þ

where m is the static mass of the positron. The average positronspin polarization from a source is given by

hv i 1 þ cos hc2
Z Emax sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1
1 þ cos h1NðEÞdE;¼222½1 þ E=ðmc Þ
0

hPi ¼

ð3Þ

where NðEÞ is the energy distribution of positrons and Emax is the
maximum positron energy. Here, NðEÞ is not necessarily the sameas the energy distribution of the radioisotopes, because NðEÞ is
modiﬁed by the energy discrimination of positrons resulting fromself-absorption inside the source and absorption in the absorbers
and moderators. Also, the open angle, h, depends on the source

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M. Maekawa et al. / Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

and sample geometry for conventional positron annihilation experiments, and on the source and moderator geometry for slow positron beam generation. Eqs. (1)–(3) suggest that positron sources
with a higher energy end-point are better for generating highly
spin-polarized positron beams.
Some of the low energy positrons will be absorbed inside thesource. The energy spectrum of positrons emitted from the sourceis given byNS ðEÞ ¼

1
2

Z dS

N0 ðEÞ½AðzÞ=A0 T S ðE; zÞdz;ð4Þ

0where N0 ðEÞ is the original energy distribution of positrons emitted
from nuclei, AðzÞ is the depth distribution of the source activity,
Rd
A0 ¼ 0 S AðzÞdz; dS is the source thickness, and T S ðE; zÞ is the transmission probability of positrons at a depth of z and an energy of E
in the source material. If an absorber with a thickness of dA is placedin front of the source, the energy distribution becomesNA ðEÞ ¼ N S ðEÞT A ðE; dA Þ;ð5Þ

where T A ðE; dA Þ is the transmission probability of the positrons. The
transmission probability is generally given by

TðE; zÞ ¼ exp½ðz=z0 Þm ;

ð6Þ

z0 ¼ aEn =½qCð1 þ 1=mÞ;ð7Þ

where m and n are the material dependent constants, q is the material density, and a = 4.0 lg cm2 keVn. Thus, T S ðE; zÞ and T A ðE; dA Þ
can be obtained using appropriate values of m; n, and q.
When a slow positron beam is generated using a moderator,
positrons with a particular energy distribution are converted toslow positrons. The faster positrons are transmitted without being
moderated. Positrons stopped far from the reemission surface
annihilate without reaching it. Therefore, the moderator also functions as an absorber to change the positron energy distribution.
Thus, for the ﬁnal positron energy distribution, including theself-absorption in the source, the absorption and the moderation
is given byNðEÞ ¼ NS ðEÞT A ðE; dA ÞeM ðE; dM Þ;ð8Þ

where dM is the moderator thickness and eM ðE; dM Þ is the moderator
efﬁciency that is given by(eM ðE; dM Þ ¼

Rd
P em 0 M pðE; zÞ sinhðz=LÞ= sinhðdM =LÞdz; transmission type
Rd
P em 0 M pðE; zÞ expðz=LÞdz;reflection type
ð9Þ

where Pem is the positron branching ratio of reemission into a vacuum and the inner reﬂection of positrons, pðE; zÞ is the positron
implantation proﬁle (¼ dTðE; zÞ=dz), and L is the positron diffusion
length [14].
The 68Ge–68Ga source that we produced using a GaN target
material has a higher energy end-point (1.9 MeV) than that of22
Na (0.55 MeV). Fig. 1(a) shows the initial energy distribution,
N 0 ðEÞ [15], the energy distribution of the positrons emitted fromthe source, N S ðEÞ, and the ﬁnal energy distribution, NðEÞ. The conditions for these energy distributions are: AðzÞ shown in the following subsection, dS = 0.5 mm, a GaN target density of q = 6.15 g/cm3,
m = 2.0, n = 1.6, no absorber present, a tungsten moderator assembly composed of transmission and reﬂection moderators (Fig. 6(a))
where dM = 10 lm, m = 1.7, n = 1.67, q = 19.3 g/cm3, Pem = 0.33, andL = 135 nm. For comparison, Fig. 1(b) shows N 0 ðEÞ; N S ðEÞ, and NðEÞcalculated for a 22NaCl source with a uniform AðzÞ; dS = 0.1 mm, noabsorber present, and the same moderator. Consequently, using Eq.
(3) with h = 78°, the spin polarizations of the positron beams forthe 68Ge–68Ga/GaN and the 22NaCl sources are estimated to be
53% and 42% respectively. Thus, to generate highly spin-polarized

