annals of
Annals of Nuclear Energy 32 (2005) 1–11
www.elsevier.com/locate/anucene
NUCLEAR ENERGY
Measurement of thermal neutron cross sectionand resonance integral for 165Ho(n,c)166gHo
reaction by the activation method
Haluk Yucel a,*, Mustafa Karadag b
a Ankara Nuclear Research and Training Center, 06100, Besevler-Ankara, Turkeyb Gazi University, Gazi Education Faculty, 06500 Teknikokullar-Ankara, Turkey
Received 1 July 2004; accepted 25 July 2004
Available online 18 September 2004
Abstract
The thermal neutron cross section and the resonance integral of the reaction 165Ho-
(n,c)166gHo were measured by the activation method using 55Mn(n,c)56Mn monitor reaction.
The sufficiently diluted MnO2 and Ho2O3 samples with and without a cylindrical Cd case were
irradiated in an isotropic neutron field of the 241Am–Be neutron sources. The c-ray spectra
from the irradiated samples were measured with a calibrated n-type high purity Ge detector.
Thus, the thermal neutron cross section for 165Ho(n,c)166gHo reaction has been determined to
be 59.2 ± 2.5 b relative to the reference thermal neutron cross section value of 13.3 ± 0.1 b for
the 55Mn(n,c)56Mn reaction, and it generally agrees with the recent measurements within
about 1 to 12%. The resonance integral has also been measured relative to the reference value
of 14.0 ± 0.3 b for the 55Mn(n,c)56Mn reaction using an epithermal neutron spectrum of the241Am–Be neutron source. The resonance integral for 165Ho(n,c)166gHo reaction obtained
was 667 ± 46 b at a cut-off energy of 0.55 eV for 1 mm Cd thickness. The existing experimental
and evaluated data for the resonance integral are distributed from 618 to 752 b. The present
resonance integral value agrees with most of the previously reported values obtained by 197Au
standard monitor within the limits of error.
� 2004 Elsevier Ltd. All rights reserved.
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doi:10.1016/j.anucene.2004.07.009
* Corresponding author. Tel.: +90 312 2126230; fax: +90 312 2234439.
E-mail addresses: [email protected] (H. Yucel), [email protected] (M. Karadag).
2 H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11
1. Introduction
166Ho is a good therapeutic radionuclide due to its suitable half life (26.76 h), high
beta energy with 1.77 MeV (48%) and 1.85 MeV (51%) and 6.7% c-ray with 80.57
keV suitable for imaging (Hong et al., 2003; Dadachova et al., 1997). 166Ho withits favorable characteristic could be used in endovascular radionuclide therapy
(EVRT) technique in liquid filled low pressure balloon angioplasty, which is a well
known standard treatment for artherosclerotic coronary artery disease (Majali
et al., 2002). 166Ho can be produced in a nuclear reactor by the 165Ho(n,c)166gHo
reaction. The knowledge of the thermal neutron cross section and resonance integral
of 165Ho(n,c)166gHo reaction would become important because the neutron activa-
tion cross section data are used in the production of 166Ho and may also used in
other studies related to the interaction of neutrons with matter.It is the fact that gold (197Au) with the well known nuclear characteristics, as a
primary standard monitor, is generally used for the cross sections measurements
(Mughabghab, 1984; Orvini et al., 1968; De Corte, 2003; Holden, 1999; Kafala
et al., 1997; Kinsey, 1996; De Corte and Simonits, 1989; Simonits et al., 1984; Heft,
1978; Erdtmann, 1976; Steinnes, 1972, 1975; Ryves and Zieba, 1974; Van Der Linden
et al., 1974; ; Hayodom et al., 1969; Thai, 1967; Sage and Sher, 1966; Pomerance,
1951; Seren et al., 1947). However, manganese (55Mn) with favorable nuclear char-
acteristics as a secondary monitor also meets the necessary conditions (Orvini et al.,1968; Seren et al., 1947; Karadag et al., 2003; Karadag and Yucel, 2004). For exam-
ple, the Westcott correction factor, g describing 1/v departure in thermal region for55Mn as well as 197Au is close to unity at room temperature (Chang, 2003). It is obvi-
ous that the separation of principal resonances of the monitor to be used in the acti-
vation from the 1/v region is an important feature for resonance integral
measurement. So, the well separated principal resonance energy of Au monitor lies
in 4.9 eV, whereas the first resonance of 55Mn lies in 337 eV and it is quite far from
1/v region. Moreover, there are sufficient number of internationally accepted accu-rate values for the thermal neutron cross section (known to ±0.75%) and resonance
integral (known to ±2%) for 55Mn(n,c)56Mn in order to use 55Mn monitor instead of
standard 197Au monitor. Hence, the 55Mn(n,c)56Mn reaction can also be chosen as a
suitable monitor for thermal neutron cross section and resonance integral
measurements.
