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Verification of KERMA factor for beryllium at neutron energy of 14.2 MeV based on charged-particle measurement
Fusion Engineering and Design 83 (2008) 1674–1677
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Verification of KERMA factor for beryllium at neutron energy of 14.2 MeV based on charged-particle measurement Keitaro Kondo a,∗ , Kentaro Ochiai b , Isao Murata a , Chikara Konno b a b
Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, Yamada-oka 2-1, Suita, Osaka 565-0871, Japan Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan
a r t i c l e
i n f o
Article history: Available online 24 July 2008 Keywords: KERMA factor Beryllium 14 MeV neutrons JENDL-3.3 ENDF/B-VII JEFF-3.1
a b s t r a c t In previous direct measurements of nuclear heating for beryllium induced with DT neutrons, it was pointed out that the calculation with JENDL-3.2 underestimated the measured one by 25%. However, reasons of the discrepancy have not been understood clearly. Recently, we measured the ␣-particle emission doubledifferential cross section for beryllium and found that the evaluation of the 9 Be(n,2n + 2␣) reaction in nuclear data libraries have some problems. We examined KERMA factors for beryllium deduced with three latest nuclear data libraries: JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. The partial KERMA factors for 9 Be(n,2n + 2␣) reaction channel at incident neutron energy of 14.2 MeV deduced from these libraries were compared with a new partial KERMA factor calculated based on our experimental model. The partial KERMA factor from JENDL-3.3 was smaller by 20% than our experiment-based one. The reason of the discrepancy in the previous nuclear heating measurement comes from the smaller partial KERMA factor in JENDL-3.3, which is caused by significant underestimation of higher energy part of the ␣-particle emission DDX at forward emission angles. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Beryllium is one of the most important materials for fusion devices. It is used as the plasma facing material of the first wall in ITER and will be used as a neutron multiplier in the fusion blanket. These components are exposed to high neutron flux, which causes nuclear heating by recoiling nucleus or secondary emitted charged particles from nuclear reactions. In order to calculate nuclear heating, KERMA (Kinetic Energy Release in Materials) factors are essential [1]. They are deduced from evaluated nuclear data libraries and are used in nuclear design for fusion development. In order to validate accuracy for calculation of nuclear heating, direct measurements of nuclear heating for various materials induced with DT-neutrons were conducted previously at the Fusion Neutronics Source (FNS) facility in Japan Atomic Energy Research Institute [2–6]. It was pointed out that measured heating for beryllium disagreed with calculated ones with KERMA factors deduced from several nuclear data libraries [5–7]. The underestimation of calculations was no less than 25%, but problems of nuclear data have not yet been specified clearly. Beryllium is a typical light nucleus and the 9 Be(n,2n + 2␣) reaction, which is a complex 4-body breakup
reaction, has a relatively large cross section at incident neutron energy of 14 MeV. The cross section is around half of the elastic scattering cross section, while energy release by the (n,2n + 2␣) reaction is much larger than that by the elastic scattering. Thus, accurate evaluation of the double-differential cross section (DDX) for emitted ␣-particles, by which nuclear heating mainly occurs, is needed to improve the calculation accuracy. There were, however, few experimental data for emitted ␣-particles from this reaction and the nuclear data of beryllium have not been revised for near 10 years. Recently we developed an improved spectrometer for charged particles with DT-neutron incidence [8] and measured ␣-particle emission DDX for beryllium. From the measurement, several problems of evaluated nuclear data have been emerged [9]. In this study, we examine KERMA factors of beryllium deduced with stateof-the-art nuclear data libraries and compare them with a new KERMA factor calculated based on our experimental model for the 9 Be(n,2n + 2␣) reaction [10]. Through the examination, we attempt to reveal specific problems of the nuclear data and reasons of the disagreement in the previous nuclear heating measurements.
