{"title":"Normalization of ToF (n,f) Measurements in Fissile Targets: Microscopic cross-section integrals","authors":"I. Durán , R. Capote , P. Cabanelas","doi":"10.1016/j.nds.2024.01.004","DOIUrl":null,"url":null,"abstract":"<div><p>Precise normalization of ToF yield measurements of neutron induced fission in fissile targets is challenging, but the appropriate normalization is also of critical importance for nuclear energy and criticality safety, among other applications. A typical normalization relies on the Thermal Neutron Constants (TNC) recommended at the thermal point (fission <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> and capture <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> thermal cross sections) by the Neutron Standards. However, many ToF experiments do not collect data down to the thermal energy and use normalization cross-section integrals defined at different arbitrary energy intervals. Normalization fission cross-section integrals <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> are recommended in between-valleys energy regions 8.1–14.7 eV, 7.8–11 eV, 9–20 eV, and 11.7–19.5 eV for fissile targets <sup>233</sup>U, <sup>235</sup>U, <sup>239</sup>Pu, and <sup>241</sup>Pu with values equal to 689.0(10.8), 245.7(4.1), 1059(6), and 1378(33) <span><math><mi>b</mi><mo>⋅</mo><mi>e</mi><mi>V</mi></math></span>, respectively. The <sub>235</sub>U normalization integral <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> derived in this work of 245.7(4.1) <span><math><mi>b</mi><mo>⋅</mo><mi>e</mi><mi>V</mi></math></span> is in good agreement within quoted uncertainties with the Neutron Standards value of 247.5(3.0) <span><math><mi>b</mi><mo>⋅</mo><mi>e</mi><mi>V</mi></math></span>.</p><p>Additional cross-section integrals <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> in the thermal region from 20–60 meV are derived to fix both the normalization and the slope of the fission cross section at the thermal point providing additional constraints for R-matrix evaluations of experimental fission yields. Ratios <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>/</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> feature very low uncertainty due to the strong positive correlations between the numerator and the denominator and are comprehensively derived for the first time. Integral ratios <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of 39.31(54), 13.08(20), 41.65(22), and 40.46(85) are recommended as reference for fissile targets <sup>233</sup>U, <sup>235</sup>U, <sup>239</sup>Pu, and <sup>241</sup>Pu, respectively. Similarly, ratios <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>/</mo><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of 30.40(18), 31.22(12), 29.58(7), and 29.95(35) are also recommended as reference for corresponding fissile targets. These recommended ratios can be used by experimentalists to normalize their measured thin-target fission yield data, but also by evaluators to constrain their R-matrix analysis that use multiple sets of measured data renormalized as recommended in this work.</p><p>An evaluation of thermal (n,f) cross sections <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> presented in this work for all fissile targets is in excellent agreement with the Thermal Neutron Constants defined in the Neutron Standards within one-sigma uncertainty. Such agreement guarantees the reliability of our new evaluation of reference integrals based on the whole database of consistent experimental TOF data.</p></div>","PeriodicalId":49735,"journal":{"name":"Nuclear Data Sheets","volume":"193 ","pages":"Pages 95-104"},"PeriodicalIF":2.8000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S009037522400005X/pdf?md5=81f56bc93151d9f0f06777235966e6c4&pid=1-s2.0-S009037522400005X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Data Sheets","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009037522400005X","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 0
Abstract
Precise normalization of ToF yield measurements of neutron induced fission in fissile targets is challenging, but the appropriate normalization is also of critical importance for nuclear energy and criticality safety, among other applications. A typical normalization relies on the Thermal Neutron Constants (TNC) recommended at the thermal point (fission and capture thermal cross sections) by the Neutron Standards. However, many ToF experiments do not collect data down to the thermal energy and use normalization cross-section integrals defined at different arbitrary energy intervals. Normalization fission cross-section integrals are recommended in between-valleys energy regions 8.1–14.7 eV, 7.8–11 eV, 9–20 eV, and 11.7–19.5 eV for fissile targets 233U, 235U, 239Pu, and 241Pu with values equal to 689.0(10.8), 245.7(4.1), 1059(6), and 1378(33) , respectively. The 235U normalization integral derived in this work of 245.7(4.1) is in good agreement within quoted uncertainties with the Neutron Standards value of 247.5(3.0) .
Additional cross-section integrals in the thermal region from 20–60 meV are derived to fix both the normalization and the slope of the fission cross section at the thermal point providing additional constraints for R-matrix evaluations of experimental fission yields. Ratios and feature very low uncertainty due to the strong positive correlations between the numerator and the denominator and are comprehensively derived for the first time. Integral ratios of 39.31(54), 13.08(20), 41.65(22), and 40.46(85) are recommended as reference for fissile targets 233U, 235U, 239Pu, and 241Pu, respectively. Similarly, ratios of 30.40(18), 31.22(12), 29.58(7), and 29.95(35) are also recommended as reference for corresponding fissile targets. These recommended ratios can be used by experimentalists to normalize their measured thin-target fission yield data, but also by evaluators to constrain their R-matrix analysis that use multiple sets of measured data renormalized as recommended in this work.
An evaluation of thermal (n,f) cross sections presented in this work for all fissile targets is in excellent agreement with the Thermal Neutron Constants defined in the Neutron Standards within one-sigma uncertainty. Such agreement guarantees the reliability of our new evaluation of reference integrals based on the whole database of consistent experimental TOF data.
期刊介绍:
The Nuclear Data Sheets are current and are published monthly. They are devoted to compilation and evaluations of experimental and theoretical results in Nuclear Physics. The journal is mostly produced from Evaluated Nuclear Structure Data File (ENSDF), a computer file maintained by the US National Nuclear Data Center