- Email: [email protected]
Measurements of activation cross sections for 175Lu(n, α)172Tm, 176Lu(n, α)173Tm and 175Lu(n, p)175m+gYb reactions induced by neutrons around 14 MeV
Annals of Nuclear Energy 38 (2011) 1693–1697
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Measurements of activation cross sections for 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions induced by neutrons around 14 MeV Junhua Luo a,b,⇑, Fei Tuo c, Xiangzhong Kong b a
School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China c National Institute for Radiological Protection, China CDC, Beijing 100088, China b
a r t i c l e
i n f o
Article history: Received 1 April 2010 Received in revised form 2 April 2011 Accepted 11 April 2011 Available online 2 May 2011 Keywords: Neutrons Nuclear reaction Cross section Activation technique Lutetium
a b s t r a c t The cross sections for the 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions have been measured in the neutron energy range of 13.5–14.8 MeV using the activation technique. The first data for 175 Lu(n, a)172Tm reaction cross sections are presented. In our experiment, the fast neutrons were produced via the 3H(d, n)4He reaction on K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP). Induced gamma activities were measured by a high-resolution (1.69 keV at 1332 keV for 60Co) gamma-ray spectrometer with high-purity germanium (HPGe) detector. Measurements were corrected for gamma-ray attenuations, random coincidence (pile-up), dead time and fluctuation of neutron flux. The neutron fluences were determined by the cross section of 93Nb(n, 2n)92mNb or 27Al(n, a)24Na reactions. The neutron energy in the measurement was by the cross section ratios of 90Zr(n, 2n)89m+gZr and 93 Nb(n, 2n)92mNb reactions. The results were discussed and compared with experimental data found in the literature and with results of published empirical formulae. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Experimental data of neutron-induced reactions in the energy range around 13–15 MeV are needed to verify the accuracy of nuclear models used in the calculation of cross sections. Furthermore, the data are of considerable importance for practical applications, such as for integral calculations on the first wall, blanket and shield of a conceptual fusion power reactor. The data for gas production via neutron induced reactions are of great importance in the domain of fusion reactor technology, particularly of nuclear transmutation rates, nuclear heating and radiation damage due to gas formation. A lot of experimental data on neutron induced cross sections for fusion reactor technology applications have been reported and great efforts have been devoted to compilations and evaluations (CINDA-A, 2000; Mclane et al., 1988). The variations in the cross sections with the neutron energy are also of great interest for studying the excitation of nuclei to different energy levels and subsequent decay to ground state, either directly or through different energy levels including metastable state. We chose to study the neutron-induced reaction cross sections of the lutetium (Lu) isotopes mainly for three reasons. First, lutetium has the highest atomic number of all the rare earth elements (REE). It is
⇑ Corresponding author at: School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China. Tel.: +86 09368280176. E-mail address: [email protected] (J. Luo). 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.04.014
comprised of two isotopes 175Lu and 176Lu and is followed by the element hafnium. Due to its importance to s-process studies, lutetium has attracted considerable scientific interest. Second, The reaction cross sections of 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb around the neutron energies 14 MeV were only obtained by three laboratories (Sato et al., 1975; Qaim, 1976; Coleman et al., 1959), but all measurements were obtained before 1980. Furthermore, there were large discrepancies in those data. The large discrepancies are probably due to use of different methods, energy resolution of detectors, target materials and adopting different nuclear parameters. Third, for 175Lu(n, a)172Tm reaction of lutetium isotopes, the cross sections have been not reported. Thus it is necessary to measure then again and obtain excitation functions around the neutron energies of 14 MeV. About the cross sections and isomeric cross section ratios of 175Lu(n, 2n)174m,gLu in the neutron energies of 13.5–14.8 MeV for lutetium have been reported by authors (Vallis, 1966; Qaim, 1974; Frehaut and Mosinski, 1974; Dilg et al., 1968; Laurec et al., 1981; Wille and Fink, 1960; Nethaway, 1972; Veeser et al., 1977; Bayhurst et al., 1975; Luo et al., 2007b). In the present work, the cross sections of the 175Lu(n, a)172Tm, 176 Lu(n, a)173Tm and 175Lu(n, p)175m+gYb were measured in at neutron energy 13.5–14.8 MeV and a gamma-ray counting technique was applied using high-resolution gamma-ray spectrometer and data acquisition system. Pure Lu2O3 was used as the target material. The reaction yields were obtained by absolute measurement of the gamma activities of the product nuclei using a coaxial high-purity germanium detector. The neutron energies in this
1694
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697
measurement was determined by cross section ratios for the 90 Zr(n, 2n)89m+gZr and 93Nb(n, 2n)92mNb reactions (Lewis and Zieba, 1980). 2. Experimental Cross sections were measured by activation and identification of the radioactive products. This technique is very suitable for investigating low-yield reaction products and closely space low-lying isomeric states, provided their lifetimes are not too short. The details have been described over the years in many publications (Bostan and Qaim, 1994; Cserpák et al., 1994; Luo Junhua et al., 2005; Nesaraja et al., 2003; Rahman and Qaim, 1985). Here we give some salient features relevant to the present measurements. 2.1. Samples and irradiations About 3 g of Lu2O3 powder of natural isotopic composition (>99.99% pure) was pressed at 10 ton/cm2, and a pellet, 0.2 cm thick and 2.0 cm in diameter was obtained. Three such pellets were prepared. Monitor foils of Nb (99.99% pure, 0.2 mm thick) and Al (99.999% pure, 0.04 mm thick) of the same diameter as the pellets were then attached in front and at the back of each sample. Irradiation of the samples was carried out at the K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP) and lasted 128 min with a yield 4–5 1010 n/s. Neutrons were produced by the T(d, n)4He reaction with an effective deuteron beam energy of 134 keV and beam current of 230 lA. The tritium– titanium (T–Ti) target used in the generator was 2.18 mg/cm2 thick. The neutron flux was monitored by a uranium fission chamber so that corrections could be made for small variations in the yield. The groups of samples were placed at 0°, 90° or 135° angles relative to the beam direction and centered about the T–Ti target at distances of 3–5 cm. Cross sections for 93Nb(n, 2n)92mNb or 27Al (n, a)24Na reactions (Wagner et al., 1990) were selected as monitors to measure reaction cross section of the 175Lu(n, a)172Tm, 176 Lu(n, a)173Tm and 175Lu(n, p)175m+gYb. 2.2. Determination of the incident neutron energy In the D–T reaction (Q value of 17.6 MeV), induced by deuterons of energy Ed, the kinetic energy En of the neutrons emitted at angle h can be estimated (Curtis, 1969) from the following expression: 1
ðEn Þ2 ¼
Fig. 1. Angular dependence of D–T neutron energy. The neutron energies were calculated by choosing the incident deuteron energy Ed = 134 keV. The open circles show experimental data determined by the Nb/Zr method (Lewis and Zieba, 1980).