2. Neutron interaction with beryllium ∗ Corresponding author. Tel.: +81 6 6879 7803; fax: +81 6 6879 7899. E-mail address: [email protected] (K. Kondo). 0920-3796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2008.06.008
All comparison of data in the present paper is for 14.2 MeV neutron, where our experimental data were obtained. Reaction
K. Kondo et al. / Fusion Engineering and Design 83 (2008) 1674–1677
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Table 1 Reaction channels of beryllium concerning with nuclear heating and cross section data in JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 at 14.2 MeV Reaction
Q-value (MeV)
Elastic scattering 9 Be(n,␣0 )6 He(ground state) 9 Be(n,2n + 2␣) 9 Be(n,t0 )7 Li(ground state) 9 Be(n,t1 )7 Li* (1st excited)
0 −0.600 −1.573 −10.43 −10.92
*
Evaluated cross section (mb) JENDL-3.3
ENDF/B-VII.0
JEFF-3.1
975 8.96 481 14.1 4.83
1002 10.3 483 13.6 7.92
990 9.64 470* 18.7 –
Sum of individual 16 reaction channels.
channels of beryllium by neutron incidence concerning with nuclear heating are tabulated in Table 1. Evaluated cross section data for these channels in JENDL-3.3 [11], ENDF/B-VII.0 [12] and JEFF-3.1 [13] are also shown in the table. Emitted charged particles, namely t, ␣, 6 He and 7 Li, have short ranges in materials and deposit their energy to cause local heating. In the elastic scattering, recoiling beryllium nuclei deposit their kinetic energy. All inelastic scatterings are included in the (n,2n + 2␣) channel, where all of excited 9 Be nuclei are considered to decay into 2n + 2␣ without ␥-ray emission. In the 9 Be(n,t1 )7 Li*(1st excited) channel, the 7 Li nucleus is excited to the 477.6 keV state, which later emits a ␥ray, and its depositing energy becomes smaller than that of the 9 Be(n,t )7 Li 0 (ground state) channel. 3. Previous nuclear heating measurements During 1990s, direct measurements of nuclear heating for various materials induced with DT-neutrons were conducted at the FNS facility in JAERI under ITER/EDA task in order to validate prediction accuracy of nuclear heating [2–6]. In the case of beryllium, a probe material was irradiated in SS-316 [7], copper [5] and graphite assemblies [6]. Total nuclear heating and ␥-ray heating were measured by the calorimetric method and with thermo luminescence detectors. The schematic view of the experiment is shown in Fig. 1. The obtained ratio of calculation to experiment for nuclear heating is summarized in Table 2, where the calculation was carried out with various nuclear data libraries and KERMA factors. Basically the calculated values for total nuclear heating with FENDL-1 and JENDL-3.2 underestimated the experiment by around 10% and around 25%, respectively. Although the neutron spectrum at the probe material was not mono-energetic and influenced by surrounding assemblies, all experimental results for beryllium showed the same tendency; calculation results with JENDL-3.2/JENDL Fusion File brought the significant underestimation. This result indirectly proved that the KERMA factor derived from JENDL was too small. But, the specific problem of JENDL could not be pointed out, because only integral nuclear heating was observed in this study. Additionally, subjects on the KERMA factor calculation method, such as a difference between the energybalance method and the direct method, were sometimes discussed on an equal ground with problems in the nuclear data library [7]. The reasons of the discrepancy have not been specified clearly.
Fig. 1. Schematic view of previous nuclear heating measurements for beryllium. The size of the beryllium probe is 48 mm in diameter and 48 mm in height.
4. Nuclear data libraries and KERMA factors In the analysis for the previous nuclear heating measurements, several old nuclear data libraries were utilized: JENDL-3.2 [14], JENDL Fusion File [16], FENDL-1 [18] and FENDL-2.0 [19]. Nuclear data for beryllium have not been revised extensively until now. The data for beryllium in JENDL-3.3 and FENDL-2.0 were taken from JENDL Fusion File. The evaluation for beryllium of ENDF/B-VII.0 is almost same as that of ENDF/B-VI.8 [22], and the data for beryllium in FENDL-2.1 was taken from ENDF/B-VI.8. The data for beryllium in FENDL-1 was taken from ENDF/B-VI.0. The present evaluation for beryllium of JEFF-3.1, which has a conspicuous feature that the (n,2n + 2␣) channel is divided into 16 individual channels, was originally taken from EFF-3.0 mod6. We calculated the neutron KERMA factor of beryllium from JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 both by the energy-balance method and by the direct method using a simple program we made.