The motivation for the present measurements was the discrepancy among the
resonance integral values (Mughabghab, 1984; Holden, 1999; Kafala et al., 1997;
Kinsey, 1996; De Corte and Simonits, 1989; Simonits et al., 1984; Heft, 1978; Erdt-mann, 1976; Steinnes, 1975; Ryves and Zieba, 1974; Van Der Linden et al., 1974;
Steinnes, 1972; Hayodom et al., 1969; Thai, 1967; Sage and Sher, 1966; JEF-2.2,
1997; IAEA, 1987; BNL, 1973) appeared in the literature survey, which can reach
more than 21%. In the present work, it is aimed to measure more accurately the
thermal neutron cross section and the resonance integral of 165Ho(n,c)166gHo reac-
tion using an alternative monitor, 55Mn. For this purpose, the specific activities
after a bare and Cd-covered irradiations of the samples in an isotropic neutron
field, which were measured in a calibrated Ge detector, were used to obtain the
H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11 3
reaction rate per atom and also Cd ratios of 55Mn(n,c)56Mn and 165Ho(n,c)166gHo
reactions.
2. Experimental procedure
The irradiation of samples was performed by the neutrons from the three 592 GBq241Am–Be isotopic neutron sources immersed in paraffin moderator shielded with
lead. The geometrical configuration of the neutron sources and the irradiation holes
of this neutron irradiation unit installed at Ankara Nuclear Research and Training
Center has been previously described in detail elsewhere (Karadag et al., 2003; Yucel
and Karadag, 2004). According to the procedure described in our previous work
(Yucel and Karadag, 2004), the thermal neutron flux and epithermal neutron fluxat the sample irradiation position of the 241Am–Be neutron irradiator have been
measured to be (1.5 ± 0.2) · 104 and (1.4 ± 0.1) · 103 n cm�2 s�1 respectively.
The oxide forms of the analytical grade samples to be activated were filled in the
polystyrene tubes (height/diameter .2) with 1 mm wall thickness. The internal diam-
eter of tube is 5.0 mm. They were exposed to the neutrons in a fixed position in the
irradiation hole of very large volume compared to the sample volume.
In this work, the samples used were diluted with finely grained Al2O3 powder by
96.6–98.8% , because 27Al isotope has the lower neutron absorption cross section.Each of the samples of MnO2 and Ho2O3 was mixed with the sufficient amount of
Al2O3 powder. The irradiations of samples were carried out with and without a
cylindrical cadmium case. The irradiations for 10 samples for holmium, which are
individually prepared from the analytical grade stocks obtained from Aldrich Chem-
ical Corp., were repeated five times. That is, a set of 5, with and without Cd irradi-
ation data for MnO2 and Ho2O3 are obtained.
The irradiation times for the (n,c) reactions of 55Mn and 165Ho were chosen for a
period of four to six half lives, yielding enough activity to be measured in a c-raycounting system. The suitable waiting times were employed to minimize dead time
losses and eliminate the possible contribution of 843.8 keV c-ray from 27Mg (9.45
m) activity to the 846.7 keV peak of 56Mn.