sources. One of the gamma-ray spectra is shown in Fig. 2. The decay characteristics of the product radioisotopes and the natural abundances of the target isotopes under investigation are summarized in Table 1 (Browne and Firestone, 1996). 2.4. Calculation of cross sections and their uncertainties The measured cross sections can be calculated by the following formula (cf. Luo et al., 2007a):
rx ¼
½SeIc gKMD0 ½kAFCx r0 ½SeIc gKMDx ½kAFC0
where the subscript m represents the term corresponding to the monitor reaction and subscript x corresponds to the measured reaction. e is the full-energy peak efficiency of the measured characteristic gamma-ray, Ic the gamma-ray intensity, g the abundance of the target nuclide, M the mass of sample, D ¼ ekt1 ekt2 the counting collection factor, t1, t2 the time intervals from the end of the irradiation to the start and end of counting, respectively, A the atomic weight, C the measured full-energy peak area, k the decay constant and F is the total correction factor of the activity:
1 1 ðMd M n Ed Þ2 cos h þ Md Mn Ed cos2 h þ fMa þ Mn g½Ma Q þ Ed ðM a M n Þ 2 Ma þ Mn ð1Þ
where Md, Mn and Ma are the masses of deuteron, neutron and alpha particle, respectively. The effective D–T neutron energy at irradiation position was determined by the Nb/Zr method (Curtis, 1969; Lewis and Zieba, 1980; Nethaway, 1978; Pavlik et al., 1982). The measured neutron energy was shown in Fig. 1 together with the calculation using Eq. (1). The uncertainty in the neutron energy at 3 to 5 cm was estimated to be 200 keV from a consideration of the sample sizes, d+ beam diameter of about 3–4 mm, and the uncertainty in the Nb/Zr method (Lewis and Zieba, 1980). 2.3. Measurement of radioactivity The gamma-ray activity of 172Tm, 173Tm, 175gYb, 92mNb and 24Na was determined by a high-purity germanium (HPGe) detector (ORTEC, model GEM 60P, Crystal diameter: 70.1 mm, Crystal length: 72.3 mm, made in USA) with a relative efficiency of 68% and an energy resolution of 1.69 keV at 1332 keV for 60Co. The efficiency of the detector was pre-calibrated using various standard gamma
ð2Þ
Fig. 2. The c-ray spectra of about 3 h after the end of the irradiation.
1695
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697 Table 1 Reactions and associated decay data of activation products. Reaction 175
Abundance of target isotope (%) 172
Lu(n, a) Tm Lu(n, a)173Tm Lu(n, p)175mYb 175 Lu(n, p)175gYb 93 Nb(n, 2n)92mNb 27 Al(n, a)24Na
Q-value (MeV)
97.41 ± 0.02 2.59 ± 0.02 97.41 ± 0.02 97.41 ± 0.02 100 100
176 175
7.856 8.518 0.312 0.312 8.83 3.13
F ¼ fs fc fg where fs, fc and fg are correction factors for the self-absorption of the sample at a given gamma-energy, the coincidence sum effect of cascade gamma-rays in the investigated nuclide and in the counting geometry, respectively.
K¼
" L X
#, kDt i
Ui ð1 e
kT i
Þe
Mode of decay (%)
b (100) b (100) IT (100) b (100) EC (100) b (100)
Half-life of product
Ec (keV)
Ic (%)
63.6 h 8.24 h 68.2 ms 4.185 d 10.15 d 14.959 h
1093.7 398.9 – 396.3 934.4 1368.6
6.0 87.9 – 6.4 99.07 100
times (0.1–1%), etc. And some other errors contribution form the parameters of the measured nuclei and standard nuclei, such as, uncertainties of the branching ratio of the characteristic gammarays, uncertainties of the half life of the radioactive product nuclei and so on all are considered. 3. Results and discussion
US
i
where K is the neutron fluence fluctuation factor, L the number of time intervals into which the irradiation time is divided, Dti the duration of the ith time interval, Ti the time interval from the end of the ith interval to the end of irradiation, Ui the neutron flux averaged over the sample during Dti, S ¼ 1 ekT the growth factor of the product nuclide, T = total irradiation time and U is the neutron flux averaged over the sample during the total irradiation time T. The main error sources in our work result from counting statistics (1–21%), standard cross sections uncertainties (1%), detector efficiency (2–3%), weight of samples (0.1%), self-absorption of gamma-ray (0.5%) and the coincidence sum effect of cascade gammarays (0–5%), the uncertainties of irradiation, cooling and measuring
Using the relative activation technique of neutron, each of the samples was sandwiched between two Nb or Al foils which were used as monitor. Because the cross section of 93Nb(n, 2n)92mNb and 27Al(n, a)24Na reactions has been measured by many authors and the value is very accurate, we can select it as a standard. With the irradiation taking place, the neutron flux for the sample was the same as the flux for the monitors. So we can find an equation of neutron flux between them, and avoid importing the neutron flux into the calculation. After having been irradiated, the samples were cooled for about 3 h, and one sample was measured with a relative efficiency of 68% and an energy resolution of 1.69 keV at 1332 keV for 60Co. Cross section values for 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and
Table 2 Summary of cross section measurements. Reaction
This work
Literature values
En (MeV)
r
En (MeV)
r (mb)
Reference
175
Lu(n, a)172Tm
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
612 ± 129 lb 910 ± 173 lb 1126 ± 146 lb
14.5 14.5 14.5 14.5 14.5 14.5 14.5
1.31s 2.18s 1.94s 1.24s 1.98s 1.39s 2.37s
Luo et al. (2008) Kasugai et al. (1995) Csikai et al. (1997) Habbani et al. (2001) Forrest (1986) Konobeyev et al. (1996) Ait-Tahar (1987)
176
Lu(n, a)173Tm
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
704 ± 49 lb 876 ± 70 lb 919 ± 46 lb
14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.6
1.12s 1.94s 1.65s 1.92s 1.81s 1.05s 2.05s 2.3 ± 0.57
Luo et al. (2008) Kasugai et al. (1995) Csikai et al. (1997) Habbani et al. (2001) Forrest (1986) Konobeyev et al. (1996) Ait-Tahar (1987) Sato et al. (1975)
175
Lu(n, p)175m+gYb
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.6 14.7 ± 0.3 14.5
4.1s 5.0s 20.2s 3.5s 10.4s 4.9s 5.1s 18.5 ± 2.3 4.0 ± 0.7 3.42 ± 0.52
Luo et al. (2008) Kasugai et al. (1995) Doczi et al. (1997) Habbani et al. (2001) Forrest (1986) Ait-Tahar (1987) Broeders and Konobeyev (2006) Sato et al. (1975) Qaim (1976) Coleman et al. (1959)
93
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
457.9 ± 6.8 459.8 ± 6.8 459.7 ± 5.0
Wagner et al. (1990) Wagner et al. (1990) Wagner et al. (1990)
27
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
125.7 ± 0.8 121.6 ± 0.6 111.9 ± 0.5
Wagner et al. (1990) Wagner et al. (1990) Wagner et al. (1990)
Nb(n, 2n)92mNb
Al(n, a)24Na
s: semi-empirical predictions at 14.5 MeV.
