- Email: [email protected]
Evaluation review of the 250Cf neutron cross section
Applied Radiation and Isotopes 154 (2019) 108869
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Evaluation review of the
250
Cf neutron cross section
⁎
T
Mohammad Alrwashdeh , Saeed Alameri Department of Nuclear Engineering, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates
H I GH L IG H T S
research investigated the data for the cross section of the Cf isotope in the unresolved resonance region, where the incident particle with a specific energy • isThiseither neutral or charged. benchmark evaluation for the Maxwellian-averaged cross sections of total, capture, and fission reactions along with the Wescott factors. • Thermal • The present reseach is enchancing the important quantities in order to do more benchmark in near future. 250
A R T I C LE I N FO
A B S T R A C T
Keywords: JENDL CF-250 SAMMY Neutron
This research investigated the data for the cross section of the 250Cf isotope in the unresolved resonance region, where the incident particle with a specific energy is either neutral or charged. Both the angular distribution and the differential cross sections of 250Cf were evaluated in the specific energy range. In this research, the ReichMoore R-matrix approximation was used to evaluate the theoretical cross section, and sophisticated models were employed to evaluate and describe the background experimental data by including the reduction parameters for the experimental data. The evaluated resonance integral-capture cross section and thermal resonance integralcapture cross section showed a good agreement with the tabulated values found in the literature on the unresolved resonance energy region for 250Cf in the range from 0.01 meV to 20 meV.
1. Introduction The evaluated cross sections of the 250Cf isotope in the unresolved resonance region, with an energy range from 0.01 meV to 20 meV, were calculated using SAMMY code (Larson, 2007). The capabilities, such as normalization and the partial derivatives calculation for the experimental data, have been borrowed from Froehner's FITACS code (Larson, 1992). Due to the lack of thermal neutron experimental data in this energy range, the data evaluated in this work depended on the available cross sections in the literature, and the evaluated data were predicted using the evaporation, optical, and statistical models. For the energy range below 150 eV, the generation of hypothetical resonance energy levels assisted in creating the measured resonance integrals and evaluating the thermal cross sections of 250Cf, such as the total and elastic cross sections (Tompson and Prelas, 2016). The energy distribution and average number of emitted neutrons per fission are of major interest in nuclear applications of the evaluated data. In this study, the energy and resonance integrals of 250Cf depend on the average value of the parameters used in the unresolved resonance energy region and on the p-wave strength function, which is about
⁎
3.0 × 10−4 fm based on the optical model calculation (Kloet et al., 1983). The effective scattering radius of 250Cf was adjusted to fit the available experimental data. The available unresolved resonance parameters in the literature are presented in Table 1. 2. Analyses When the evaluation model is based on reliable experimental data, the output parameters are constrained by the physical observations, and the quality of the results improve. In cases for which explicit data are lacking, a more experienced data modeler will achieve more accurate calculated results by taking the systematic considerations of similar evaluations into account. Reliable results have been obtained in most described cases, particularly for the strong reaction channels. It is worth mentioning that many of the evaluated experimental nuclear data files were generated in large part with the assistance of nuclear models. In general, a five-step method generates data with good acceptance, as summarized below. Step 1: Investigate and understand the relevant physics of the data.
Corresponding author. E-mail address: [email protected] (M. Alrwashdeh).
https://doi.org/10.1016/j.apradiso.2019.108869 Received 26 June 2019; Received in revised form 11 August 2019; Accepted 15 August 2019 Available online 16 August 2019 0969-8043/ © 2019 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 154 (2019) 108869
M. Alrwashdeh and S. Alameri
Table 1 Unresolved resonance (NakagawaTsuneo, 1986).
parameters
for
250
Table 2 Thermal capture cross sections of
Cf
Reference
Quantity
250
Energy range Scattering radius Level spacing S0 S1 Capture width Fission width
150 eV–30 KeV 9.112 fm 16 eV 0.0001 0.0003 36.9 meV 0.1 meV
250
Cf. Capture cross section (barns)
Cf
9
Magnusson et al. Folger et al.8 Nakagawa et al.5 Wild et al.6 This work Adopted
1,500 1,500 2,034 ± 200 1,800 1,850 1,730 ± 200
Table 3 Resonance integrals of radiative capture cross sections of
Step 2: Review the available reliable experimental data. Step 3: Use a statistical model suitable to the available data. Step 4: Test the dataset against the presumed theory or model. Step 5: Apply the appropriate statistical method based on the nature of the data to obtain the adopted values for all needed parameters.
