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Measurements of activation cross-sections for 165Ho(n,2n)164gHo and 180W(n,2n)179gW reactions induced by neutrons around 14 MeV
Radiation Measurements 44 (2009) 68–71
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Measurements of activation cross-sections for 165Ho(n,2n)164gHo and 180W(n,2n)179gW reactions induced by neutrons around 14 MeV Kaihong Fang a, *, Yang Xiang a, Yuncheng Han a, Xiangzhong Kong a, Tieshan Wang a, Rong Liu b, Li Jiang b a b
School of Nuclear Science and Technology, Lanzhou University, Lanzhou, Gansu Province 730000, PR China Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang, Sichuan Province 621900, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2008 Received in revised form 26 October 2008 Accepted 17 November 2008
The cross-sections of 165Ho(n,2n)164gHo and 180W(n,2n)179gW reactions induced by neutrons around 14 MeV were measured using activation technique and calculated by a previously developed formulas, in which the neutron flux was determined using the monitor reaction 93Nb(n,2n)92mNb. Because both of the excited and ground states were produced in each of the two reactions, one formula was introduced to take out the effect from excited state. Comparison between this work and old data were given. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Holmium Tungsten Neutron Cross-section Activation technique
1. Introduction The cross-section of nuclear reaction is fundamental to the nuclear phenomena and basic for the application of nuclear technologies. Cross-section data for reactions induced by neutrons around 14 MeV are important for the design of fusion reactor. These data are needed to estimate induced radioactivity, nuclear transmutation, radiation damage and so on (Robert and Larry, 1984; Cheng, 1989; Markovskij et al., 2000; Igashira and Ohsaki, 2002). In the case of isomeric cross-sections, they are useful for various studies such as transfer of angular momentum, spin-dependence of nuclear level density, refinements in gamma transition theories and testing of theoretical nuclear models (Kao and Alford, 1975; Eapen and Salaita, 1975; Nuray, 1977; Vanska and Rieppo, 1981). Thus the precise cross-sections of all kinds of nuclear reactions are very important and necessary. In this work, the cross-sections of 165Ho(n,2n)164gHo and 180 W(n,2n)179gW reactions induced by the 14 MeV neutrons have been measured. The products contain not only the ground state but also the corresponding excited state, so the products of the excited states will decay to corresponding ground states while irradiating, cooling and IT ð100%Þ measurement process. For instance, 164m Ho ! 164g Ho, in the process of calculating the cross-section of the 165Ho(n,2n)164gHo
* Corresponding author. Tel.: þ86 931 8913551. E-mail address: [email protected] (K. Fang). 1350-4487/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.11.001
reaction Cx in formula (1) should be subtracted the contribution from 164m Ho. Furthermore, the half-lives of 164mHo and 164gHo (37.5 min and 29 min, respectively) are in the same order of magnitude that leads to the effect is very obvious. Since there are a few data from the reports and also differentia among them (Qaim and Graca, 1975; Qaim, 1974; Reggoug and Paic, 1982; Sakane et al., 2001; Sethi and Mukherjee, 1966; Steiner et al., 1969), it’s necessary to remeasure the cross-sections of these two reactions. It should be mentioned that for 180W(n,2n)179gW reaction there is only one report for single energy point in 1975 (Qaim and Graca, 1975), this work thus covers a slightly broader range of energies. 2. Experiment All the samples (holmium powder of 99.9% purity, tungsten powder of 99.8% purity) and columbium (Filatenkov et al., 1999, of monitor 99.99%) were made into round disks with a diameter of 2.0 cm, the thickness of samples was 1.5 mm and 1.7 mm, the thickness of columbium was 0.3–0.5 mm. Each of samples was sandwiched between two Nb foils. The samples were placed at 50 – 135 angles relative to the deuteron beam direction and centered about the T–Ti target at distances of 3.5 cm. Irradiations were carried out at the K-400 Intense Neutron Generator at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, and lasted from 0.5 to 1 h with
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