6.4 ± 0.4 mb 7.4 ± 0.6 mb 8.2 ± 0.5 mb
1696
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697
175
Lu(n, p)175m+gYb reactions were obtained relative to those of the Nb(n, 2n)92mNb or 27Al(n, a)24Na reaction. The cross sections measured in the present work are summarized in Table 2 and are compared with the values given in the literatures and with results of published empirical formulae (Ait-Tahar, 1987; Broeders and Konobeyev, 2006; Csikai et al., 1997; Doczi et al., 1997; Forrest, 1986; Habbani et al., 2001; Kasugai et al., 1995; Konobeyev et al., 1996; Luo et al., 2008). The previous measurements were made with c-ray counting with Ge (Li) detectors (Coleman et al., 1959; Qaim, 1976; Sato et al., 1975). The 398.9 keV (Ic = 87.9%) gamma-ray emitted in the 173Tm decay and 396.3 keV (Ic = 6.4%) gamma-ray emitted in the 175Yb decay were used to deduce the values of the 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reaction cross sections, respectively. It can be seen from Table 2 that the cross sections for 176Lu (n, a)173Tm reaction our measurements are not in agreement with the literature values (Ait-Tahar, 1987; Csikai et al., 1997; Forrest, 1986; Habbani et al., 2001; Kasugai et al., 1995; Konobeyev et al., 1996; Luo et al., 2008; Sato et al., 1975). For the cross section of 175 Lu(n, p)175m+gYb reaction, our results are somewhat higher than those of Ait-Tahar (1987), Broeders and Konobeyev (2006), Coleman et al. (1959), Csikai et al. (1997), Habbani et al. (2001), Kasugai et al. (1995), Konobeyev et al. (1996), Luo et al. (2008), and Qaim, 1976, while our results are lower than that of Doczi et al. (1997), Forrest (1986), and Sato et al. (1975). It should be mentioned that this work presents the first data for the 175Lu(n, a)172Tm reaction. For the 176Lu(n, a)173Tm and 175 Lu(n, p)175m+gYb reactions, the literature data are one energy. This work thus covers a slightly broader range of energies. 93
4. Conclusions We have measured the activation cross sections for 175Lu (n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions on lutetium isotopes induced by 13.5–14.8 MeV neutrons. Our work gives more accurate measurement of cross sections for 175Lu (n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions, during the work we used more newly nuclear data for decay characteristics of the product nuclei and the natural abundances and we also used a high-purity germanium detector (HPGe) which have better energy resolution than GeLi detector that used by early experimenter. The accuracy of the cross sections obtained in the early years were limited, because there are 175Lu, 176Lu for the lutetium and overlapping of the gamma-peaks from different isotopes could not be neglected in the gamma-spectrum measurements with the use of bad resolution power detectors. The decay data such as half and branching ratio of the radioactive product nuclei were less accurate at that early time. In recent years, the reliabilities of the results have improved with the use of the high-resolution Ge semiconductor detectors and the more accurate above-mentioned parameters. A good plan of irradiation and cooling time is also important and in our experiment we selected different irradiation time according to the half life of the product nuclei. In addition, the present measurements were performed in the Low Background Laboratory of Chinese Academy of Engineering Physics and disturbance from environmental radiation was reduced to a very low level. In conclusion, our data would improve the quality of the neutron cross section database. Acknowledgments We would like to thank the Intense Neutron Generator group at Chinese Academy of Engineering Physics for performing the irradiations.
This work was supported by the Key Project of Chinese Ministry of Education (No. 211184) and the Program for Long Yuan Young Innovative Talents of Gansu Province, China.