Table 2 The ratio of calculation to experiment, which was obtained from the previous study for nuclear heating of beryllium induced with DT neutrons Material of the experimental assembly (library used for MCNP calculation)
JENDL-3.2 [14] (FSXLIB-J3.2 [15])
JENDL-Fusion File [16] (FSXLIB-JFF [17])
FENDL-1 (FENDL/MC-1.0) [18]
FENDL-2.0 (FENDL/MC-2.0) [19]
SS-316 [7] Copper [5] Graphite [6]
0.7* 0.75* 0.75
– – 0.75
0.85 0.9 0.9
0.8 – 0.9
*
FUSION-J3.2 [20] and DLC-99 [21] libraries for neutron and ␥-ray were used for nuclear heating calculation.
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Table 3 Calculated neutron KERMA factor for beryllium at 14.2 MeV from JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 both by energy-balance method and by direct method Neutron KERMA factor (MeV-barn)
JENDL-3.3 ENDF/B-VII.0 JEFF-3.1
Direct method
Energy-balance method
2.79 3.08 3.17
2.78 3.05 3.15
Fig. 2. The measured DDX and the evaluated data for 9 Be(n,x␣) reaction at emission angle of 20◦ .
The calculated values are shown in Table 3. The quite small differences, which are less than 1%, between the values obtained with the two methods prove that the energy balance is conserved in all the libraries. Table 4 shows the calculated partial KERMA for the elastic scattering and (n,2n + 2␣) channels by the direct method. For the elastic scattering channel, the values are consistent each other and the difference is less than 2%. On the other hand, the values for the (n,2n + 2␣) channel show the significant large differences among these three libraries. The difference between JENDL-3.3 and JEFF3.1 is around 16%. This disagreement will come from a difference of the ␣-particle emission DDX evaluated in these libraries [9]. Fig. 2 shows our measured DDX for the 9 Be(n,x␣) reaction at the emission angle of 20◦ with those in JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. A significant underestimation appears in the higher energy part of the DDX evaluated in JENDL-3.3, while JEFF-3.1 shows a good agreement. The angular distribution of emitted ␣-particles is strongly forward-peaked, thus this difference of DDX at forward angles largely influences deduced KERMA factors. 5. Comparison with experiment-based KERMA factor In order to certify the reason of the disagreement of the partial KERMA designated in the preceding section, we attempted to estimate the partial KERMA based on our experiment. We developed an experimental model for the 9 Be(n,2n + 2␣) reaction based Table 4 Partial neutron KERMA of beryllium for the elastic scattering and (n,2n + 2␣) channels calculated with JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 by direct method at 14.2 MeV
JENDL-3.3 ENDF/B-VII.0 JEFF-3.1 Present work
Ratio (direct method/ energy-balance method)
Partial KERMA for elastic scattering (MeV-barn)
Partial KERMA for (n,2n + 2␣) reaction (MeV-barn)
0.668 0.662 0.654 –
1.93 2.20 2.31 2.41
1.004 1.007 1.008
on our measurement of the ␣-particle emission DDX [10]. For this model, a branching ratio for many reaction channels all of which contribute to the (n,2n + 2␣) reaction was determined as the experimental DDXs both for emitted ␣-particles and for neutrons were reproduce well in 4 space. A feature of this model is consideration of the 9 Be(n,␣)6 He*(Ex≥1.8 MeV) reaction channel to explain the large emission of high energy ␣-particles in forward angles. Employing the experimental model, we calculated the partial KERMA by the direct method. The obtained partial KERMA for the 9 Be(n,2n + 2␣) channel is 2.41 MeV-barn at neutron energy of 14.2 MeV. The partial KERMA factors for the same channel calculated with JENDL-3.3 and ENDF/B-VII.0 shown in Table 4 underestimate our experimentbased one by 20% and 9%, respectively. The partial KERMA factor with JEFF-3.1 is by 4% smaller than ours, but the difference is acceptable when ambiguity of our modeling is considered. The tendency is consistent with the previous direct measurements of nuclear heating. We conclude that the problem of the JENDL evaluation is that the high energy part of the ␣-particle emission DDX is significantly underestimated in forward angles. This problem makes the partial KERMA of the 9 Be(n,2n + 2␣) channel too small. From the comparison, the superiority of the latest JEFF-3.1 was demonstrated. This study proved that detailed measurements of differential cross sections for charged-particle emission reaction and investigation of its reaction model are very important for evaluation and verification of KERMA factors of light nuclei. Such differential data offer important information which cannot be obtained only from measurements of integral nuclear heating. 