a flux rate yield of about 3 1010–4 1010 n/s. Neutrons in the 14 MeV region were produced by the means of the T(d,n)4He reaction with a deuteron beam of 220 keV and beam current of 350 mA. The solid tritium–titanium (T–Ti) target used in the generator was about 2.18 mg/cm2 thick. During irradiation, the neutron flux was monitored by accompanying a-particles so that the corrections could be made for small variations in the yield. The neutron energies in the measurements were determined by crosssections ratio for 93Nb(n,2n)92mNb and 90Zr(n,2n)89mZr reactions (Lewis and Zieba, 1980). The activated samples were studied for their g-activities by a low background, high efficiency g-ray spectrometry, using a well calibrated GEM-60P coaxial high-purity germanium (HPGe) detector (crystal diameter: 70.1 mm, crystal length: 72.3 mm) (ORTEC, made in U.S.A.) with a relative efficiency of w68% and an energy resolution of w1.7 keV (FWHM) at 1.33 MeV. The uncertainty in the absolute efficiency curve at 5.5 cm was estimated to be w2%, while the uncertainty of the activity of the standard source was w1%. The decay characteristics of the radioactive product nuclides and the natural abundances of the target isotopes under investigation are summarized in Table 1. 3. Result and discussion
The measured cross-sections sx were calculated by the activation formula (Wang et al., 1990):
3Ig hKSMD 0 ½lAFCx s ; 3Ig hKSMD x ½lAFC0 0
(1)
where the subscripts 0 and x represent terms corresponding to the monitor reaction and the measured reaction, s0 is the cross-section of monitor reaction, 3 is the full-energy peak efficiency of the measured characteristic g-ray, Ig is the g-ray intensity, h is the abundance of the target nuclide, S ¼ 1 elT is the growth factor of the residual nuclide, l is the decay constant, T is the total irradiation time, M is the mass of sample, D ¼ elt1 elt2 is the counting collection factor, t1 and t2 are time intervals from the end of the irradiation to the start and finish of counting, respectively, A is the atomic weight, C is the measured full-energy peak area and F is the total correction factor of the activity:
F ¼ fs fc fg ;
(2)
where fs, fc and fg are the correction factors for the self-absorption of the sample at a given g-energy, the coincidence sum effect of cascade g-rays in the investigated nuclide and in the counting geometry, respectively. K is the neutron fluence fluctuation factor:
" K ¼
L X
Fi 1 e
lDti
lTi
e
# .
In this calculation, we divided the total irradiation time into L parts, where L is the number of time intervals in which the irradiation time is divided, Dti is the duration of the ith time interval, Ti is the time interval from the end of the ith interval to the end of irradiation, Fi is the neutron flux averaged over the sample during the Dti, F is the neutron flux averaged over the sample during the total irradiation time T. In order to take out the effect from the excited state, we chose the formula detailed in the previous literatures (Luo et al., 2008; Zhou et al., 2005, 2006). The growth of product gY from the m Y / gY process is shown in Fig. 1. During the irradiation (T1), the number of the products mY and g Y (here, gY only from the mY / gY process) are:
MNA hFsm 1 elm t ; Alm
Nm ðtÞ ¼
Ng ðtÞ ¼
(4)
MNA hFsm Xit 1 1 elm t lg lg lm A MNA hFsm Xit 1 1 lg t þ e : lg lm lg A
(5)
In the cooling process, the number of the products only from the mY / gY process) are:
3.1. The cross-section calculation
sx ¼
69
FS:
0
Nm ðt 0 Þ ¼ Nm ðT1 Þelm t ¼
Ng ðt 0 Þ ¼
0 MNA hFsm Xit
1 elm T1 elm t A lg lm l 0 MNA hFsm Xit m
1 elg T1 elg t : A lg lg lm
In the process of measurement, gY (gY only from the process) is:
Ng ðt 00 Þ ¼
165
Ho(n,2n)164mHo 100 Ho(n,2n)164gHo 180 W(n,2n)179mW 0.13 180 W(n,2n)179gW 93 Nb(n,2n)92mNb 100
37.5 min
165
29 min 6.40 min 37.05 min 10.15 d
94.0
Ig(%)
m
Y / gY
(8) So the count of full-energy peak from the measured characteristic g-ray of gY (gY only from the mY / gY process) is:
Probability of transition (m/g)
0.137 100%
73.4 2.0 221.5 8.51 99.72% 133.84 0.111 934.44 99.074 99.07%
(7)
MNA hFsm Xit 00
1 elm T1 elm T2 elm t A lg lm l 00 MNA hFsm Xit m
1 elg T1 elg T2 elg t : A lg lg lm
(3)
Eg (keV)
(6)
dNg ðt 0 Þ ¼ lm Nm ðt 0 ÞXit lg Ng ðt 0 Þ; dt
Table 1 The abundance ratios of targets and the decay data of products (Browne and Firestone, 1996). Half-live of products
Y and gY (gY
0 MNA hFsm 1 elm T1 elm t ; Alm
i
Reaction channels Abundance of target isotope (%)
m
Fig. 1. The development of product gY from
m
Y.