References Ait-Tahar, S., 1987. Nucl. Phys. 13, 121. Bayhurst, B.P., Gilmore, J.S., Prestwood, R.J., Wilhelmy, J.B., Jarmie, N., Erkkila, B.H., Hardekopf, R.A., 1975. Cross sections for (n, xn) reactions between 7.5 and 28 MeV. Phys. Rev. C 12, 451–467. Bostan, M., Qaim, S.M., 1994. Excitation functions of threshold reactions on45 Sc and55 Mn induced by 6 to 13 MeV neutrons. Phys. Rev. C49, 266–271. Broeders, C.H.M., Konobeyev, A.Yu., 2006. Semi-empirical systematics of (n, p) reaction cross-section at 14.5, 20, and 30 MeV. Nucl. Phys. A 780, 130–145. Browne, E., Firestone, R.B., 1996. Table of Isotopes. Wiley, New York. CINDA-A, 2000. The Index to Literature and Computer Files on Microscopic Neutron Data. International Atomic Energy Agency. Coleman, R.F., Hawker, B.E., O‘connor, L.P., Perkin, J.L., 1959. Cross sections for (n, p) and (n, a) reactions with 14.5 MeV neutrons. Proc. Phys. Soc. (Lond.) 73, 215– 219. Cserpák, F., Sudár, S., Csika, J., Qaim, S.M., 1994. Excitation functions and isomeric cross section ratios of the63 Cu(n, a)60 Com,g,65 Cu(n, a)62 Com,g, and60 Ni(n, p)60 Com,g processes from 6 to 15 MeV. Phys. Rev. C49, 1525–1533. Csikai, J., Semkova, V., Doczi, R., Majdeddin, A.D., Varnagy, M., Buczko, Cs.M., Fenyvesi, A., 1997. Fusion Eng. Des. 37, 65. Curtis, L.F., 1969. Introduction to Neutron Physics, D. Van Nostrand Company, Princeton, NJ. Dilg, W., Vonach, H., Winkler, G., Hille, P., 1968. Measurement of (n, 2n) reactions cross-sections on heavy nuclei. Nucl. Phys. A 118, 9–16. Doczi, R., Semkova, V., Majdeddin, A.D., Buczko, Cs.M., Csikai, J., 1997. INDC(HUN)032, NDS, IAEA. Forrest, R.A., 1986. AERE-R 12419, Harwell Laboratory. Frehaut, J., Mosinski, G., 1974. Measurement of the (n, 2n) cross-sections for56 Fe,59 Co,89 Y,169 Tm,175 Lu,181 Ta,197 Au,209 Bi,238 U and of the (n,3n) cross-section for238 U from threshold to 15 MeV incident neutron energy. R,CEA-R4627. Habbani, F.I., Osman, Khalda, T., 2001. Systematics for the cross-sections of the reactions (n, p), (n, a) and (n, 2n) at 14.5 MeV neutrons. Appl. Radia. Isoto. 54, 283–290. Kasugai, Y., Ikeda, Y., Yamamito, H., Kawade, K., 1995. in: JAERI-Conf. 95-008. Konobeyev, A.Yu., Lunev, V.P., shubin, Yu.N., 1996. Nucl. Instr. Meth. B 108, 233– 242. Laurec, J., Adam, A., De Bruyne, T., 1981. Measurement of the (n, 2n) reaction cross sections of the nuclei Y-89,93 Nb,103 Rh,107 Ag,169 Tm,175 Lu, and197 Au at 14.1 and 14.8 MeV. Report CEA-R-5109. Lewis, V.E., Zieba, K.J., 1980. A transfer standard for d+T neutron fluence and energy. Nucl. Instr. Meth. 174, 141–144. Luo, Junhua, Liu, Gang, Tuo, Fei, Kong, Xiangzhong, Liu, Rong, Jiang, Li, Lou, Benchao, 2007a. Activation cross section for reactions induced by 14 MeV neutrons on natural ruthenium. Phys. Rev. C76, 057601. Luo, Junhua, Tuo, Fei, Zhou, Fengqun, Kong, Xiangzhong, 2008. Semi-empirical systematics for the cross-sections of the reactions (n,a), (n, p) and (n,2n) at 14.5 MeV neutrons on the basis of experimental data measured by Lanzhou University. Nucl Instru. Meth B 266 (22), 4862–4868. Luo, Junhua, Xu, Xiaosan, Cao, Xuexiang, Kong, Xiangzhong, 2007b. Activation cross sections and isomeric cross-section ratios for the (n, 2n) reactions on175 Lu,198 Pt and82 Se from 13.5 to 14.6 MeV. Nucl. Instr. Meth. B 265, 453–460. Mclane, V., Dunford, C.L., Rose, P.F., 1988. Neutron Cross Sections, vol. 2. Academic, New York. Nesaraja, C.D., Sudár, S., Qaim, S.M., 2003. Cross sections for the formation of 69Znm,g and 71Znm,g in neutron induced reactions near their thresholds: Effect of reaction channel on the isomeric cross-section ratio. Phys. Rev. C68, 024603. Nethaway, D.R., 1972. Cross sections for several (n, 2n) reactions at 14 MeV. Nucl. Phys. A 190, 635–644. Nethaway, D.R., 1978. The93 Nb (n, 2n)92m Nb cross section. J. Inorg. Nucl. Chem. 40, 1285–1288. Pavlik, A., Winkler, H., Vonach, H., Paulsen, A., Liskin, H., 1982. Precise measurement of cross sections for the90 Zr (n, 2n)89 Zr reaction from threshold to 20 MeV. J. Phys. G; Nucl. Phys. 8, 1283–1286. 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., 1976. Measurement of (n, p) reaction cross sections at 14.7 MeV using high-pressure liquid chromatography in the region of rare earths, Radiochem. and Radioanal. Letters 25, 335–339. Rahman, M.M., Qaim, S.M., 1985. Excitation functions of some neutron threshold reactions on isotopes of molybdenum. Nucl. Phys. A 435, 43–53. Sato, T., Kanda, Y., Kumabe, I., 1975. Activation cross sections for (n, p) and (n, a) reactions on Nd, Sm, Yb and Lu at 14.6 MeV. J. Nucl. Sci. Technol. 12 (11), 681– 685, Tokyo. Vallis, D.G., 1966. Cross sections for (n, 2n) reaction at 14.7 MeV of some odd-proton nuclei. Report AWRE-O-76/66.
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697 Veeser, L.R., Arthur, E.D., Young, P.G., 1977. Cross sections for (n, 2n) and (n, 3n) reaction above 14 MeV. Phys. Rev. C 16, 1792–1802. Wagner, M., Vonach, H., Pavlik, A., Strohmaier, B., Tagesen, S., and Martinez-Rico, J., 1990. Physik Daten-Physics Data, Evaluation of Cross Sections for 14 Important Neutron-dosimetry Reactions. Fachinformationszentrum Karlsruhe.