Author
Cf.
Resonance integral (barns) 8
Folger et al. Nakagawa et al.5 Wild et al.6 This work Adopted
The experimental data can then be processed by the R-matrix SAMMY code using the well-known Bayes method, whereupon the output can be validated. In general, the evaluation and validation of nuclear data can be achieved as shown in the flow chart in Fig. 1. The measured and evaluated values of the 250Cf capture cross sections are shown in Table 2. The thermal capture cross sections are scattered between the values of 1,500 and 2,034 barns. As is evident, the two recent measurements of the capture cross section by Halperin et al. (NakagawaTsuneo, 1986; Wild et al., 1985) and Gavrilov et al. (Chiaveri, 2012) are in good agreement with each other, as the uncertainty in Halperin's measurement is about 200. The adopted value of the capture cross section presented in the literature is 1,730 ± 220 barns, which is derived by averaging the measured values of Folger et al. (Folger et al., 1968; Magnusson et al., 1954) and Halperin et al. A value of < 350 barns for the fission cross section was reported by Metta et al. (1965) where the experimental values, which were compiled in EXFOR (http://wwwndc.jaea.go.jp/; http://www.nndc.bnl.gov/e) were less than 350 barns. It is worth mentioning that no evidence was found in the present work of thermal neutron induced fission in 250Cf, probably because of the small fission cross section. The value of the resonance integral radiative capture cross section for 250Cf has been measured by both Halperin et al. and Gavrilov et al. and the absorption cross section has been obtained by Folger et al. However, there are large discrepancies between Halperin's and Gavrilov's measured values, as shown in Table 3. The adopted value of the resonance integral radiative capture cross section, 8,300 ± 3,300
250
5,300 11,600 5,000 6,300 8,300 ± 3,300
barns,13 was reached by averaging the two recent measurements presented by Halperin and Gavrilov, and in this work the value of the evaluated cross section is about 6,300 barns. Pervious evaluations were successful to using the same method for 233U and 239Pu (Alrwashdeh, 2018a, 2018b, Alrwashdeh et al., 2013, 2014, Alrwashdeh and Wang, 2014, 2016). The Maxwellian-averaged cross-section (MACS) at thermal energy range is used to interpret the thermal benchmark by employing the calculated Wescott factors (gw, and K1 parameters), defined as follows:
(
1
gw = 1/2σx π 2 σ0x
)
Where gf represents the Wescott fission factor and ga represents the Wescott absorption factor, respectively, and
k1 = γσ0f gf − σ0a ga Where σ0f and σ0a are the MACS for fission and absorption reactions at 0.0253 eV, respectively. Table 4 shows comparison between the values evaluated by Japanese Nuclear Data Library (JENDL) and the values evaluated in this study, slightly differences between JENDL and this study due to the difference in evaluating method and experimental data fitting.
Fig. 1. Flow chart for evaluating experimental nuclear data. 2
Applied Radiation and Isotopes 154 (2019) 108869
M. Alrwashdeh and S. Alameri
Table 4 Maxwellian-averaged cross sections for the different reactions on Quantity
JENDL 4.0
Averaged cross section Total Capture Fission gt gc gf
208.1 213.2 208.8 112.0 0.976 0.978 0.973
11
doi.org/10.1016/j.apradiso.2019.108869. 250
Cf (barn).