70
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
Cg ¼ ¼
Z
T3
0
lg Ng ðt 00 Þ Fgs Fgg
end, we obtained the cross-sections of W(n,2n)179gW as follows, in Table 2.
p
Igg 3g dt 00
MNA hFsm Xit Igg 3pg l g
1 elm T1 elm T2 AFgs Fgg lm lg lm MN hFsm X Igg 3p l g A it m
1 elm T3 AFgs Fgg lg lg lm 1 elg T1 elg T2 1 elg T3 : (9)
But the process above doesn’t contain the neutron fluence fluctuation factor – the K factor. Using formula (3) and dividing the total irradiation time (T1) into L parts, with the homologous analysis above we can get:
Cg0
2 2 p Igg 3g Kg Xit lg Sm Dm lm Sg Dg Fms Fmg Fmc
Cm : ¼ p Ilm 3m Km Sm Dmm Fgs Fgg lg lg lm
(10)
In the formula,
Sm ¼ 1 elm T1 ;
Reaction channel Our works
The errors in this work are mainly from statistic uncertainty (4% for tungsten), the error of detector’s efficiency (2.5%), the errors from correction factors of self-absorption (3.5%) (Storm and Israel, 1970), the errors transmitted from the corresponding excited states, and the errors transmitted from every element in formula (1), however, we did not calculate these errors caused by the uncertainties of the abundance of target isotope and half-live of products in Table 1. For instance, the uncertainty of the abundance of 180W is nearly 30% (Browne and Firestone, 1996). According to the previous results in Table 2, there is some discrepancy between them, unfortunately, each of them has unacceptable error. So we concluded them as following:
(1) There are five reports for 165Ho(n,2n) 164gHo reaction, as shown in Fig. 2. Since energy of characteristic-g between 164gHo and 164m Ho is low, High-Purity Germanium detector’s detection efficiency error is increased, which is the main source of the error. It is therefore proposed to use lithium–silicon detectors for further measurements. By the way, from previous work (Fang et al., 2008) of 165Ho(n,2n) 164mHo reaction, we get the cross-sections of 165Ho(n,2n) 164gþmHo reaction: 1365 128 mb at 14.1 0.2 MeV, 1427 150 mb at 14.6 0.3 MeV. Compared with the result of 165Ho(n,2n) 164gþmHo reaction from ENDFB6 (1960 mb at 14.1 MeV, 1986 mb at 14.6 MeV), our data is much smaller.
Reference Crosssection (mb)
165
Energy (MeV)
Cross-section References (mb)
Ho(n,2n)164gHo 14.1 0.2 513 58
14.28 0.05 439 57.07
14.6 0.3 449 61
14.58 0.05 401 52.13 14.7 14.7 0.15
831 123 831 123
14.7 0.025 600 120 14
W(n,2n)179gW
3.2. Discussions
Dm ¼ elm T2 1 elm T3 ; Dg ¼ elg T2 1 elg T3 ; P P l2g Dm Li¼ 1 Fi 1 elm Ti elm ti l2m Dg Li¼ 1 Fi 1 elg Ti elg ti Kg ¼ ; F l2g Sm Dm l2m Sg Dg PL lm Ti elm ti p i ¼ 1 Fi 1 e MNA hFsm Irm 3m Km Sm Dmm ; Km ¼ : Cm ¼ FSm AFms Fmg Fmc lm
Table 2 Summary of the cross-section measurements in present work.
180
Ho(n,2n)164gHo and
Sg ¼ 1 elg T1 ;
Briefly, the subscripts g and m represent ground state and excited state, respectively. Such as Igg is characteristic-g intensity of ground state, Fgg and Fmg mean the correction factors for the self-absorption of the sample for the characteristic gamma ray from ground state and excited state, and Xit represents the transition of branching ratio from excited state to ground state, Cg0 is the deducted part of the measured value from the full-peak characteristic g-ray of ground state, and the detailed distributions of other parameters, see references (Zhou et al., 2005, 2006). At the
Energy (MeV)
165
180
13.5 0.3 1239 368 14.7 0.3 14.1 0.2 1361 357
730 100
1866 176
Sakane et al., 2001 Sakane et al., 2001 Qaim, 1974 Reggoug and Paic, 1982 Steiner et al., 1969 Sethi and Mukherjee, 1966 Qaim and Graca, 1975 Fig. 2.