1697
Gesellschaft für wissenschaftlich-technische Information mbH, in the Federal Republic of Germany. No. 13-5. Wille, R.G., Fink, R.W., 1960. Activation cross sections for 14.8 MeV neutrons and some new radioactive nuclides in the rare earth region. Phys. Rev 118, 242–248.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Measurements of activation cross sections for 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions induced by neutrons around 14 MeV Junhua Luo a,b,⇑, Fei Tuo c, Xiangzhong Kong b a
School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China c National Institute for Radiological Protection, China CDC, Beijing 100088, China b
a r t i c l e
i n f o
Article history: Received 1 April 2010 Received in revised form 2 April 2011 Accepted 11 April 2011 Available online 2 May 2011 Keywords: Neutrons Nuclear reaction Cross section Activation technique Lutetium
a b s t r a c t The cross sections for the 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions have been measured in the neutron energy range of 13.5–14.8 MeV using the activation technique. The first data for 175 Lu(n, a)172Tm reaction cross sections are presented. In our experiment, the fast neutrons were produced via the 3H(d, n)4He reaction on K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP). Induced gamma activities were measured by a high-resolution (1.69 keV at 1332 keV for 60Co) gamma-ray spectrometer with high-purity germanium (HPGe) detector. Measurements were corrected for gamma-ray attenuations, random coincidence (pile-up), dead time and fluctuation of neutron flux. The neutron fluences were determined by the cross section of 93Nb(n, 2n)92mNb or 27Al(n, a)24Na reactions. The neutron energy in the measurement was by the cross section ratios of 90Zr(n, 2n)89m+gZr and 93 Nb(n, 2n)92mNb reactions. The results were discussed and compared with experimental data found in the literature and with results of published empirical formulae. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Experimental data of neutron-induced reactions in the energy range around 13–15 MeV are needed to verify the accuracy of nuclear models used in the calculation of cross sections. Furthermore, the data are of considerable importance for practical applications, such as for integral calculations on the first wall, blanket and shield of a conceptual fusion power reactor. The data for gas production via neutron induced reactions are of great importance in the domain of fusion reactor technology, particularly of nuclear transmutation rates, nuclear heating and radiation damage due to gas formation. A lot of experimental data on neutron induced cross sections for fusion reactor technology applications have been reported and great efforts have been devoted to compilations and evaluations (CINDA-A, 2000; Mclane et al., 1988). The variations in the cross sections with the neutron energy are also of great interest for studying the excitation of nuclei to different energy levels and subsequent decay to ground state, either directly or through different energy levels including metastable state. We chose to study the neutron-induced reaction cross sections of the lutetium (Lu) isotopes mainly for three reasons. First, lutetium has the highest atomic number of all the rare earth elements (REE). It is
⇑ Corresponding author at: School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China. Tel.: +86 09368280176. E-mail address: [email protected] (J. Luo). 0306-4549/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2011.04.014
comprised of two isotopes 175Lu and 176Lu and is followed by the element hafnium. Due to its importance to s-process studies, lutetium has attracted considerable scientific interest. Second, The reaction cross sections of 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb around the neutron energies 14 MeV were only obtained by three laboratories (Sato et al., 1975; Qaim, 1976; Coleman et al., 1959), but all measurements were obtained before 1980. Furthermore, there were large discrepancies in those data. The large discrepancies are probably due to use of different methods, energy resolution of detectors, target materials and adopting different nuclear parameters. Third, for 175Lu(n, a)172Tm reaction of lutetium isotopes, the cross sections have been not reported. Thus it is necessary to measure then again and obtain excitation functions around the neutron energies of 14 MeV. About the cross sections and isomeric cross section ratios of 175Lu(n, 2n)174m,gLu in the neutron energies of 13.5–14.8 MeV for lutetium have been reported by authors (Vallis, 1966; Qaim, 1974; Frehaut and Mosinski, 1974; Dilg et al., 1968; Laurec et al., 1981; Wille and Fink, 1960; Nethaway, 1972; Veeser et al., 1977; Bayhurst et al., 1975; Luo et al., 2007b). In the present work, the cross sections of the 175Lu(n, a)172Tm, 176 Lu(n, a)173Tm and 175Lu(n, p)175m+gYb were measured in at neutron energy 13.5–14.8 MeV and a gamma-ray counting technique was applied using high-resolution gamma-ray spectrometer and data acquisition system. Pure Lu2O3 was used as the target material. The reaction yields were obtained by absolute measurement of the gamma activities of the product nuclei using a coaxial high-purity germanium detector. The neutron energies in this
1694
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697
measurement was determined by cross section ratios for the 90 Zr(n, 2n)89m+gZr and 93Nb(n, 2n)92mNb reactions (Lewis and Zieba, 1980). 2. Experimental Cross sections were measured by activation and identification of the radioactive products. This technique is very suitable for investigating low-yield reaction products and closely space low-lying isomeric states, provided their lifetimes are not too short. The details have been described over the years in many publications (Bostan and Qaim, 1994; Cserpák et al., 1994; Luo Junhua et al., 2005; Nesaraja et al., 2003; Rahman and Qaim, 1985). Here we give some salient features relevant to the present measurements. 2.1. Samples and irradiations About 3 g of Lu2O3 powder of natural isotopic composition (>99.99% pure) was pressed at 10 ton/cm2, and a pellet, 0.2 cm thick and 2.0 cm in diameter was obtained. Three such pellets were prepared. Monitor foils of Nb (99.99% pure, 0.2 mm thick) and Al (99.999% pure, 0.04 mm thick) of the same diameter as the pellets were then attached in front and at the back of each sample. Irradiation of the samples was carried out at the K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP) and lasted 128 min with a yield 4–5 1010 n/s. Neutrons were produced by the T(d, n)4He reaction with an effective deuteron beam energy of 134 keV and beam current of 230 lA. The tritium– titanium (T–Ti) target used in the generator was 2.18 mg/cm2 thick. The neutron flux was monitored by a uranium fission chamber so that corrections could be made for small variations in the yield. The groups of samples were placed at 0°, 90° or 135° angles relative to the beam direction and centered about the T–Ti target at distances of 3–5 cm. Cross sections for 93Nb(n, 2n)92mNb or 27Al (n, a)24Na reactions (Wagner et al., 1990) were selected as monitors to measure reaction cross section of the 175Lu(n, a)172Tm, 176 Lu(n, a)173Tm and 175Lu(n, p)175m+gYb. 2.2. Determination of the incident neutron energy In the D–T reaction (Q value of 17.6 MeV), induced by deuterons of energy Ed, the kinetic energy En of the neutrons emitted at angle h can be estimated (Curtis, 1969) from the following expression: 1
ðEn Þ2 ¼
Fig. 1. Angular dependence of D–T neutron energy. The neutron energies were calculated by choosing the incident deuteron energy Ed = 134 keV. The open circles show experimental data determined by the Nb/Zr method (Lewis and Zieba, 1980).