positron beams, it is important to use positron sources with higher
energy end-points.
2.2. Source activity
The 68Ge–68Ga and 44Ti–44Sc positron sources have relatively
long half-lives and higher energy end-points (288 days and
1.9 MeV, 48 years and 1.5 MeV, respectively) [16]. The cross section of the nuclear reaction 45Sc (p, 2n)44Ti is small, whereas the
production of 68Ge–68Ga is easier. The stable isotopes of Ga are
69
Ga (60.1%) and 71Ga (39.9%). The total amount of 68Ge–68Ga produced by 69Ga(p, 2n)68Ge and 71Ga(p, 4n)68Ge continuously increases when the proton energy (Ep ) increases from 15 to
150 MeV. The net positron intensity emitted from the target is reduced for higher proton energies because 68Ge–68Ga is produced ina deeper region of the target. As shown later, the optimum protonenergy for obtaining a high positron emission efﬁciency from thetarget surface ranges from 20 to 30 MeV. The cross section of
69
Ga(p, 2n)68Ge (0.465  1024 cm2)) is threefold higher than thatof 71Ga(p, 4n)68Ge (0.137  1024 cm2). High purity 69Ga should
be used as a target material; in our preliminary research, molten
Ga reacted with the other metal components of the source capsuleduring irradiation, which eventually destroyed the capsule. To
avoid this problem, we propose GaN as a target material, although
the amount of 69Ga(p, 2n)68Ge is decreased because of the reduced
69
Ga content.
Fig. 2(a) shows the depth proﬁle of 68Ge–68Ga in a GaN target
simulated by the Induced Radioactivity Analysis Code (IRAC) [17]at various proton energies. The total activity is only half that of
the 69Ga target. Assuming a proton current of 3 lA and an irradiation duration of 100 h, the total activities of 68Ge–68Ga are estimated to be 175, 359, and 497 MBq for Ep = 20, 25, and 30 MeV,
respectively.
The net positron intensity emitted outside from the target is given byIðdS Þ ¼

1
2

Z Emax Z dS
0AðzÞT S ðE; zÞN0 ðEÞdzdE:

ð10Þ

0

Fig. 2(b) shows the net positron emission rate as a function oftarget thickness using the depth proﬁles shown in Fig. 2(a). The
greatest positron yield is obtained for Ep = 25 MeV and a target
thickness of 1 mm. However, the emission efﬁciency for each total
activity is highest for Ep = 20 MeV and target thickness of 0.5 mm.
The positron beam ﬂux obtained for typical proton beam conditions (3 lA, 100 h) is of the order of 104 e+/s. The ﬂux could be enhanced by repeating the proton bombardment because of the long
half-life of 68Ge–68Ga. Thus, it is feasible to produce 68Ge–68Ga
with a strong enough intensity for generating a positron beam.
3. Development of spin-polarized positron beam
3.1. Source production
Fig. 3 shows schematic diagrams of the source capsule. The target material was a GaN single crystal with a diameter of 8 mm anda thickness of 0.475 mm. To avoid metallization during irradiation,
the GaN target was placed in a carbon tray. The tray containing thetarget was set on an irradiation stage equipped with a watercooled jacket to protect against heat damage during ion irradiation.
The irradiation chamber was evacuated to a base pressure of
5  104 Pa. The target was directly irradiated with 20 MeV proton
beam with a maximum current of 3.5 lA using the cyclotron at the
Takasaki Advanced Radiation Research Institute of the Japan Atomic Energy Agency. The efﬁciency of the source production was estimated to be 0.5 MBq/lA/h from the annihilation gamma ray

M. Maekawa et al. / Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

(a)

11

(b)

Fig. 1. Calculated energy spectrum of the emitted positrons from the nuclei [N 0 ðEÞ], from the source surface [N S ðEÞ], and the ﬁnal energy spectrum [NðEÞ] taking into accountthe absorption inside the source and moderator shown in Fig. 6(a) for (a) 68Ge–68Ga/GaN and (b) 22Na.

(a)

(b)

Fig. 2. (a) Simulated depth proﬁles of 68Ge–68Ga in a GaN target produced by proton bombardment with energies of 20, 25, and 30 MeV. (b) Net positron emission rate from68
Ge–68Ga/GaN as a function of target thickness.