165
Ho(n,2n)164gHo.
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
(2) Only Qaim and Graca (1975) reported the cross-section of the 180 W(n,2n)179gW reaction with single energy point. In this term, we didn’t show any graph to compare. Due to the low abundance of isotope 180W and the low branching ratio of 179g W characteristics-g energy, additionally, the greater absorption coefficient of tungsten samples, these factors brought many troubles to the measurement, and caused a great error. However, for testing the applicability of the statistical model to the (n,2n) reaction on nuclides rather away from the stability line, these data should be useful. By the way, from previous work (Fang et al., 2008) of 180W(n,2n)179mW reaction, we get that the cross-sections of 180W(n,2n)179gþmW reaction are 1735 373 mb at 13.5 0.3 MeV, 1928 363 mb at 14.1 0.2 MeV. Acknowledgements The authors are grateful to the crew of the K-400 Neutron Generator at Institute of Nuclear Physics and Chemistry of China Academy of Engineering Physics (CAEP) for their excellent support. References Browne, E., Firestone, R.B., 1996. Table of Radioactive Isotopes, USA, 232 pp. Cheng, E.T., 1989. Radioactivity aspects of fusion reactors. Fusion Eng. Des. 10, 231–242. Eapen, P.K., Salaita, G.N., 1975. Isomeric cross-section ratios for (n,2n) reactions at 14.8 MeV. J. Inorg. Chem. 37, 1121–1124. Fang, Kaihong, Xu, Shiwei, Lan, Changlin, Xu, Xiaosan, Kong, Xiangzhong, Liu, Rong, Jiang, Li, 2008. Cross-section measurement for the reactions producing shortlived nuclei induced by neutrons around 14 MeV. Appl. Radiat. Isot. 66,1104–1107. Filatenkov, A.A., Chuvaev, S.V., Aksenov, V.N., Yakovlev, V.A., Malyshenkov, A.V., Vasil’ev, S.K., Avrigeanu, M., Avrigeanu, V., Smith, D.L., Ikeda, Y., Wallner, A., Kutschera, W., Priller, A., Steier, P., Vonach, H., Mertens, G., Rochow, W., 1999. Rep. RI-252. Igashira, M., Ohsaki, T., 2002. Neutron economy and nuclear data for transmutation of long-lived fission products. Prog. Nucl. Energy 40, 555–560.
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Kao, T.H., Alford, W.L., 1975. Isomeric cross sections for the (n,2n) reaction on 82Se, 81 Br, and 45Sc at 15.1 MeV. Nucl. Phys. A 237, 11–17. Lewis, V.E., Zieba, K.J., 1980. A transfer standard for d þ t neutron fluence and energy. Nucl. Instrum. Methods 174, 141–144. Luo, Junhua, Tuo, Fei, , XiangzhongKong, Jiang, Li, 2008. Measurements of activation cross-sections for the 96Ru(n,d*)95gTc reaction for neutrons with energies between 13.3 and 15.0 MeV. Appl. Radiat. Isot., doi:10.1016/ j.apradiso.2008.04.017. Markovskij, D.V., Forrest, R.A., Freiesleben, H., Kovalchuk, V.D., Richter, D., Seidel, K., Tereshkin, V.I., Unholzer, S., 2000. Experimental investigation of radioactivities induced in fusion reactor structural materials by 14-MeV neutrons. Fusion Eng. Des. 51–52, 695–700. Nuray, B., 1977. Isomeric cross section ratios in the 197Au(n,2n)197Au reaction. Nucl. Instrum. Methods 146, 535–539. Qaim, S.M., 1974. Total (n,2n) cross sections and isomeric cross-section ratios at 14.7 MeV in the region of rare earths. Nucl. Phys. A 224, 319–330. Qaim, S.M., Graca, C., 1975. Neutron activation cross sections at 14.7 MeV for isotopes of tungsten. Nucl. Phys. A 242, 317–322. Reggoug, A., Paic, G., 1982. Measurement of (n,2n) reaction cross sections by X-ray spectroscopy. Berrada M. Univ. Mohammed V, Rabat, Annual Rep. 5, 14. Robert, K.S., Larry, R.G., 1984. Measurement of the 27Al(n,2n)26Al reaction cross section for fusion reactor application. J. Nucl. Mater. 