References
This work 215.3 210.2 209.6 109.3 0.977 0.979 0.975
Alrwashdeh, M., 2018a. Covariance data evaluation for 233U. Appl. Radiat. Isot. 133, 105–110. Alrwashdeh, M., 2018b. 239Pu evaluation comparison study. Ann. Nucl. Energy 118, 313–316. Alrwashdeh, M., Wang, K., 2014. Development of a code FITWR for nuclear cross section statistical analysis. Ann. Nucl. Energy 70, 130–134. Alrwashdeh, M., Wang, K., 2016. U233 data evaluation for criticality study. ASME J. Nucl. Rad. Sci. 2 (3) 034501-1–034501-5. Alrwashdeh, Mohammad, Jian, Kai Yu, Abdalla, Aniseh, Wang, Kan, 2013. Nuclear data statistical treatment. In: 2013 21st International Conference on Nuclear Engineering, Pp. V005T11A020-V005t11a020. American Society of Mechanical Engineers. Alrwashdeh, Mohammad, Abdalla, Aniseh, Wang, Kan, 2014. 233U evaluation comparison study. In: 2014 22nd International Conference on Nuclear Engineering, Pp. V004T11A001-V004t11a001. American Society of Mechanical Engineers. Chiaveri, E., 2012. Proposal for n_TOF Experimental Area 2. No. CERN-INTC-2012-029. Folger, R.L., et al., 1968. Foil Measurements of Integral Cross Sections of Higher Mass Actinides. No. DP-MS-67-112; CONF-680307-6. Du Pont de Nemours (EI) and Co., Aiken, SC Savannah River Lab. http://wwwndc.jaea.go.jp/cgi-bin/Tab80WWW.cgi?/data/JENDL/JENDL-4-prc/intern/ Cf250.intern. http://www.nndc.bnl.gov/exfor/exfor.htm. Kloet, W.M., Gibson, B.F., Stephenson Jr., G.J., Henley, E.M., 1983. Parity nonconserving asymmetry in neutron-deuteron and proton-deuteron scattering. Phys. Rev. C 27 (6), 2529. Larson, N.M., 1992. Cross Section Parameterization in the Resolved Resonance Region. No. CONF-921046–7. Oak Ridge National Lab. Larson, Nancy M., 2007. SAMMY, Multilevel R-Matrix Fits to Neutron and ChargedParticle Cross-Section Data Using Bayes' Equations. Magnusson, L.B., et al., 1954. Berkelium and californium isotopes produced in neutron irradiation of plutonium. Phys. Rev. 96.6, 1576. Metta, D., et al., 1965. Nuclear constants of nine transplutonium nuclides. J. Inorg. Nucl. Chem. 27 (1), 33–39. Nakagawa, Tsuneo, 1986. Evaluation of Neutron Nuclear Data for 250 Cf and 251 Cf. No. JAERI-M–86-086. Japan Atomic Energy Research Inst. Tompson Jr, Robert V., and Mark A. Prelas. Isotope energy conversion and spent nuclear fuel storage systems. U.S. Patent Application 14/870,845, filed March 31, 2016. Wild, J.F., Baisden, P.A., Dougan, R.J., Hulet, E.K., Lougheed, R.W., Landrum, J.H., 1985. Light-charged-particle emission in the spontaneous fission of Cf 250, Fm 256, and Fm 257. Phys. Rev. C 32 (no. 2), 488.
