Unrecognized Sources of Uncertainties (USU) in Experimental Nuclear Data

Evaluated nuclear data uncertainties are often perceived as unrealistic, most often because they are thought to be too small. The impact of this issue in applied nuclear science has been discussed widely in recent years. Commonly suggested causes are: poor estimates of specific error components, neglect of uncertainty correlations, and overlooked known error sources. However, instances have been reported where very careful, objective assessments of all known error sources have been made with realistic error magnitudes and correlations provided, yet the resulting evaluated uncertainties still appear to be inconsistent with observed scatter of predicted mean values. These discrepancies might be attributed to significant unrecognized sources of uncertainty (USU) that limit the accuracy to which these physical quantities can be determined. The objective of our work has been to develop procedures for revealing and including USU estimates in nuclear data evaluations involving experimental input data. We conclude that the presence of USU may be revealed, and estimates of magnitudes made, through quantitative analyses. This paper identifies several specific clues that can be explored by evaluators in identifying the existence of USU. It then describes numerical procedures to generate quantitative estimates of USU magnitudes. Key requirements for these procedures to be viable are that sufficient numbers of data points be available, for statistical reasons, and that additional supporting information about the measurements be provided by the experimenters. Realistic examples are described to illustrate these procedures and demonstrate their outcomes as well as limitations. Our work strongly supports the view that USU is an important issue in nuclear data evaluation, with significant consequences for applications, and that this topic warrants further investigation by the nuclear science community.

[1]  Denise Neudecker,et al.  Peelle’s Pertinent Puzzle: A Fake Due to Improper Analysis , 2012 .

[2]  Roberto Capote,et al.  A New Formulation of the Unified Monte Carlo Approach (UMC-B) and Cross-Section Evaluation for the Dosimetry Reaction 55 Mn(n,γ) 56 Mn , 2012 .

[3]  Oleg Shcherbakov,et al.  Neutron-Induced Fission of 233U, 238U, 232Th, 239Pu, 237Np, natPb and 209Bi Relative to 235U in the Energy Range 1-200 MeV , 2002 .

[4]  M Sahagia,et al.  Results of an international comparison for the activity measurement of 177Lu. , 2012, Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine.

[5]  Andrew L. Rukhin,et al.  Weighted means statistics in interlaboratory studies , 2009 .

[6]  A G Steele,et al.  Outlier rejection for the weighted-mean KCRV , 2005 .

[7]  Roberto Capote,et al.  Uncertainties of mass extrapolations in Hartree-Fock-Bogoliubov mass models , 2014 .

[8]  Guohui Zhang,et al.  Measurement of Cross Sections for the 10 B(n,α) 7 Li Reaction at 4.0 and 5.0 MeV Using an Asymmetrical Twin Gridded Ionization Chamber , 2011 .

[9]  Gunter H. R. Kegel,et al.  Prompt fission neutron energy spectra induced by fast neutrons , 1995 .

[10]  Peter Steier,et al.  Accelerator mass spectrometry measurement of the reaction Cl35(n,γ)Cl36 at keV energies , 2019, Physical Review C.

[11]  Kathrin Buczak,et al.  Precise measurement of the thermal and stellar $^{54}$Fe($n, \gamma$)$^{55}$Fe cross sections via AMS , 2016, 1611.09006.

[12]  D. Smith A unified Monte Carlo approach to fast neutron cross section data evaluation. , 2008 .

[13]  Sergey A Badikov,et al.  Procedure for statistical analysis of one-parameter discrepant experimental data. , 2012, Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine.

[14]  Alan D. Martin,et al.  Review of Particle Physics , 2018, Physical Review D.

[15]  S. E. Aumeier,et al.  The simultaneous evaluation of the standards and other cross sections of importance for technology , 1997 .

[16]  Pavel Obložinský Workshop on Neutron Cross Section Covariances , 2008 .

[17]  A. V. Ignatyuk,et al.  Uncertainties and Covariances of the Fission Cross Sections and the Fission Neutron Multiplicities for Actinides , 2008 .

[18]  Alex Hermanne,et al.  Reference Cross Sections for Charged-particle Monitor Reactions , 2018 .