122/123, 1071–1077. Sakane, H., Kasugai, Y., Shibata, M., Iida, T., Kawade, K., Takahashi, A., Fukahori, T., 2001. Measurement of activation cross-sections for (n,2n) reactions producing short-lived nuclei in the energy range between 13.4 and 14.9 MeV. Ann. Nucl. Energy 28, 1175–1192. Sethi, B., Mukherjee, S.K., 1966. The decay of 164Ho. Nucl. Phys. 85, 227–240. Steiner, E., Huber, P., Salathe, W., Wagner, R., 1969. (n,2n) cross-sections and isomer cross-section ratios of Ge-76 and Ho-165 in the energy range from 12.5 to 18.5 MeV. Helv. Phys. Acta 43, 17 (in German). Storm, E., Israel, H.I., 1970. Atomic Data and Nucl. Data Tables 7, 565. Vanska, R., Rieppo, R., 1981. The experimental isomeric cross-section ratio in the nuclear activation technique. Nucl. Instrum. Methods 179, 525–532. Wang, YongChang, Yuan, JunQian, Ren, ZhongLiang, 1990. Cross section measurement for 62Ni(n,a)59Fe reaction. High Energy Phys. Nucl. Phys. 14, 1117–1120 (in Chinese). Zhou, FengQun, Luo, JunHua, Yi, YanLing, Tuo, Fei, Kong, Xiangzhong, 2005. A formula used to subtract the effect of excited state to ground state in measurement of cross section of nuclear reaction. High Energy Phys. Nucl. Phys. 29, 741–744 (in Chinese). Zhou, Fengqun, Zhang, Yimin, Tuo, Fei, Yi, Yanling, Kong, Xiangzhong, 2006. Crosssection measurements for the 128Te(n,2n)127mTe reaction induced by neutrons around 14 MeV. Appl. Radiat. Isot 64, 815–817.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Measurements of activation cross-sections for 165Ho(n,2n)164gHo and 180W(n,2n)179gW reactions induced by neutrons around 14 MeV Kaihong Fang a, *, Yang Xiang a, Yuncheng Han a, Xiangzhong Kong a, Tieshan Wang a, Rong Liu b, Li Jiang b a b
School of Nuclear Science and Technology, Lanzhou University, Lanzhou, Gansu Province 730000, PR China Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang, Sichuan Province 621900, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2008 Received in revised form 26 October 2008 Accepted 17 November 2008
The cross-sections of 165Ho(n,2n)164gHo and 180W(n,2n)179gW reactions induced by neutrons around 14 MeV were measured using activation technique and calculated by a previously developed formulas, in which the neutron flux was determined using the monitor reaction 93Nb(n,2n)92mNb. Because both of the excited and ground states were produced in each of the two reactions, one formula was introduced to take out the effect from excited state. Comparison between this work and old data were given. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Holmium Tungsten Neutron Cross-section Activation technique
1. Introduction The cross-section of nuclear reaction is fundamental to the nuclear phenomena and basic for the application of nuclear technologies. Cross-section data for reactions induced by neutrons around 14 MeV are important for the design of fusion reactor. These data are needed to estimate induced radioactivity, nuclear transmutation, radiation damage and so on (Robert and Larry, 1984; Cheng, 1989; Markovskij et al., 2000; Igashira and Ohsaki, 2002). In the case of isomeric cross-sections, they are useful for various studies such as transfer of angular momentum, spin-dependence of nuclear level density, refinements in gamma transition theories and testing of theoretical nuclear models (Kao and Alford, 1975; Eapen and Salaita, 1975; Nuray, 1977; Vanska and Rieppo, 1981). Thus the precise cross-sections of all kinds of nuclear reactions are very important and necessary. In this work, the cross-sections of 165Ho(n,2n)164gHo and 180 W(n,2n)179gW reactions induced by the 14 MeV neutrons have been measured. The products contain not only the ground state but also the corresponding excited state, so the products of the excited states will decay to corresponding ground states while irradiating, cooling and IT ð100%Þ measurement process. For instance, 164m Ho ! 164g Ho, in the process of calculating the cross-section of the 165Ho(n,2n)164gHo
* Corresponding author. Tel.: þ86 931 8913551. E-mail address: [email protected] (K. Fang). 1350-4487/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.11.001