3. Conclusions The evaluation of some important quantities have been investigated for 250Cf, where most of the evaluated cross sections and quantities, such as the capture cross section and the resonance integral capture cross section, showed a good agreement with values found in the literature. In addition, the thermal benchmark evaluation for the Maxwellian-averaged cross sections of total, capture, and fission reactions along with the Wescott factors are in good agreements with the evaluated values by the Japanese Evaluated Nuclear Data Library. These important quantities have significant for improvement the performance for fission reactor applications to get much more reliable parameters for fission products behavior in thermal nuclear power reactor. Acknowledgments This study was supported by Khalifa University of Science and Technology Faculty Start-Up Fund, FSU 8474000067. Appendix A. Supplementary data Supplementary data to this article can be found online at https://
3
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Evaluation review of the
250
Cf neutron cross section
⁎
T
Mohammad Alrwashdeh , Saeed Alameri Department of Nuclear Engineering, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates
H I GH L IG H T S
research investigated the data for the cross section of the Cf isotope in the unresolved resonance region, where the incident particle with a specific energy • isThiseither neutral or charged. benchmark evaluation for the Maxwellian-averaged cross sections of total, capture, and fission reactions along with the Wescott factors. • Thermal • The present reseach is enchancing the important quantities in order to do more benchmark in near future. 250
A R T I C LE I N FO
A B S T R A C T
Keywords: JENDL CF-250 SAMMY Neutron
This research investigated the data for the cross section of the 250Cf isotope in the unresolved resonance region, where the incident particle with a specific energy is either neutral or charged. Both the angular distribution and the differential cross sections of 250Cf were evaluated in the specific energy range. In this research, the ReichMoore R-matrix approximation was used to evaluate the theoretical cross section, and sophisticated models were employed to evaluate and describe the background experimental data by including the reduction parameters for the experimental data. The evaluated resonance integral-capture cross section and thermal resonance integralcapture cross section showed a good agreement with the tabulated values found in the literature on the unresolved resonance energy region for 250Cf in the range from 0.01 meV to 20 meV.
1. Introduction The evaluated cross sections of the 250Cf isotope in the unresolved resonance region, with an energy range from 0.01 meV to 20 meV, were calculated using SAMMY code (Larson, 2007). The capabilities, such as normalization and the partial derivatives calculation for the experimental data, have been borrowed from Froehner's FITACS code (Larson, 1992). Due to the lack of thermal neutron experimental data in this energy range, the data evaluated in this work depended on the available cross sections in the literature, and the evaluated data were predicted using the evaporation, optical, and statistical models. For the energy range below 150 eV, the generation of hypothetical resonance energy levels assisted in creating the measured resonance integrals and evaluating the thermal cross sections of 250Cf, such as the total and elastic cross sections (Tompson and Prelas, 2016). The energy distribution and average number of emitted neutrons per fission are of major interest in nuclear applications of the evaluated data. In this study, the energy and resonance integrals of 250Cf depend on the average value of the parameters used in the unresolved resonance energy region and on the p-wave strength function, which is about
⁎
3.0 × 10−4 fm based on the optical model calculation (Kloet et al., 1983). The effective scattering radius of 250Cf was adjusted to fit the available experimental data. The available unresolved resonance parameters in the literature are presented in Table 1. 2. Analyses When the evaluation model is based on reliable experimental data, the output parameters are constrained by the physical observations, and the quality of the results improve. In cases for which explicit data are lacking, a more experienced data modeler will achieve more accurate calculated results by taking the systematic considerations of similar evaluations into account. Reliable results have been obtained in most described cases, particularly for the strong reaction channels. It is worth mentioning that many of the evaluated experimental nuclear data files were generated in large part with the assistance of nuclear models. In general, a five-step method generates data with good acceptance, as summarized below. Step 1: Investigate and understand the relevant physics of the data.
Corresponding author. E-mail address: [email protected] (M. Alrwashdeh).
https://doi.org/10.1016/j.apradiso.2019.108869 Received 26 June 2019; Received in revised form 11 August 2019; Accepted 15 August 2019 Available online 16 August 2019 0969-8043/ © 2019 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 154 (2019) 108869
M. Alrwashdeh and S. Alameri
Table 1 Unresolved resonance (NakagawaTsuneo, 1986).
parameters
for
250
Table 2 Thermal capture cross sections of
Cf
Reference
Quantity
250
Energy range Scattering radius Level spacing S0 S1 Capture width Fission width
150 eV–30 KeV 9.112 fm 16 eV 0.0001 0.0003 36.9 meV 0.1 meV
250
Cf. Capture cross section (barns)
Cf
9
Magnusson et al. Folger et al.8 Nakagawa et al.5 Wild et al.6 This work Adopted
1,500 1,500 2,034 ± 200 1,800 1,850 1,730 ± 200
Table 3 Resonance integrals of radiative capture cross sections of
Step 2: Review the available reliable experimental data. Step 3: Use a statistical model suitable to the available data. Step 4: Test the dataset against the presumed theory or model. Step 5: Apply the appropriate statistical method based on the nature of the data to obtain the adopted values for all needed parameters.