sources. One of the gamma-ray spectra is shown in Fig. 2. The decay characteristics of the product radioisotopes and the natural abundances of the target isotopes under investigation are summarized in Table 1 (Browne and Firestone, 1996). 2.4. Calculation of cross sections and their uncertainties The measured cross sections can be calculated by the following formula (cf. Luo et al., 2007a):
rx ¼
½SeIc gKMD0 ½kAFCx r0 ½SeIc gKMDx ½kAFC0
where the subscript m represents the term corresponding to the monitor reaction and subscript x corresponds to the measured reaction. e is the full-energy peak efficiency of the measured characteristic gamma-ray, Ic the gamma-ray intensity, g the abundance of the target nuclide, M the mass of sample, D ¼ ekt1 ekt2 the counting collection factor, t1, t2 the time intervals from the end of the irradiation to the start and end of counting, respectively, A the atomic weight, C the measured full-energy peak area, k the decay constant and F is the total correction factor of the activity:
1 1 ðMd M n Ed Þ2 cos h þ Md Mn Ed cos2 h þ fMa þ Mn g½Ma Q þ Ed ðM a M n Þ 2 Ma þ Mn ð1Þ
where Md, Mn and Ma are the masses of deuteron, neutron and alpha particle, respectively. The effective D–T neutron energy at irradiation position was determined by the Nb/Zr method (Curtis, 1969; Lewis and Zieba, 1980; Nethaway, 1978; Pavlik et al., 1982). The measured neutron energy was shown in Fig. 1 together with the calculation using Eq. (1). The uncertainty in the neutron energy at 3 to 5 cm was estimated to be 200 keV from a consideration of the sample sizes, d+ beam diameter of about 3–4 mm, and the uncertainty in the Nb/Zr method (Lewis and Zieba, 1980). 2.3. Measurement of radioactivity The gamma-ray activity of 172Tm, 173Tm, 175gYb, 92mNb and 24Na was determined by a high-purity germanium (HPGe) detector (ORTEC, model GEM 60P, Crystal diameter: 70.1 mm, Crystal length: 72.3 mm, made in USA) with a relative efficiency of 68% and an energy resolution of 1.69 keV at 1332 keV for 60Co. The efficiency of the detector was pre-calibrated using various standard gamma
ð2Þ
Fig. 2. The c-ray spectra of about 3 h after the end of the irradiation.
1695
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697 Table 1 Reactions and associated decay data of activation products. Reaction 175
Abundance of target isotope (%) 172
Lu(n, a) Tm Lu(n, a)173Tm Lu(n, p)175mYb 175 Lu(n, p)175gYb 93 Nb(n, 2n)92mNb 27 Al(n, a)24Na
Q-value (MeV)
97.41 ± 0.02 2.59 ± 0.02 97.41 ± 0.02 97.41 ± 0.02 100 100
176 175
7.856 8.518 0.312 0.312 8.83 3.13
F ¼ fs fc fg where fs, fc and fg are correction factors for the self-absorption of the sample at a given gamma-energy, the coincidence sum effect of cascade gamma-rays in the investigated nuclide and in the counting geometry, respectively.
K¼
" L X
#, kDt i
Ui ð1 e
kT i
Þe
Mode of decay (%)
b (100) b (100) IT (100) b (100) EC (100) b (100)
Half-life of product
Ec (keV)
Ic (%)
63.6 h 8.24 h 68.2 ms 4.185 d 10.15 d 14.959 h
1093.7 398.9 – 396.3 934.4 1368.6
6.0 87.9 – 6.4 99.07 100
times (0.1–1%), etc. And some other errors contribution form the parameters of the measured nuclei and standard nuclei, such as, uncertainties of the branching ratio of the characteristic gammarays, uncertainties of the half life of the radioactive product nuclei and so on all are considered. 3. Results and discussion
US
i
where K is the neutron fluence fluctuation factor, L the number of time intervals into which the irradiation time is divided, Dti the duration of the ith time interval, Ti the time interval from the end of the ith interval to the end of irradiation, Ui the neutron flux averaged over the sample during Dti, S ¼ 1 ekT the growth factor of the product nuclide, T = total irradiation time and U is the neutron flux averaged over the sample during the total irradiation time T. The main error sources in our work result from counting statistics (1–21%), standard cross sections uncertainties (1%), detector efficiency (2–3%), weight of samples (0.1%), self-absorption of gamma-ray (0.5%) and the coincidence sum effect of cascade gammarays (0–5%), the uncertainties of irradiation, cooling and measuring
Using the relative activation technique of neutron, each of the samples was sandwiched between two Nb or Al foils which were used as monitor. Because the cross section of 93Nb(n, 2n)92mNb and 27Al(n, a)24Na reactions has been measured by many authors and the value is very accurate, we can select it as a standard. With the irradiation taking place, the neutron flux for the sample was the same as the flux for the monitors. So we can find an equation of neutron flux between them, and avoid importing the neutron flux into the calculation. After having been irradiated, the samples were cooled for about 3 h, and one sample was measured with a relative efficiency of 68% and an energy resolution of 1.69 keV at 1332 keV for 60Co. Cross section values for 175Lu(n, a)172Tm, 176Lu(n, a)173Tm and
Table 2 Summary of cross section measurements. Reaction
This work
Literature values
En (MeV)
r
En (MeV)
r (mb)
Reference
175
Lu(n, a)172Tm
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
612 ± 129 lb 910 ± 173 lb 1126 ± 146 lb
14.5 14.5 14.5 14.5 14.5 14.5 14.5
1.31s 2.18s 1.94s 1.24s 1.98s 1.39s 2.37s
Luo et al. (2008) Kasugai et al. (1995) Csikai et al. (1997) Habbani et al. (2001) Forrest (1986) Konobeyev et al. (1996) Ait-Tahar (1987)
176
Lu(n, a)173Tm
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
704 ± 49 lb 876 ± 70 lb 919 ± 46 lb
14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.6
1.12s 1.94s 1.65s 1.92s 1.81s 1.05s 2.05s 2.3 ± 0.57
Luo et al. (2008) Kasugai et al. (1995) Csikai et al. (1997) Habbani et al. (2001) Forrest (1986) Konobeyev et al. (1996) Ait-Tahar (1987) Sato et al. (1975)
175
Lu(n, p)175m+gYb
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.6 14.7 ± 0.3 14.5
4.1s 5.0s 20.2s 3.5s 10.4s 4.9s 5.1s 18.5 ± 2.3 4.0 ± 0.7 3.42 ± 0.52
Luo et al. (2008) Kasugai et al. (1995) Doczi et al. (1997) Habbani et al. (2001) Forrest (1986) Ait-Tahar (1987) Broeders and Konobeyev (2006) Sato et al. (1975) Qaim (1976) Coleman et al. (1959)
93
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
457.9 ± 6.8 459.8 ± 6.8 459.7 ± 5.0
Wagner et al. (1990) Wagner et al. (1990) Wagner et al. (1990)
27
13.5 ± 0.2 14.1 ± 0.2 14.8 ± 0.2
125.7 ± 0.8 121.6 ± 0.6 111.9 ± 0.5
Wagner et al. (1990) Wagner et al. (1990) Wagner et al. (1990)
Nb(n, 2n)92mNb
Al(n, a)24Na
s: semi-empirical predictions at 14.5 MeV.