reaction Cx in formula (1) should be subtracted the contribution from 164m Ho. Furthermore, the half-lives of 164mHo and 164gHo (37.5 min and 29 min, respectively) are in the same order of magnitude that leads to the effect is very obvious. Since there are a few data from the reports and also differentia among them (Qaim and Graca, 1975; Qaim, 1974; Reggoug and Paic, 1982; Sakane et al., 2001; Sethi and Mukherjee, 1966; Steiner et al., 1969), it’s necessary to remeasure the cross-sections of these two reactions. It should be mentioned that for 180W(n,2n)179gW reaction there is only one report for single energy point in 1975 (Qaim and Graca, 1975), this work thus covers a slightly broader range of energies. 2. Experiment All the samples (holmium powder of 99.9% purity, tungsten powder of 99.8% purity) and columbium (Filatenkov et al., 1999, of monitor 99.99%) were made into round disks with a diameter of 2.0 cm, the thickness of samples was 1.5 mm and 1.7 mm, the thickness of columbium was 0.3–0.5 mm. Each of samples was sandwiched between two Nb foils. The samples were placed at 50 – 135 angles relative to the deuteron beam direction and centered about the T–Ti target at distances of 3.5 cm. Irradiations were carried out at the K-400 Intense Neutron Generator at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, and lasted from 0.5 to 1 h with
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
a flux rate yield of about 3 1010–4 1010 n/s. Neutrons in the 14 MeV region were produced by the means of the T(d,n)4He reaction with a deuteron beam of 220 keV and beam current of 350 mA. The solid tritium–titanium (T–Ti) target used in the generator was about 2.18 mg/cm2 thick. During irradiation, the neutron flux was monitored by accompanying a-particles so that the corrections could be made for small variations in the yield. The neutron energies in the measurements were determined by crosssections ratio for 93Nb(n,2n)92mNb and 90Zr(n,2n)89mZr reactions (Lewis and Zieba, 1980). The activated samples were studied for their g-activities by a low background, high efficiency g-ray spectrometry, using a well calibrated GEM-60P coaxial high-purity germanium (HPGe) detector (crystal diameter: 70.1 mm, crystal length: 72.3 mm) (ORTEC, made in U.S.A.) with a relative efficiency of w68% and an energy resolution of w1.7 keV (FWHM) at 1.33 MeV. The uncertainty in the absolute efficiency curve at 5.5 cm was estimated to be w2%, while the uncertainty of the activity of the standard source was w1%. The decay characteristics of the radioactive product nuclides and the natural abundances of the target isotopes under investigation are summarized in Table 1. 3. Result and discussion
The measured cross-sections sx were calculated by the activation formula (Wang et al., 1990):
3Ig hKSMD 0 ½lAFCx s ; 3Ig hKSMD x ½lAFC0 0
(1)
where the subscripts 0 and x represent terms corresponding to the monitor reaction and the measured reaction, s0 is the cross-section of monitor reaction, 3 is the full-energy peak efficiency of the measured characteristic g-ray, Ig is the g-ray intensity, h is the abundance of the target nuclide, S ¼ 1 elT is the growth factor of the residual nuclide, l is the decay constant, T is the total irradiation time, M is the mass of sample, D ¼ elt1 elt2 is the counting collection factor, t1 and t2 are time intervals from the end of the irradiation to the start and finish of counting, respectively, A is the atomic weight, C is the measured full-energy peak area and F is the total correction factor of the activity:
F ¼ fs fc fg ;
(2)
where fs, fc and fg are the correction factors for the self-absorption of the sample at a given g-energy, the coincidence sum effect of cascade g-rays in the investigated nuclide and in the counting geometry, respectively. K is the neutron fluence fluctuation factor:
" K ¼
L X
Fi 1 e
lDti
lTi
e
# .
In this calculation, we divided the total irradiation time into L parts, where L is the number of time intervals in which the irradiation time is divided, Dti is the duration of the ith time interval, Ti is the time interval from the end of the ith interval to the end of irradiation, Fi is the neutron flux averaged over the sample during the Dti, F is the neutron flux averaged over the sample during the total irradiation time T. In order to take out the effect from the excited state, we chose the formula detailed in the previous literatures (Luo et al., 2008; Zhou et al., 2005, 2006). The growth of product gY from the m Y / gY process is shown in Fig. 1. During the irradiation (T1), the number of the products mY and g Y (here, gY only from the mY / gY process) are:
MNA hFsm 1 elm t ; Alm
Nm ðtÞ ¼
Ng ðtÞ ¼
(4)
MNA hFsm Xit 1 1 elm t lg lg lm A MNA hFsm Xit 1 1 lg t þ e : lg lm lg A
(5)
In the cooling process, the number of the products only from the mY / gY process) are:
3.1. The cross-section calculation
sx ¼
69
FS:
0
Nm ðt 0 Þ ¼ Nm ðT1 Þelm t ¼
Ng ðt 0 Þ ¼
0 MNA hFsm Xit
1 elm T1 elm t A lg lm l 0 MNA hFsm Xit m
1 elg T1 elg t : A lg lg lm
In the process of measurement, gY (gY only from the process) is:
Ng ðt 00 Þ ¼
165
Ho(n,2n)164mHo 100 Ho(n,2n)164gHo 180 W(n,2n)179mW 0.13 180 W(n,2n)179gW 93 Nb(n,2n)92mNb 100
37.5 min
165
29 min 6.40 min 37.05 min 10.15 d
94.0
Ig(%)
m
Y / gY
(8) So the count of full-energy peak from the measured characteristic g-ray of gY (gY only from the mY / gY process) is:
Probability of transition (m/g)
0.137 100%
73.4 2.0 221.5 8.51 99.72% 133.84 0.111 934.44 99.074 99.07%
(7)
MNA hFsm Xit 00
1 elm T1 elm T2 elm t A lg lm l 00 MNA hFsm Xit m
1 elg T1 elg T2 elg t : A lg lg lm
(3)
Eg (keV)
(6)
dNg ðt 0 Þ ¼ lm Nm ðt 0 ÞXit lg Ng ðt 0 Þ; dt
Table 1 The abundance ratios of targets and the decay data of products (Browne and Firestone, 1996). Half-live of products
Y and gY (gY
0 MNA hFsm 1 elm T1 elm t ; Alm
i
Reaction channels Abundance of target isotope (%)
m
Fig. 1. The development of product gY from
m
Y.
70
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
Cg ¼ ¼
Z
T3
0
lg Ng ðt 00 Þ Fgs Fgg
end, we obtained the cross-sections of W(n,2n)179gW as follows, in Table 2.
p
Igg 3g dt 00
MNA hFsm Xit Igg 3pg l g
1 elm T1 elm T2 AFgs Fgg lm lg lm MN hFsm X Igg 3p l g A it m
1 elm T3 AFgs Fgg lg lg lm 1 elg T1 elg T2 1 elg T3 : (9)
But the process above doesn’t contain the neutron fluence fluctuation factor – the K factor. Using formula (3) and dividing the total irradiation time (T1) into L parts, with the homologous analysis above we can get:
Cg0
2 2 p Igg 3g Kg Xit lg Sm Dm lm Sg Dg Fms Fmg Fmc
Cm : ¼ p Ilm 3m Km Sm Dmm Fgs Fgg lg lg lm
(10)
In the formula,
Sm ¼ 1 elm T1 ;
Reaction channel Our works
The errors in this work are mainly from statistic uncertainty (4% for tungsten), the error of detector’s efficiency (2.5%), the errors from correction factors of self-absorption (3.5%) (Storm and Israel, 1970), the errors transmitted from the corresponding excited states, and the errors transmitted from every element in formula (1), however, we did not calculate these errors caused by the uncertainties of the abundance of target isotope and half-live of products in Table 1. For instance, the uncertainty of the abundance of 180W is nearly 30% (Browne and Firestone, 1996). According to the previous results in Table 2, there is some discrepancy between them, unfortunately, each of them has unacceptable error. So we concluded them as following:
(1) There are five reports for 165Ho(n,2n) 164gHo reaction, as shown in Fig. 2. Since energy of characteristic-g between 164gHo and 164m Ho is low, High-Purity Germanium detector’s detection efficiency error is increased, which is the main source of the error. It is therefore proposed to use lithium–silicon detectors for further measurements. By the way, from previous work (Fang et al., 2008) of 165Ho(n,2n) 164mHo reaction, we get the cross-sections of 165Ho(n,2n) 164gþmHo reaction: 1365 128 mb at 14.1 0.2 MeV, 1427 150 mb at 14.6 0.3 MeV. Compared with the result of 165Ho(n,2n) 164gþmHo reaction from ENDFB6 (1960 mb at 14.1 MeV, 1986 mb at 14.6 MeV), our data is much smaller.