The detector used in the measurements was an n-type high pure germanium
(HPGe) manufactured by Canberra, Inc. The resolution of this detector was
1.80 keV for 1332.5 keV (60Co) and 0.97 keV for 122 keV (57Co) and its relative effi-
ciency was 22.6%. The c detection efficiency as a function of energy for the HPGe
detector was determined using the powder radioactive standard containing a mixtureof 109Cd, 57Co, 123mTe, 51Cr, 113Sn, 85Sr, 137Cs, 60Co and 88Y radionuclides, obtained
from Isotope Products Laboratories Inc., traceable to NIST. The counting times var-
ied between 25 and 50 h for Ho2O3 samples, and between 2.5 and 10 h for MnO2
samples predetermined for each measurement were high enough to ensure good sta-
tistical quality of data. Dead times were typically less than 0.1%.
Nuclear data used for the determination of the radioactivities for thermal neutron
cross section and resonance integral measurements are given in Table 1 (Kinsey,
1996; El Nimr et al., 1981; Moens et al., 1979; Tuli, 2000).
Table 1
Nuclear decay data used in the analyses
Nuclear reaction Cd transmission
factora,e, FCd
Effective resonance
energye,b, Er (eV)
Half-lifec (h) Detected c-rayd
Energy (keV) Intensity (%)
55Mn(n,c)56Mn 1.00 468 2.5789(1) 846.75(2) 98.9(3)165Ho(n,c)166gHo 0.99 9.73 26.763(4) 80.574(8) 6.71(8)
a El Nimr et al. (1981); De Corte and Simonits (2003).b Moens et al. (1979).c Tuli (2000).d NuDat (Kinsey, 1996).e For ECd = 0.55 eV.
4 H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11
3. Experimental analysis
3.1. Thermal neutron cross section determination
The thermal neutron cross section for the reaction 165Ho(n,c)166gHo has been
determined relative to that for the 55Mn(n,c)56Mn reaction, using reaction rates of
Ho and Mn as follows:
r0;Ho ¼R� RCd
FCd
� �Ho
R� RCd
FCd
� �Mn
� Gth;Mn
Gth;Ho
� r0;Mn; ð1Þ
where R and RCd are reaction rates per atom for bare and Cd-covered isotope irra-
diation, respectively, Gth is self-shielding factor for thermal neutrons, r0 is thermal
neutron cross section and FCd is the cadmium transmission factor, which accounts
for the fact that the specific count rate of a cadmium covered isotope is, in some
cases, significantly differ from the specific count rate of the bare isotope induced
by epithermal neutrons. Since the Westcott correction factors, g(20 �C) are 1.0004(Ryves and Zieba, 1974) for 55Mn and 1.0016 (Chang, 2003) for 165Ho, they are
not introduced into Eq. (1).
After a bare and Cd-covered sample irradiations, the reaction rates R and RCd for
both the monitor isotope, 55Mn and the investigated isotope, 165Ho are determined by
R or RCd ¼A�sp or Aþ
sp
� �� F g �M
h � NA � c � epð2Þ
with
A�sp or Aþ
sp ¼Np=tm
w � S � D � C ; ð3Þ
where, A�sp; Aþ
sp are specific activities obtained after a bare and Cd-covered isotope
irradiation; Np is the net number of counts under the full-energy peak collected dur-
ing measuring time, tm; w is the weight of irradiated element, S ¼ 1� e�ktirr is the sat-
uration factor with k = decay constant, tirr is the irradiation time; D ¼ e�ktd is the
H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11 5
decay factor with td = decay time; C ¼ ð1� e�ktmÞ=ktm is the measurement factor cor-
recting for decay during the measuring time, tm; M is the atomic weight; h is the iso-
topic abundance; NA is the Avogadro�s number; c is the absolute c-ray emission
probability; ep is the full-energy peak detection efficiency; and Fg is the correction
factor for c-ray attenuation. The correction factors for c-ray attenuations inAl2O3–1.2% Ho2O3 sample at 80.57 keV from 166Ho and Al2O3–3.4% MnO2 sample
at 846.7 keV from 56Mn at a fixed geometry for the case of a cylinder, coaxially posi-
tioned with the detector have been calculated to be 1.11 and 1.03, respectively. In the
calculations, the total mass attenuation coefficients, l/q for the compounds used, are
taken from the XCOM database of Berger et al. (1999).
