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: haluk.yucel@taek.gov.tr (H. Yucel), mkaradag@gazi.edu.tr (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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