Reference Crosssection (mb)
165
Energy (MeV)
Cross-section References (mb)
Ho(n,2n)164gHo 14.1 0.2 513 58
14.28 0.05 439 57.07
14.6 0.3 449 61
14.58 0.05 401 52.13 14.7 14.7 0.15
831 123 831 123
14.7 0.025 600 120 14
W(n,2n)179gW
3.2. Discussions
Dm ¼ elm T2 1 elm T3 ; Dg ¼ elg T2 1 elg T3 ; P P l2g Dm Li¼ 1 Fi 1 elm Ti elm ti l2m Dg Li¼ 1 Fi 1 elg Ti elg ti Kg ¼ ; F l2g Sm Dm l2m Sg Dg PL lm Ti elm ti p i ¼ 1 Fi 1 e MNA hFsm Irm 3m Km Sm Dmm ; Km ¼ : Cm ¼ FSm AFms Fmg Fmc lm
Table 2 Summary of the cross-section measurements in present work.
180
Ho(n,2n)164gHo and
Sg ¼ 1 elg T1 ;
Briefly, the subscripts g and m represent ground state and excited state, respectively. Such as Igg is characteristic-g intensity of ground state, Fgg and Fmg mean the correction factors for the self-absorption of the sample for the characteristic gamma ray from ground state and excited state, and Xit represents the transition of branching ratio from excited state to ground state, Cg0 is the deducted part of the measured value from the full-peak characteristic g-ray of ground state, and the detailed distributions of other parameters, see references (Zhou et al., 2005, 2006). At the
Energy (MeV)
165
180
13.5 0.3 1239 368 14.7 0.3 14.1 0.2 1361 357
730 100
1866 176
Sakane et al., 2001 Sakane et al., 2001 Qaim, 1974 Reggoug and Paic, 1982 Steiner et al., 1969 Sethi and Mukherjee, 1966 Qaim and Graca, 1975 Fig. 2.
165
Ho(n,2n)164gHo.
K. Fang et al. / Radiation Measurements 44 (2009) 68–71
(2) Only Qaim and Graca (1975) reported the cross-section of the 180 W(n,2n)179gW reaction with single energy point. In this term, we didn’t show any graph to compare. Due to the low abundance of isotope 180W and the low branching ratio of 179g W characteristics-g energy, additionally, the greater absorption coefficient of tungsten samples, these factors brought many troubles to the measurement, and caused a great error. However, for testing the applicability of the statistical model to the (n,2n) reaction on nuclides rather away from the stability line, these data should be useful. By the way, from previous work (Fang et al., 2008) of 180W(n,2n)179mW reaction, we get that the cross-sections of 180W(n,2n)179gþmW reaction are 1735 373 mb at 13.5 0.3 MeV, 1928 363 mb at 14.1 0.2 MeV. Acknowledgements The authors are grateful to the crew of the K-400 Neutron Generator at Institute of Nuclear Physics and Chemistry of China Academy of Engineering Physics (CAEP) for their excellent support. References Browne, E., Firestone, R.B., 1996. Table of Radioactive Isotopes, USA, 232 pp. Cheng, E.T., 1989. Radioactivity aspects of fusion reactors. Fusion Eng. Des. 10, 231–242. Eapen, P.K., Salaita, G.N., 1975. Isomeric cross-section ratios for (n,2n) reactions at 14.8 MeV. J. Inorg. Chem. 37, 1121–1124. Fang, Kaihong, Xu, Shiwei, Lan, Changlin, Xu, Xiaosan, Kong, Xiangzhong, Liu, Rong, Jiang, Li, 2008. Cross-section measurement for the reactions producing shortlived nuclei induced by neutrons around 14 MeV. Appl. Radiat. Isot. 66,1104–1107. Filatenkov, A.A., Chuvaev, S.V., Aksenov, V.N., Yakovlev, V.A., Malyshenkov, A.V., Vasil’ev, S.K., Avrigeanu, M., Avrigeanu, V., Smith, D.L., Ikeda, Y., Wallner, A., Kutschera, W., Priller, A., Steier, P., Vonach, H., Mertens, G., Rochow, W., 1999. Rep. RI-252. Igashira, M., Ohsaki, T., 2002. Neutron economy and nuclear data for transmutation of long-lived fission products. Prog. Nucl. Energy 40, 555–560.
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