6. Summary We examined the partial KERMA factors for the 9 Be(n,2n + 2␣) channel deduced with state-of-the-art nuclear data libraries: JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. They were compared with a new partial KERMA factor calculated based on our experimental model for the 9 Be(n,2n + 2␣) reaction at incident neutron energy of 14.2 MeV. The partial KERMA factor from JENDL-3.3 was smaller by 20% than our experiment-based one, while that from JEFF-3.1 agreed well with ours. We found that the origin of the smaller partial KERMA factor for beryllium in JENDL-3.3, which was already pointed out in the previous integral measurement of nuclear heating, was the significant underestimation of the high energy part of the ␣-particle emission DDX at forward emission angles. The superiority of JEFF-3.1 for beryllium was demonstrated through the present study. This study proved that differential data are very important for verification of KERMA factors especially for light nuclei. References [1] M.A. Abdou, C.W. Maynard, Calculation method for nuclear heating. Part I. Theoretical and computational algorithms, Nucl. Sci. Eng. 56 (1975) 360–398. [2] A. Kumar, M.Z. Youssef, M.A. Abdou, Y. Ikeda, C. Konno, K. Kosako, Y. Oyama, T. Nakamura, Direct nuclear heating measurements in fusion neutron environment and analysis, Fusion Eng. Des. 18 (1991) 397–405. [3] Y. Ikeda, A. Kumar, C. Konno, K. Kosako, Y. Oyama, F. Maekawa, H. Maekawa, M.Z. Youssef, M.A. Abdou, Measurement and analysis of nuclear heat deposi-
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´ M. Herman, N.M. Greene, R.D. McKnight, D.L. [12] M.B. Chadwick, P. Obloˇzinsky, Smith, et al., ENDF/B-VII.0: Next generation evaluated nuclear data library for nuclear science and technology, Nucl. Data Sheets 107 (2006) 2931– 3060. [13] A.J. Koning, R. Forrest, M. Kellett, R. Mills, H. Henriksson, Y. Rugama, The JEFF-3.1 Nuclear Data Library, JEFF Report 21, OECD Nuclear Energy Agency, 2006. [14] T. Nakagawa, K. Shibata, S. Chiba, T. Fukahori, Y. Nakajima, Y. Kikuchi, T. Kawano, Y. Kanda, T. Ohsawa, H. Matsunobu, M. Kawai, A. Zukeran, T. Watanabe, S. Igarasi, K. Kosako, T. Asami, Japanese evaluated nuclear data library version 3 revision2: JENDL-3.2, J. Nucl. Sci. Technol. 32 (1995) 1259–1271. [15] K. Kosako, F. Maekawa, Y. Oyama, Y. Uno, H. Maekawa, FSXLIB-J3R2: A Continuous Energy Cross Library for MCNP Based on JENDL-3.2, JAERI-Data: Code 94-020, Japan Atomic Energy Research Institute, 1994. [16] S. Chiba, T. Fukahori, K. Shibata, B. Yu, K. Kosako, N. Yamamuro, JENDL fusion file 99, J. Nucl. Sci. Technol. 39 (2002) 187–194. [17] K. Kosako, Present status of cross section libraries, in: JAERI-Conf 96-005, Japan Atomic Energy Research Institute, 1996, pp. 55–62. [18] S. Ganesan, H. Wienke, FENDL: MC-1. 0 Library of Continuous Energy Cross Sections in ACE Format for Neutron-Photon Transport Calculations with the Monte Carlo Neutron and Photon Transport Code System MCNP 4A, in: IAEANDS-169, International Atomic Energy Agency, 1995. [19] H. Wienke, M. Herman, FENDL/MG-2.0 and FENDL/MC-2.0, The processed cross-section libraries for neutron-photon transport calculations, version 1 of February 1998, IAEA-NDS–176, Rev. 1, International Atomic Energy Agency, 1998. [20] K. Maki, H. Kawasaki, K. Kosako, Y. Seki, Nuclear Heating Constant KERMA Library, JAERI-M 91-073, 1991. [21] R.W. Roussin, J.R. Knight, J.H. Hubbell, R.J. Howerton, Description of DLC 99: HUGO Package of Photon Interaction Data in ENDF: B-V Format, ORNL: RSIC-6, ENDF-335, 1983. [22] V. McLane, Members of the Cross section Evaluation Working Group, ENDF201, ENDF/B-VI Summary Documentation, BNL-NCS-17541, 4th ed., National Nuclear Data Center, Brookhaven National Laboratory, Upton, New York Supplement I, 1996.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Verification of KERMA factor for beryllium at neutron energy of 14.2 MeV based on charged-particle measurement Keitaro Kondo a,∗ , Kentaro Ochiai b , Isao Murata a , Chikara Konno b a b
Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, Yamada-oka 2-1, Suita, Osaka 565-0871, Japan Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan
a r t i c l e
i n f o
Article history: Available online 24 July 2008 Keywords: KERMA factor Beryllium 14 MeV neutrons JENDL-3.3 ENDF/B-VII JEFF-3.1
a b s t r a c t In previous direct measurements of nuclear heating for beryllium induced with DT neutrons, it was pointed out that the calculation with JENDL-3.2 underestimated the measured one by 25%. However, reasons of the discrepancy have not been understood clearly. Recently, we measured the ␣-particle emission doubledifferential cross section for beryllium and found that the evaluation of the 9 Be(n,2n + 2␣) reaction in nuclear data libraries have some problems. We examined KERMA factors for beryllium deduced with three latest nuclear data libraries: JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. The partial KERMA factors for 9 Be(n,2n + 2␣) reaction channel at incident neutron energy of 14.2 MeV deduced from these libraries were compared with a new partial KERMA factor calculated based on our experimental model. The partial KERMA factor from JENDL-3.3 was smaller by 20% than our experiment-based one. The reason of the discrepancy in the previous nuclear heating measurement comes from the smaller partial KERMA factor in JENDL-3.3, which is caused by significant underestimation of higher energy part of the ␣-particle emission DDX at forward emission angles. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Beryllium is one of the most important materials for fusion devices. It is used as the plasma facing material of the first wall in ITER and will be used as a neutron multiplier in the fusion blanket. These components are exposed to high neutron flux, which causes nuclear heating by recoiling nucleus or secondary emitted charged particles from nuclear reactions. In order to calculate nuclear heating, KERMA (Kinetic Energy Release in Materials) factors are essential [1]. They are deduced from evaluated nuclear data libraries and are used in nuclear design for fusion development. In order to validate accuracy for calculation of nuclear heating, direct measurements of nuclear heating for various materials induced with DT-neutrons were conducted previously at the Fusion Neutronics Source (FNS) facility in Japan Atomic Energy Research Institute [2–6]. It was pointed out that measured heating for beryllium disagreed with calculated ones with KERMA factors deduced from several nuclear data libraries [5–7]. The underestimation of calculations was no less than 25%, but problems of nuclear data have not yet been specified clearly. Beryllium is a typical light nucleus and the 9 Be(n,2n + 2␣) reaction, which is a complex 4-body breakup
reaction, has a relatively large cross section at incident neutron energy of 14 MeV. The cross section is around half of the elastic scattering cross section, while energy release by the (n,2n + 2␣) reaction is much larger than that by the elastic scattering. Thus, accurate evaluation of the double-differential cross section (DDX) for emitted ␣-particles, by which nuclear heating mainly occurs, is needed to improve the calculation accuracy. There were, however, few experimental data for emitted ␣-particles from this reaction and the nuclear data of beryllium have not been revised for near 10 years. Recently we developed an improved spectrometer for charged particles with DT-neutron incidence [8] and measured ␣-particle emission DDX for beryllium. From the measurement, several problems of evaluated nuclear data have been emerged [9]. In this study, we examine KERMA factors of beryllium deduced with stateof-the-art nuclear data libraries and compare them with a new KERMA factor calculated based on our experimental model for the 9 Be(n,2n + 2␣) reaction [10]. Through the examination, we attempt to reveal specific problems of the nuclear data and reasons of the disagreement in the previous nuclear heating measurements.