(a)

(b)

Fig. 3. (a) Schematic and (b) photograph of the source capsule.

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M. Maekawa et al. / Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

energy spectrum. This is in good agreement with the results fromour simulation. An additional photopeak was detected at
1.07 MeV with a half-life of 280 days, which was attributed to
one of the gamma rays from 68Ga. The irradiation was carriedout over 400 h in total in 20 sessions. The irradiation did not cause
any signiﬁcant physical changes, indicating GaN is sufﬁciently
durable as a target material. Fig. 4 shows the net source activity
as a function of the elapsed irradiation time.
3.2. Beam generation
To maintain the spin polarization of positrons during the beamtransportation, an electrostatic system was used because the positron spin polarization is easily destroyed even by weak magnetic
ﬁelds. Electrostatic beam transportation can also be used when acontrollable magnetic ﬁeld is applied to a sample. Fig. 5 shows
an overview of the positron beam apparatus. The GaN target was
moved to the positron gun position after irradiation. The positrons
emitted from the GaN target were moderated by a tungsten-mesh
moderator composed of 33 tungsten meshes with a wire diameterof 10 lm. [18]. To improve the efﬁciency, a tungsten ring and tungsten foils (25 lm thick) were added (Fig. 5). The moderator assembly was annealed by an electron beam above 1800 °C for 1 h in a
vacuum. The slow positrons were extracted by an extraction gridand focused by a modiﬁed SOA gun [19–21] (Fig. 5). The slow positron beam was transported approximately 2 m by nine einzel
lenses to a measurement chamber. The longitudinally polarized
beam was bent 90° using a magnetic or electrostatic deﬂector.
The magnetic deﬂector produced a longitudinally polarized beam,
whereas the electrostatic deﬂector produced a transversely polarized beam. The beam was transported with an energy of 5–
15 keV. The ﬁnal beam energy was adjusted using a deceleration/
acceleration tube installed in the measurement chamber.
Consequently, a positron beam with a diameter of 5 mm and aﬂux of 5  103 e+/s was obtained. This ﬂux was consistent with thevalue derived from the source intensity (200 MBq), the escape efﬁciency from the GaN target (0.1) and the remoderation efﬁciency(2  104 ).
3.3. Spin polarization
The spin polarizations of the 68Ge–68Ga/GaN source and thepositron beam were determined from the magnetic quenching of
the positronium in fused silica. The para-positronium annihilation
probability increases in the magnetic ﬁeld because of the mixing
with the ortho-positronium of the zero magnetic quantum number. The para-positronium annihilation probability is asymmetricupon ﬁeld reversal; the asymmetry can be used to determine thespin polarization of the positrons. This method was ﬁrst demon-

strated by Nagashima et al. using ACAR [22]. They reported thatthe precision of this method was 18% compared to 5% for the lifetime method. Nagai et al. showed that positron spin polarization
can be determined using DBAR measurements [23]. Furthermore,
Hirade developed a similar method based on the ortho-positronium annihilation lifetime observed in polymers [24].
Fig. 7 shows the polarimeter, which consisted of a cylindricalneodymium magnet (diameter: 22.5 mm; magnetic ﬁelds: 0.25
or 0.55 T) and a return yoke with a cross section of 10  30 mm.
The magnetic ﬁeld could be changed to 0, ±0.25 T and ±0.55 T at
the sample position by changing the permanent magnet. Fig. 8
shows the S parameters of fused silica, observed using the68
Ge–68Ga/GaN source and the positron beam with an incident
positron energy of 15 keV, as a function of the magnetic ﬁeld.
The distance between the source and the fused silica was 7 mm.
These results were ﬁtted with the following equation:

IPs ¼

jcp y2Co0

ð1 þ y2 Þ

F o0 þ

c þ y2 cp

Co0 ¼ j o

F 0;

C ð1 þ y2 Þ p

ð11Þ

þ cpickoff ;ð12Þ

y2 co þ cp
þ cpickoff ;1 þ y2ð13Þ

1 þ y2

Cp0 ¼ jjcp
p0

F o0 ¼

ð1 þ yÞ2 ð1  PÞ þ ð1  yÞ2 ð1 þ PÞ;
8ð1 þ y2 Þ

ð14ÞF p0 ¼

ð1  yÞ2 ð1  PÞ þ ð1 þ yÞ2 ð1 þ PÞ;
8ð1 þ y2 Þ

ð15Þ

S ¼ aIPs þ b;