6.4 ± 0.4 mb 7.4 ± 0.6 mb 8.2 ± 0.5 mb
1696
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697
175
Lu(n, p)175m+gYb reactions were obtained relative to those of the Nb(n, 2n)92mNb or 27Al(n, a)24Na reaction. The cross sections measured in the present work are summarized in Table 2 and are compared with the values given in the literatures and with results of published empirical formulae (Ait-Tahar, 1987; Broeders and Konobeyev, 2006; Csikai et al., 1997; Doczi et al., 1997; Forrest, 1986; Habbani et al., 2001; Kasugai et al., 1995; Konobeyev et al., 1996; Luo et al., 2008). The previous measurements were made with c-ray counting with Ge (Li) detectors (Coleman et al., 1959; Qaim, 1976; Sato et al., 1975). The 398.9 keV (Ic = 87.9%) gamma-ray emitted in the 173Tm decay and 396.3 keV (Ic = 6.4%) gamma-ray emitted in the 175Yb decay were used to deduce the values of the 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reaction cross sections, respectively. It can be seen from Table 2 that the cross sections for 176Lu (n, a)173Tm reaction our measurements are not in agreement with the literature values (Ait-Tahar, 1987; Csikai et al., 1997; Forrest, 1986; Habbani et al., 2001; Kasugai et al., 1995; Konobeyev et al., 1996; Luo et al., 2008; Sato et al., 1975). For the cross section of 175 Lu(n, p)175m+gYb reaction, our results are somewhat higher than those of Ait-Tahar (1987), Broeders and Konobeyev (2006), Coleman et al. (1959), Csikai et al. (1997), Habbani et al. (2001), Kasugai et al. (1995), Konobeyev et al. (1996), Luo et al. (2008), and Qaim, 1976, while our results are lower than that of Doczi et al. (1997), Forrest (1986), and Sato et al. (1975). It should be mentioned that this work presents the first data for the 175Lu(n, a)172Tm reaction. For the 176Lu(n, a)173Tm and 175 Lu(n, p)175m+gYb reactions, the literature data are one energy. This work thus covers a slightly broader range of energies. 93
4. Conclusions We have measured the activation cross sections for 175Lu (n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions on lutetium isotopes induced by 13.5–14.8 MeV neutrons. Our work gives more accurate measurement of cross sections for 175Lu (n, a)172Tm, 176Lu(n, a)173Tm and 175Lu(n, p)175m+gYb reactions, during the work we used more newly nuclear data for decay characteristics of the product nuclei and the natural abundances and we also used a high-purity germanium detector (HPGe) which have better energy resolution than GeLi detector that used by early experimenter. The accuracy of the cross sections obtained in the early years were limited, because there are 175Lu, 176Lu for the lutetium and overlapping of the gamma-peaks from different isotopes could not be neglected in the gamma-spectrum measurements with the use of bad resolution power detectors. The decay data such as half and branching ratio of the radioactive product nuclei were less accurate at that early time. In recent years, the reliabilities of the results have improved with the use of the high-resolution Ge semiconductor detectors and the more accurate above-mentioned parameters. A good plan of irradiation and cooling time is also important and in our experiment we selected different irradiation time according to the half life of the product nuclei. In addition, the present measurements were performed in the Low Background Laboratory of Chinese Academy of Engineering Physics and disturbance from environmental radiation was reduced to a very low level. In conclusion, our data would improve the quality of the neutron cross section database. Acknowledgments We would like to thank the Intense Neutron Generator group at Chinese Academy of Engineering Physics for performing the irradiations.
This work was supported by the Key Project of Chinese Ministry of Education (No. 211184) and the Program for Long Yuan Young Innovative Talents of Gansu Province, China.