Author
Cf.
Resonance integral (barns) 8
Folger et al. Nakagawa et al.5 Wild et al.6 This work Adopted
The experimental data can then be processed by the R-matrix SAMMY code using the well-known Bayes method, whereupon the output can be validated. In general, the evaluation and validation of nuclear data can be achieved as shown in the flow chart in Fig. 1. The measured and evaluated values of the 250Cf capture cross sections are shown in Table 2. The thermal capture cross sections are scattered between the values of 1,500 and 2,034 barns. As is evident, the two recent measurements of the capture cross section by Halperin et al. (NakagawaTsuneo, 1986; Wild et al., 1985) and Gavrilov et al. (Chiaveri, 2012) are in good agreement with each other, as the uncertainty in Halperin's measurement is about 200. The adopted value of the capture cross section presented in the literature is 1,730 ± 220 barns, which is derived by averaging the measured values of Folger et al. (Folger et al., 1968; Magnusson et al., 1954) and Halperin et al. A value of < 350 barns for the fission cross section was reported by Metta et al. (1965) where the experimental values, which were compiled in EXFOR (http://wwwndc.jaea.go.jp/; http://www.nndc.bnl.gov/e) were less than 350 barns. It is worth mentioning that no evidence was found in the present work of thermal neutron induced fission in 250Cf, probably because of the small fission cross section. The value of the resonance integral radiative capture cross section for 250Cf has been measured by both Halperin et al. and Gavrilov et al. and the absorption cross section has been obtained by Folger et al. However, there are large discrepancies between Halperin's and Gavrilov's measured values, as shown in Table 3. The adopted value of the resonance integral radiative capture cross section, 8,300 ± 3,300
250
5,300 11,600 5,000 6,300 8,300 ± 3,300
barns,13 was reached by averaging the two recent measurements presented by Halperin and Gavrilov, and in this work the value of the evaluated cross section is about 6,300 barns. Pervious evaluations were successful to using the same method for 233U and 239Pu (Alrwashdeh, 2018a, 2018b, Alrwashdeh et al., 2013, 2014, Alrwashdeh and Wang, 2014, 2016). The Maxwellian-averaged cross-section (MACS) at thermal energy range is used to interpret the thermal benchmark by employing the calculated Wescott factors (gw, and K1 parameters), defined as follows:
(
1
gw = 1/2σx π 2 σ0x
)
Where gf represents the Wescott fission factor and ga represents the Wescott absorption factor, respectively, and
k1 = γσ0f gf − σ0a ga Where σ0f and σ0a are the MACS for fission and absorption reactions at 0.0253 eV, respectively. Table 4 shows comparison between the values evaluated by Japanese Nuclear Data Library (JENDL) and the values evaluated in this study, slightly differences between JENDL and this study due to the difference in evaluating method and experimental data fitting.
Fig. 1. Flow chart for evaluating experimental nuclear data. 2
Applied Radiation and Isotopes 154 (2019) 108869
M. Alrwashdeh and S. Alameri
Table 4 Maxwellian-averaged cross sections for the different reactions on Quantity
JENDL 4.0
Averaged cross section Total Capture Fission gt gc gf
208.1 213.2 208.8 112.0 0.976 0.978 0.973
11
doi.org/10.1016/j.apradiso.2019.108869. 250
Cf (barn).