3.2. Resonance integral determination
The resonance integral, I0(a) for a 1/E1 + a real epithermal neutron spectrum is de-
fined as (De Corte et al., 1979):
I0ðaÞ ¼Z 1
ECd
rðEÞ � ð1eVÞa
E1þa dE; ð4Þ
where r(E), is the cross section as a function of energy E, ECd is the cadmium cut-off
energy. According to the definition of the EANDC (Goldstein et al., 1961), effective
cadmium cut-off energy is set at 0.55 eV for a detector, having a r(v)–1/v cross sec-
tion for the (n,c) reaction up to 1–2 eV, irradiated in an isotropic neutron flux as a
small sample in a cylindrical Cd box (height/diameter @ 2) with a wall thickness of 1mm. I0(a) is the resonance integral, which should be used in the calculation of the
epithermal activation in a particular irradiation position, characterized by epither-
mal neutron spectrum shaping factor, a which is energy independent. The relation-
ship between I0, as tabulated in literature, and I0(a) for the conversion is given by:
I0ðaÞ ¼ ð1eVÞa I0 � 0:426r0
ðErÞaþ 0:426r0
ð2aþ 1ÞðECdÞa� �
; ð5Þ
where Er is effective resonance energy (eV), as defined by Ryves (Ryves, 1969; Ryves
and Paul, 1968), and the literature values of Er for55Mn and 165Ho are given in Table
1, the term (I0 � 0.426r0) represents the reduced resonance integral, i.e. with the 1/v
tail subtracted. Eq. (5) is only valid for ECd = 0.55 eV. The epithermal neutron flux
shape factor, a appeared in Eq. (4) and Eq. (5), at the sample irradiation position of
the used irradiation hole of the present neutron irradiator, was experimentally deter-
mined to be 0.083 ± 0.016 (Yucel and Karadag, 2004).The measured I0(a) value for the 165Ho(n,c)166gHo reaction has been determined
relative to that for the 55Mn(n,c)56Mn reaction as a standard monitor by the follow-
ing relation:
I0ðaÞHo ¼ I0ðaÞMn �ðCR� 1ÞMn
ðCR� 1ÞHo
� r0;Ho
r0;Mn
� Gepi;Mn
Gepi;Ho
� Gth;Ho
Gth;Mn
; ð6Þ
where CR is cadmium ratio defined by CR ¼ A�sp
Aþsp� F Cd. In Eq. (6), the cadmium ra-
tios for both Mn and Ho are determined from the measured activities, the thermal
6 H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11
and epithermal self-shielding factors, Gth and Gepi are estimated from the simplified
procedure in Section 4 and reference values of r0,Mn, I0(a)Mn are used. Then, the ob-
tained I0(a) value for165Ho(n,c)166gHo reaction was converted to I0 by using Eq. (5),
and the final result for 165Ho(n,c)166gHo reaction is given in Table 5, together with
other results appeared in literature.
4. Neutron self-shielding correction factors
The thermal neutron self-shielding correction factor, Gth depends on the size and
shape of the sample and for a finite cylinder of radius R and length L in isotropic
neutron field, it can be approximately calculated by (Karadag et al., 2003):
Gth ffiR � Gslab þ L � Ginf :cyl
Rþ L; ð7Þ
where Gslab and Ginf.cyl are the self-shielding factors for a slab and an infinite cylin-
der, respectively. In the approximation, the effect of neutron scattering in the sample
has also been taken into account by applying the necessary correction for this effect
given by the following relation (Wachspress, 1958):
G�th ¼
Gth
1�P
sPt
ð1� GthÞ; ð8Þ
where G�th is the thermal neutron self-shielding factor corrected for scattering,P
t = (P
a +P
s),P
s are respectively, total and scattering macroscopic cross sections
which can be calculated by using the tabulated elemental values given in Table 2 forO, Al, Mn and Ho (Fukahori et al., 1997; Coplen, 2001; McLane, 2001). The calcu-
lated thermal neutron self-shielding factors for MnO2 and Ho2O3 samples, diluted
with Al2O3, are given in Table 3.