2. Neutron interaction with beryllium ∗ Corresponding author. Tel.: +81 6 6879 7803; fax: +81 6 6879 7899. E-mail address: [email protected] (K. Kondo). 0920-3796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2008.06.008
All comparison of data in the present paper is for 14.2 MeV neutron, where our experimental data were obtained. Reaction
K. Kondo et al. / Fusion Engineering and Design 83 (2008) 1674–1677
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Table 1 Reaction channels of beryllium concerning with nuclear heating and cross section data in JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 at 14.2 MeV Reaction
Q-value (MeV)
Elastic scattering 9 Be(n,␣0 )6 He(ground state) 9 Be(n,2n + 2␣) 9 Be(n,t0 )7 Li(ground state) 9 Be(n,t1 )7 Li* (1st excited)
0 −0.600 −1.573 −10.43 −10.92
*
Evaluated cross section (mb) JENDL-3.3
ENDF/B-VII.0
JEFF-3.1
975 8.96 481 14.1 4.83
1002 10.3 483 13.6 7.92
990 9.64 470* 18.7 –
Sum of individual 16 reaction channels.
channels of beryllium by neutron incidence concerning with nuclear heating are tabulated in Table 1. Evaluated cross section data for these channels in JENDL-3.3 [11], ENDF/B-VII.0 [12] and JEFF-3.1 [13] are also shown in the table. Emitted charged particles, namely t, ␣, 6 He and 7 Li, have short ranges in materials and deposit their energy to cause local heating. In the elastic scattering, recoiling beryllium nuclei deposit their kinetic energy. All inelastic scatterings are included in the (n,2n + 2␣) channel, where all of excited 9 Be nuclei are considered to decay into 2n + 2␣ without ␥-ray emission. In the 9 Be(n,t1 )7 Li*(1st excited) channel, the 7 Li nucleus is excited to the 477.6 keV state, which later emits a ␥ray, and its depositing energy becomes smaller than that of the 9 Be(n,t )7 Li 0 (ground state) channel. 3. Previous nuclear heating measurements During 1990s, direct measurements of nuclear heating for various materials induced with DT-neutrons were conducted at the FNS facility in JAERI under ITER/EDA task in order to validate prediction accuracy of nuclear heating [2–6]. In the case of beryllium, a probe material was irradiated in SS-316 [7], copper [5] and graphite assemblies [6]. Total nuclear heating and ␥-ray heating were measured by the calorimetric method and with thermo luminescence detectors. The schematic view of the experiment is shown in Fig. 1. The obtained ratio of calculation to experiment for nuclear heating is summarized in Table 2, where the calculation was carried out with various nuclear data libraries and KERMA factors. Basically the calculated values for total nuclear heating with FENDL-1 and JENDL-3.2 underestimated the experiment by around 10% and around 25%, respectively. Although the neutron spectrum at the probe material was not mono-energetic and influenced by surrounding assemblies, all experimental results for beryllium showed the same tendency; calculation results with JENDL-3.2/JENDL Fusion File brought the significant underestimation. This result indirectly proved that the KERMA factor derived from JENDL was too small. But, the specific problem of JENDL could not be pointed out, because only integral nuclear heating was observed in this study. Additionally, subjects on the KERMA factor calculation method, such as a difference between the energybalance method and the direct method, were sometimes discussed on an equal ground with problems in the nuclear data library [7]. The reasons of the discrepancy have not been specified clearly.