References
This work 215.3 210.2 209.6 109.3 0.977 0.979 0.975
Alrwashdeh, M., 2018a. Covariance data evaluation for 233U. Appl. Radiat. Isot. 133, 105–110. Alrwashdeh, M., 2018b. 239Pu evaluation comparison study. Ann. Nucl. Energy 118, 313–316. Alrwashdeh, M., Wang, K., 2014. Development of a code FITWR for nuclear cross section statistical analysis. Ann. Nucl. Energy 70, 130–134. Alrwashdeh, M., Wang, K., 2016. U233 data evaluation for criticality study. ASME J. Nucl. Rad. Sci. 2 (3) 034501-1–034501-5. Alrwashdeh, Mohammad, Jian, Kai Yu, Abdalla, Aniseh, Wang, Kan, 2013. Nuclear data statistical treatment. In: 2013 21st International Conference on Nuclear Engineering, Pp. V005T11A020-V005t11a020. American Society of Mechanical Engineers. Alrwashdeh, Mohammad, Abdalla, Aniseh, Wang, Kan, 2014. 233U evaluation comparison study. In: 2014 22nd International Conference on Nuclear Engineering, Pp. V004T11A001-V004t11a001. American Society of Mechanical Engineers. Chiaveri, E., 2012. Proposal for n_TOF Experimental Area 2. No. CERN-INTC-2012-029. Folger, R.L., et al., 1968. Foil Measurements of Integral Cross Sections of Higher Mass Actinides. No. DP-MS-67-112; CONF-680307-6. Du Pont de Nemours (EI) and Co., Aiken, SC Savannah River Lab. http://wwwndc.jaea.go.jp/cgi-bin/Tab80WWW.cgi?/data/JENDL/JENDL-4-prc/intern/ Cf250.intern. http://www.nndc.bnl.gov/exfor/exfor.htm. Kloet, W.M., Gibson, B.F., Stephenson Jr., G.J., Henley, E.M., 1983. Parity nonconserving asymmetry in neutron-deuteron and proton-deuteron scattering. Phys. Rev. C 27 (6), 2529. Larson, N.M., 1992. Cross Section Parameterization in the Resolved Resonance Region. No. CONF-921046–7. Oak Ridge National Lab. Larson, Nancy M., 2007. SAMMY, Multilevel R-Matrix Fits to Neutron and ChargedParticle Cross-Section Data Using Bayes' Equations. Magnusson, L.B., et al., 1954. Berkelium and californium isotopes produced in neutron irradiation of plutonium. Phys. Rev. 96.6, 1576. Metta, D., et al., 1965. Nuclear constants of nine transplutonium nuclides. J. Inorg. Nucl. Chem. 27 (1), 33–39. Nakagawa, Tsuneo, 1986. Evaluation of Neutron Nuclear Data for 250 Cf and 251 Cf. No. JAERI-M–86-086. Japan Atomic Energy Research Inst. Tompson Jr, Robert V., and Mark A. Prelas. Isotope energy conversion and spent nuclear fuel storage systems. U.S. Patent Application 14/870,845, filed March 31, 2016. Wild, J.F., Baisden, P.A., Dougan, R.J., Hulet, E.K., Lougheed, R.W., Landrum, J.H., 1985. Light-charged-particle emission in the spontaneous fission of Cf 250, Fm 256, and Fm 257. Phys. Rev. C 32 (no. 2), 488.
3. Conclusions The evaluation of some important quantities have been investigated for 250Cf, where most of the evaluated cross sections and quantities, such as the capture cross section and the resonance integral capture cross section, showed a good agreement with values found in the literature. In addition, the thermal benchmark evaluation for the Maxwellian-averaged cross sections of total, capture, and fission reactions along with the Wescott factors are in good agreements with the evaluated values by the Japanese Evaluated Nuclear Data Library. These important quantities have significant for improvement the performance for fission reactor applications to get much more reliable parameters for fission products behavior in thermal nuclear power reactor. Acknowledgments This study was supported by Khalifa University of Science and Technology Faculty Start-Up Fund, FSU 8474000067. Appendix A. Supplementary data Supplementary data to this article can be found online at https://
3