The epithermal neutron self-shielding correction factor, Gepi is defined by:
Gepi ¼IeffI0
; ð9Þ
where I0, Ieff are the infinitely diluted resonance integral and the effective resonance
integral, respectively. I0 and Ieff have been calculated by using the procedure described
Table 2
Absorption, scattering and total microscopic cross sections for thermal neutrons, and atomic weights for
elements of interest
Element Atomic weight, M (g/mol) Microscopic cross sections (b)
Absorption, ra Scattering, rs Total, rt
8O 15.9994 1.9 · 10�4 3.78 3.78
13Al 26.9815 0.231 1.41 1.64
25Mn 54.9380 13.41 2.17 15.58
67Ho 164.930 65 10.8 75.8
Table 3
The calculated neutron self-shielding factors for diluted MnO2 and Ho2O3 samples
Dilution of
samples used
Thermal self-shielding
factor, Gth from Eq. (7)
Thermal self-shielding
factor including scattering,
G�th from Eq. (8)
Epithermal self-shielding
factor, Gepi from Eq. (9)
Al2O3–3.4% MnO2 0.996 0.997 0.903
Al2O3–1.2% Ho2O3 0.997 0.997 0.890
H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11 7
in detail (Karadag et al., 2003). Thus, the epithermal neutron self-shielding factors,
Gepi for the cylindrical sample geometry were calculated and given in Table 3. In this
work, the dilution percentages for the samples were kept to be high as 96.6% for
MnO2 and 98.8% for Ho2O3 in order to reduce epithermal neutron self-shielding ef-
fects, but considering good counting statistics in the measurements. Because the reso-
nances of 27Al lie in high neutron energy region (5.9, 34.8, 87.3 keV), the effect of 27 Al
resonances is negligible. However, the effect of 27Al on the epithermal neutron self-
shielding has been taken into account in the present procedure.
5. Results and discussion
The thermal neutron cross section for the 165Ho(n,c)166gHo reaction has been ob-
tained relative to the reference cross section value of 13.3 ± 0.1 b of 55Mn(n,c)56Mn
Table 4
Experimental uncertainties for the thermal neutron cross section and resonance integral measurements
Thermal neutron cross
section measurement
Resonance integral
measurement
Uncertainties due to Uncertainties (%) Uncertainties due to Uncertainties (%)
165Ho 55Mn 165Ho 55Mn
Statistical error* 0.56 0.39 Cadmium ratio 1.50 1.60
Detection efficiency 2.51 2.75 Epithermal neutron
self-shielding factor
1.5 0.20
Mass of sample 0.01 0.01 Thermal neutron
self-shielding factor
0.1 0.01
Half-life 0.02 0.004 Reference thermal
neutron cross section
1.31 0.75
c-ray emission
probability
1.19 0.30 Monitor resonance
integral
– 2.14
Thermal neutron
self-shielding factor
0.1 0.01 Cadmium transmission
factor
1 –
Cadmium transmission
factor
1 – a-shape parameter 3.57 4.43
Monitor thermal
neutron cross section
– 0.75
Total uncertainty 3.01 2.89 Total uncertainty 4.47 5.23
*Errors are based on counting statistics of ±1.65r.
8 H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11
reaction. The experimental uncertainties for the 165Ho and 55Mn are given in Table
4. The main sources of the uncertainties are due to statistical errors (0.56% for 165Ho
and 0.39% for 55Mn) and detection efficiencies ( 2.51% for 165Ho and 2.75% for55Mn). The data obtained with different irradiation and counting times of activation
samples were relatively close to each other, and the difference of the results is withinabout 1.0%. A consistency is found among the measured data.