ð16Þ

where IPs is the para-positronium annihilation intensity, Co0 and Cp0
are the total annihilation rates of perturbed para- and ortho-positronium, j (=0.95) is the contact density, cp (=8 ns1) and co(=0.007 ns1) are the self-annihilation rates of para- and ortho-positronium in a vacuum, cpickoff (=0.663 ns1) is the pick-off annihilation rate of ortho-positronium, and a and b are constants. y isgiven by y ¼ x=½ð1 þ x2 Þ1=2 þ 1 with x = 4lB=ðjEhf Þ, where l is theBohr magneton, B is the magnetic ﬁeld, Ehf is the hyperﬁne splittingenergy of positronium. With P; a, and b as free ﬁtting parameters,
the spin polarizations of the source and the beam were determined
to be 65 ± 3% and 47 ± 8%, respectively. The spin polarization obtained for the source was in good agreement with that predictedfrom the maximum spin polarization for the source (92%) and theopen angle (55°). The spin polarization of the beam was several percent smaller than that calculated in subsection 2.1. This discrepancy
may be caused by depolarization, for example, at the edge of themagnetic deﬂector and at the entrance of the pole piece. This spinpolarization was much higher than for the 58Co (20%) and 22Na
(30%) sources without absorbers [5,6,25]. Gidley reported a maximum spin polarization of 66 %, which was obtained by using a
22
Na source with a special MgO-smoked tungsten moderator andabsorbers, although the beam ﬂux was reduced [4]. Thus, it isimportant to use positron sources with higher energy end-points
to generate highly spin-polarized positron beam.
3.4. DBAR on ferromagnetic Fe

Fig. 4. Net source activity as a function of the elapsed time.

The ﬁeld-reversal asymmetry of the DBAR spectra for ferromagnetic Fe [26–30] was measured using the 68Ge–68Ga/GaN source
and the positron beam. The sample was a polycrystalline Fe(15  15  2 mm3) that was mechanically and electrochemicallyM. Maekawa et al. / Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

13

Fig. 5. Schematic of the spin-polarized positron beam line.

(a)

(b)

Fig. 6. Schematic of (a) the moderator assembly and (b) the positron gun.

polished and heat-treated at 1150 °C for 2 h in a vacuum. The differential DBAR spectra [N" (p) and N# (p)] were obtained by altering
the ﬁeld polarity. The subscript " or #indicates whether the positron polarization and the magnetic ﬁeld direction was parallel or
antiparallel. The total spectrum area contained more than 1  106
events and the intensities were normalized to unity.
Fig. 9 shows the differential DBAR spectra in a magnetic ﬁeld of
0.55 T. A photon energy of Ec ¼ 1 keV corresponded to an electron
momentum of p ¼ 3:92  103 m0 c. The ﬁnite differential intensity
means that there is a ﬁeld-reversal asymmetry, which arise fromthe enhanced annihilation between the spin-up positrons andspin-down 3d unpaired electrons [31–33]. The amplitudes of thedifferential DBAR spectra obtained using the source and the beam
were similar. This also shows that our positron beam was sufﬁciently spin-polarized.
4. Summary
We produced a 68Ge–68Ga source by irradiating a GaN target
with high-energy protons. The 68Ge–68Ga activity was increased
by repeating the irradiation. A spin-polarized positron beam wasthen generated using the source. Measurements of the DBAR spectra of fused silica and ferromagnetic Fe in magnetic ﬁeld demonstrated that the beam was sufﬁciently spin-polarized.

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M. Maekawa et al. / Nuclear Instruments and Methods in Physics Research B 308 (2013) 9–14

Fig. 7. Schematic of the polarimeter in the chamber.

Acknowledgment
This work was supported by JSPS KAKENHI Grant No.
24310072.
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Fig. 8. Magnetic ﬁeld dependences of S parameters of fused silica obtained using
the 68Ge–68Ga source and a slow positron beam (E = 15 keV). Solid and broken lines
denote the ﬁtting curves calculated from Eqs. (11)–(16).

Fig. 9. Differential DBAR spectra of Fe samples obtained in an external magnet ﬁeldof 0.55 T. This spectrum is folded at p = 0 to enhance the statistics.

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