Fig. 1. Schematic view of previous nuclear heating measurements for beryllium. The size of the beryllium probe is 48 mm in diameter and 48 mm in height.
4. Nuclear data libraries and KERMA factors In the analysis for the previous nuclear heating measurements, several old nuclear data libraries were utilized: JENDL-3.2 [14], JENDL Fusion File [16], FENDL-1 [18] and FENDL-2.0 [19]. Nuclear data for beryllium have not been revised extensively until now. The data for beryllium in JENDL-3.3 and FENDL-2.0 were taken from JENDL Fusion File. The evaluation for beryllium of ENDF/B-VII.0 is almost same as that of ENDF/B-VI.8 [22], and the data for beryllium in FENDL-2.1 was taken from ENDF/B-VI.8. The data for beryllium in FENDL-1 was taken from ENDF/B-VI.0. The present evaluation for beryllium of JEFF-3.1, which has a conspicuous feature that the (n,2n + 2␣) channel is divided into 16 individual channels, was originally taken from EFF-3.0 mod6. We calculated the neutron KERMA factor of beryllium from JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 both by the energy-balance method and by the direct method using a simple program we made.
Table 2 The ratio of calculation to experiment, which was obtained from the previous study for nuclear heating of beryllium induced with DT neutrons Material of the experimental assembly (library used for MCNP calculation)
JENDL-3.2 [14] (FSXLIB-J3.2 [15])
JENDL-Fusion File [16] (FSXLIB-JFF [17])
FENDL-1 (FENDL/MC-1.0) [18]
FENDL-2.0 (FENDL/MC-2.0) [19]
SS-316 [7] Copper [5] Graphite [6]
0.7* 0.75* 0.75
– – 0.75
0.85 0.9 0.9
0.8 – 0.9
*
FUSION-J3.2 [20] and DLC-99 [21] libraries for neutron and ␥-ray were used for nuclear heating calculation.
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Table 3 Calculated neutron KERMA factor for beryllium at 14.2 MeV from JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 both by energy-balance method and by direct method Neutron KERMA factor (MeV-barn)
JENDL-3.3 ENDF/B-VII.0 JEFF-3.1
Direct method
Energy-balance method
2.79 3.08 3.17
2.78 3.05 3.15
Fig. 2. The measured DDX and the evaluated data for 9 Be(n,x␣) reaction at emission angle of 20◦ .