The measured thermal neutron cross section value for 165Ho(n,c)166gHo reaction
given in Table 5 together with other literature values is 59.2 ± 2.5 b. The present re-
sult for thermal neutron cross section for the 165Ho(n,c)166gHo reaction is in good
agreement with the measurement of Seren et al. (1947), De Corte (2003), Zimmer-
man et al. (1967) and De Corte and Simonits (1989) and is close to within 2–6.5%
with the values obtained by Holden (1999), Kafala et al. (1997), NGATLAS (Ko-
pecky et al., 1997), NuDat (Kinsey, 1996), Simonits et al. (1984), Mughabghab
Table 5
Thermal neutron cross section and resonance integral for 165Ho(n,c)166gHo reaction
Year References Thermal neutron
cross section,
r0 (b)
Resonance
integral,
I0 (b)
Cadmium
cut-off energy,
ECd (eV)
Monitor
used
This work 59.2 ± 2.5 667 ± 46 0.55 Mn
2003 De Corte (2003) 58.5 ± 1.3 – – Au
2001 ENDF/B-VI (McLane, 2001) 64.700 – – –
1999 Holden (1999) 58 670 0.50 Au
1998 Danon et al. (1998) 64.4 ± 2.8 – – –
1997 JEF-2.2 (1997) 66.500 752 – –
1997 Kafala et al. (1997) 61.2 ± 0.8 671 ± 8 0.55 Au
1997 NGATLAS (Kopecky et al., 1997) 62.93 – – –
1996 NuDat (Kinsey, 1996) 61.2 ± 1.1 650 ± 22 0.50 Au
1989 De Corte and Simonits (1989) 58.1 ± 23 636 ± 32 – Au
1987 IAEA (1987) 64.7 ± 1.2 660 ± 35 – –
1984 Simonits et al. (1984) 61.2 ± 3.0 670 ± 37 0.55 Au
1984 Mughabghab (1984) 61.2 ± 1.1 650 ± 22 0.50 Au
1978 Heft (1978) 61.4 ± 1.0 718 ± 40 0.50 Au, Sc,
Co, U
1976 Erdtmann (1976) 63 ± 3.3 660 ± 30 0.50 Au
1975 Steinnes (1975) – 660 ± 30 0.50 Au
1974 Ryves and Zieba (1974) 61.2 ± 1.1 618 ± 33 0.10 Au, Mn
1974 Van Der Linden et al. (1974) – 626 ± 93 0.55 Au
1973 BNL (1973) 63.0 ± 3.3 700 ± 20 0.50 –
1972 Steinnes (1972) 65 ± 2 710 ± 30 0.50 Au
1969 Hayodom et al. (1969) – 628 0.50 Au
1968 Holden and Walker (1968) 62 – – –
1967 Thai (1967) – 628 0.50 Au
1967 Zimmerman et al. (1967) 60 ± 2 – – –
1966 Sage and Sher (1966) – 696 ± 45 0.50 Au
1964 Esch and Feiner (1964) 61.2 ± 1.1 – – –
1962 Keisch and Faler (1962) 64 ± 6 – – Co
1951 Pomerance (1951) 64 ± 3 – – Au
1947 Seren et al. (1947) 59.6 ± 12 – – Au
H. Yucel, M. Karadag / Annals of Nuclear Energy 32 (2005) 1–11 9
(1984), Heft (1978), Erdtmann (1976), Ryves and Zieba (1974), BNL (1973), Holden
and Walker (1968) and Esch and Feiner (1964), but disagrees with the measurements
of Danon et al. (1998), ENDF/B-VI (McLane, 2001), JEF-2.2 (1997), IAEA (1987),
Steinnes (1972), Keisch and Faler (1962) and Pomerance (1951) by 8–13%.
The present resonance integral value for 165Ho(n,c)166gHo reaction given in Table5 has been found to be 667 ± 46 b, by assuming the cadmium cut-off energy as 0.55
eV, and relative to the reference value of 14.0 ± 0.3 b for the 55Mn(n,c)56Mn reac-
tion. The present value for the resonance integral for the 165Ho(n,c)166gHo reaction
agrees well with the measurement of Kafala et al. (1997) and Simonits et al. (1984)
and is close to 6.2% with the value measured by Van Der Linden et al. (1974). The
discrepancies between Holden (1999), NuDat (Kinsey, 1996), De Corte and Simonits
(1989), IAEA (1987), Mughabghab (1984), Erdtmann (1976), Steinnes (1975), BNL
(1973), Steinnes (1972), Hayodom et al. (1969), Thai (1967) and Sage and Sher (1966)with assumed Cd cut-off energy of 0.50 eV, and the present result are about 0.4–
6.5%. However, the present result disagrees with the measurements of Ryves and
Zieba (1974), Heft (1978) and JEF-2.2 (1997) by 7–13%.
The results obtained for 165Ho(n,c)166gHo reaction show that the thermal neutron
cross section and resonance integral for other isotopes could also be determined
accurately when 55Mn secondary monitor is employed with an activation method.
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