References Ait-Tahar, S., 1987. Nucl. Phys. 13, 121. Bayhurst, B.P., Gilmore, J.S., Prestwood, R.J., Wilhelmy, J.B., Jarmie, N., Erkkila, B.H., Hardekopf, R.A., 1975. Cross sections for (n, xn) reactions between 7.5 and 28 MeV. Phys. Rev. C 12, 451–467. Bostan, M., Qaim, S.M., 1994. Excitation functions of threshold reactions on45 Sc and55 Mn induced by 6 to 13 MeV neutrons. Phys. Rev. C49, 266–271. Broeders, C.H.M., Konobeyev, A.Yu., 2006. Semi-empirical systematics of (n, p) reaction cross-section at 14.5, 20, and 30 MeV. Nucl. Phys. A 780, 130–145. Browne, E., Firestone, R.B., 1996. Table of Isotopes. Wiley, New York. CINDA-A, 2000. The Index to Literature and Computer Files on Microscopic Neutron Data. International Atomic Energy Agency. Coleman, R.F., Hawker, B.E., O‘connor, L.P., Perkin, J.L., 1959. Cross sections for (n, p) and (n, a) reactions with 14.5 MeV neutrons. Proc. Phys. Soc. (Lond.) 73, 215– 219. Cserpák, F., Sudár, S., Csika, J., Qaim, S.M., 1994. Excitation functions and isomeric cross section ratios of the63 Cu(n, a)60 Com,g,65 Cu(n, a)62 Com,g, and60 Ni(n, p)60 Com,g processes from 6 to 15 MeV. Phys. Rev. C49, 1525–1533. Csikai, J., Semkova, V., Doczi, R., Majdeddin, A.D., Varnagy, M., Buczko, Cs.M., Fenyvesi, A., 1997. Fusion Eng. Des. 37, 65. Curtis, L.F., 1969. Introduction to Neutron Physics, D. Van Nostrand Company, Princeton, NJ. Dilg, W., Vonach, H., Winkler, G., Hille, P., 1968. Measurement of (n, 2n) reactions cross-sections on heavy nuclei. Nucl. Phys. A 118, 9–16. Doczi, R., Semkova, V., Majdeddin, A.D., Buczko, Cs.M., Csikai, J., 1997. INDC(HUN)032, NDS, IAEA. Forrest, R.A., 1986. AERE-R 12419, Harwell Laboratory. Frehaut, J., Mosinski, G., 1974. Measurement of the (n, 2n) cross-sections for56 Fe,59 Co,89 Y,169 Tm,175 Lu,181 Ta,197 Au,209 Bi,238 U and of the (n,3n) cross-section for238 U from threshold to 15 MeV incident neutron energy. R,CEA-R4627. Habbani, F.I., Osman, Khalda, T., 2001. Systematics for the cross-sections of the reactions (n, p), (n, a) and (n, 2n) at 14.5 MeV neutrons. Appl. Radia. Isoto. 54, 283–290. Kasugai, Y., Ikeda, Y., Yamamito, H., Kawade, K., 1995. in: JAERI-Conf. 95-008. Konobeyev, A.Yu., Lunev, V.P., shubin, Yu.N., 1996. Nucl. Instr. Meth. B 108, 233– 242. Laurec, J., Adam, A., De Bruyne, T., 1981. Measurement of the (n, 2n) reaction cross sections of the nuclei Y-89,93 Nb,103 Rh,107 Ag,169 Tm,175 Lu, and197 Au at 14.1 and 14.8 MeV. Report CEA-R-5109. Lewis, V.E., Zieba, K.J., 1980. A transfer standard for d+T neutron fluence and energy. Nucl. Instr. Meth. 174, 141–144. Luo, Junhua, Liu, Gang, Tuo, Fei, Kong, Xiangzhong, Liu, Rong, Jiang, Li, Lou, Benchao, 2007a. Activation cross section for reactions induced by 14 MeV neutrons on natural ruthenium. Phys. Rev. C76, 057601. Luo, Junhua, Tuo, Fei, Zhou, Fengqun, Kong, Xiangzhong, 2008. Semi-empirical systematics for the cross-sections of the reactions (n,a), (n, p) and (n,2n) at 14.5 MeV neutrons on the basis of experimental data measured by Lanzhou University. Nucl Instru. Meth B 266 (22), 4862–4868. Luo, Junhua, Xu, Xiaosan, Cao, Xuexiang, Kong, Xiangzhong, 2007b. Activation cross sections and isomeric cross-section ratios for the (n, 2n) reactions on175 Lu,198 Pt and82 Se from 13.5 to 14.6 MeV. Nucl. Instr. Meth. B 265, 453–460. Mclane, V., Dunford, C.L., Rose, P.F., 1988. Neutron Cross Sections, vol. 2. Academic, New York. Nesaraja, C.D., Sudár, S., Qaim, S.M., 2003. Cross sections for the formation of 69Znm,g and 71Znm,g in neutron induced reactions near their thresholds: Effect of reaction channel on the isomeric cross-section ratio. Phys. Rev. C68, 024603. Nethaway, D.R., 1972. Cross sections for several (n, 2n) reactions at 14 MeV. Nucl. Phys. A 190, 635–644. Nethaway, D.R., 1978. The93 Nb (n, 2n)92m Nb cross section. J. Inorg. Nucl. Chem. 40, 1285–1288. Pavlik, A., Winkler, H., Vonach, H., Paulsen, A., Liskin, H., 1982. Precise measurement of cross sections for the90 Zr (n, 2n)89 Zr reaction from threshold to 20 MeV. J. Phys. G; Nucl. Phys. 8, 1283–1286. 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., 1976. Measurement of (n, p) reaction cross sections at 14.7 MeV using high-pressure liquid chromatography in the region of rare earths, Radiochem. and Radioanal. Letters 25, 335–339. Rahman, M.M., Qaim, S.M., 1985. Excitation functions of some neutron threshold reactions on isotopes of molybdenum. Nucl. Phys. A 435, 43–53. Sato, T., Kanda, Y., Kumabe, I., 1975. Activation cross sections for (n, p) and (n, a) reactions on Nd, Sm, Yb and Lu at 14.6 MeV. J. Nucl. Sci. Technol. 12 (11), 681– 685, Tokyo. Vallis, D.G., 1966. Cross sections for (n, 2n) reaction at 14.7 MeV of some odd-proton nuclei. Report AWRE-O-76/66.
J. Luo et al. / Annals of Nuclear Energy 38 (2011) 1693–1697 Veeser, L.R., Arthur, E.D., Young, P.G., 1977. Cross sections for (n, 2n) and (n, 3n) reaction above 14 MeV. Phys. Rev. C 16, 1792–1802. Wagner, M., Vonach, H., Pavlik, A., Strohmaier, B., Tagesen, S., and Martinez-Rico, J., 1990. Physik Daten-Physics Data, Evaluation of Cross Sections for 14 Important Neutron-dosimetry Reactions. Fachinformationszentrum Karlsruhe.
1697
Gesellschaft für wissenschaftlich-technische Information mbH, in the Federal Republic of Germany. No. 13-5. Wille, R.G., Fink, R.W., 1960. Activation cross sections for 14.8 MeV neutrons and some new radioactive nuclides in the rare earth region. Phys. Rev 118, 242–248.