The calculated values are shown in Table 3. The quite small differences, which are less than 1%, between the values obtained with the two methods prove that the energy balance is conserved in all the libraries. Table 4 shows the calculated partial KERMA for the elastic scattering and (n,2n + 2␣) channels by the direct method. For the elastic scattering channel, the values are consistent each other and the difference is less than 2%. On the other hand, the values for the (n,2n + 2␣) channel show the significant large differences among these three libraries. The difference between JENDL-3.3 and JEFF3.1 is around 16%. This disagreement will come from a difference of the ␣-particle emission DDX evaluated in these libraries [9]. Fig. 2 shows our measured DDX for the 9 Be(n,x␣) reaction at the emission angle of 20◦ with those in JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. A significant underestimation appears in the higher energy part of the DDX evaluated in JENDL-3.3, while JEFF-3.1 shows a good agreement. The angular distribution of emitted ␣-particles is strongly forward-peaked, thus this difference of DDX at forward angles largely influences deduced KERMA factors. 5. Comparison with experiment-based KERMA factor In order to certify the reason of the disagreement of the partial KERMA designated in the preceding section, we attempted to estimate the partial KERMA based on our experiment. We developed an experimental model for the 9 Be(n,2n + 2␣) reaction based Table 4 Partial neutron KERMA of beryllium for the elastic scattering and (n,2n + 2␣) channels calculated with JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1 by direct method at 14.2 MeV
JENDL-3.3 ENDF/B-VII.0 JEFF-3.1 Present work
Ratio (direct method/ energy-balance method)
Partial KERMA for elastic scattering (MeV-barn)
Partial KERMA for (n,2n + 2␣) reaction (MeV-barn)
0.668 0.662 0.654 –
1.93 2.20 2.31 2.41
1.004 1.007 1.008
on our measurement of the ␣-particle emission DDX [10]. For this model, a branching ratio for many reaction channels all of which contribute to the (n,2n + 2␣) reaction was determined as the experimental DDXs both for emitted ␣-particles and for neutrons were reproduce well in 4 space. A feature of this model is consideration of the 9 Be(n,␣)6 He*(Ex≥1.8 MeV) reaction channel to explain the large emission of high energy ␣-particles in forward angles. Employing the experimental model, we calculated the partial KERMA by the direct method. The obtained partial KERMA for the 9 Be(n,2n + 2␣) channel is 2.41 MeV-barn at neutron energy of 14.2 MeV. The partial KERMA factors for the same channel calculated with JENDL-3.3 and ENDF/B-VII.0 shown in Table 4 underestimate our experimentbased one by 20% and 9%, respectively. The partial KERMA factor with JEFF-3.1 is by 4% smaller than ours, but the difference is acceptable when ambiguity of our modeling is considered. The tendency is consistent with the previous direct measurements of nuclear heating. We conclude that the problem of the JENDL evaluation is that the high energy part of the ␣-particle emission DDX is significantly underestimated in forward angles. This problem makes the partial KERMA of the 9 Be(n,2n + 2␣) channel too small. From the comparison, the superiority of the latest JEFF-3.1 was demonstrated. This study proved that detailed measurements of differential cross sections for charged-particle emission reaction and investigation of its reaction model are very important for evaluation and verification of KERMA factors of light nuclei. Such differential data offer important information which cannot be obtained only from measurements of integral nuclear heating. 6. Summary We examined the partial KERMA factors for the 9 Be(n,2n + 2␣) channel deduced with state-of-the-art nuclear data libraries: JENDL-3.3, ENDF/B-VII.0 and JEFF-3.1. They were compared with a new partial KERMA factor calculated based on our experimental model for the 9 Be(n,2n + 2␣) reaction at incident neutron energy of 14.2 MeV. The partial KERMA factor from JENDL-3.3 was smaller by 20% than our experiment-based one, while that from JEFF-3.1 agreed well with ours. We found that the origin of the smaller partial KERMA factor for beryllium in JENDL-3.3, which was already pointed out in the previous integral measurement of nuclear heating, was the significant underestimation of the high energy part of the ␣-particle emission DDX at forward emission angles. The superiority of JEFF-3.1 for beryllium was demonstrated through the present study. This study proved that differential data are very important for verification of KERMA factors especially for light nuclei. References [1] M.A. Abdou, C.W. Maynard, Calculation method for nuclear heating. Part I. Theoretical and computational algorithms, Nucl. Sci. Eng. 56 (1975) 360–398. [2] A. Kumar, M.Z. Youssef, M.A. Abdou, Y. Ikeda, C. Konno, K. Kosako, Y. Oyama, T. Nakamura, Direct nuclear heating measurements in fusion neutron environment and analysis, Fusion Eng. Des. 18 (1991) 397–405. [3] Y. Ikeda, A. Kumar, C. Konno, K. Kosako, Y. Oyama, F. Maekawa, H. Maekawa, M.Z. Youssef, M.A. Abdou, Measurement and analysis of nuclear heat deposi-
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