[19]  Naohiko Otuka,et al.  Experimental Nuclear Reaction Data Uncertainties: Basic Concepts and Documentation , 2012 .

[20]  F. Calvino,et al.  High-accuracy determination of the 238U/ 235U fission cross section ratio up to ≈ 1 GeV at n_TOF at CERN , 2014, 1410.7737.

[21]  Donald L. Smith,et al.  Probability, statistics, and data uncertainties in nuclear science and technology , 1991 .

[22]  Roberto Capote,et al.  An Investigation of the Performance of the Unified Monte Carlo Method of Neutron Cross Section Data Evaluation , 2008 .

[23]  A. Couture,et al.  Neutron capture cross section of {sup 241}Am , 2008 .

[24]  G. Noguere,et al.  New fit of thermal neutron constants (TNC) for 233,235U, 239,241Pu and 252Cf(sf): Microscopic vs. maxwellian data , 2017 .

[25]  F. H. Fröhner Evaluation of Data with Systematic Errors , 2003 .

[26]  R. Q. Wright,et al.  ENDF/B-VIII.0: The 8 th Major Release of the Nuclear Reaction Data Library with CIELO-project Cross Sections, New Standards and Thermal Scattering Data , 2018 .

[27]  Richard R. Spencer,et al.  A Measurement of the Average Number of Prompt Neutrons from Spontaneous Fission of Californium-252 , 1982 .

[28]  M. W. Herman,et al.  IAEA CIELO Evaluation of Neutron-induced Reactions on 235U and 238U Targets , 2018 .

[29]  Yacine Kadi,et al.  Experimental neutron capture data of 58Ni from the CERN n_TOF facility , 2014, 1402.1032.

[30]  J. W. Behrens,et al.  Measurements of the Neutron-Induced Fission Cross Sections of 240Pu, 242Pu, and 244Pu Relative to 235U from 0.1 to 30 MeV , 1977 .

[31]  D. Neudecker,et al.  How accurately we know the standard $^{252}$Cf(sf) neutron multiplicity? , 2019, 1908.00272.

[32]  V. Khryachkov,et al.  The cross-section of the 10B(n,α)7Li reaction measured in the MeV energy range , 2006 .

[33]  Petter Helgesson,et al.  Uncertainty-driven nuclear data evaluation including thermal (n,α) applied to 59 Ni , 2017 .

[34]  C. L. Dunford,et al.  Evaluated Nuclear Data File, ENDF/B-VI , 1992 .

[35]  Roberto Capote,et al.  An ENDF-6 Compatible Evaluation for Neutron Induced Reactions of 232Th in the Unresolved Resonance Region , 2008 .

[36]  Hayes,et al.  Review of Particle Physics. , 1996, Physical review. D, Particles and fields.

[37]  Arjan J. Koning,et al.  Bayesian Monte Carlo method for nuclear data evaluation , 2015 .

[38]  G. Noguere,et al.  Experiments in the EXFOR library for evaluation of thermal neutron constants , 2017 .

[39]  F. Käppeler,et al.  Neutron Capture Cross Section of 232Th , 2001 .

[40]  P. R. Graves-Morris,et al.  Pade Approximants and their Applications , 1974 .

[41]  R Willink Statistical determination of a comparison reference value using hidden errors , 2002 .

[42]  F. Calvino,et al.  Experimental neutron capture data of 58Ni from the CERN n_TOF facility , 2014 .

[43]  Arjan J. Koning,et al.  TENDL: Complete Nuclear Data Library for Innovative Nuclear Science and Technology , 2019, Nuclear Data Sheets.

[44]  Roberto Capote,et al.  Applying a Template of Expected Uncertainties to Updating 239Pu(n,f) Cross-section Covariances in the Neutron Data Standards Database , 2020 .

[45]  R. Capote,et al.  Evaluation of the Neutron Data Standards , 2018 .

[46]  K Kossert,et al.  LSC measurements of the half-life of 40K. , 2004, Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine.

[47]  N. M. Larson,et al.  ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data , 2011 .

[48]  G. A. Baker Essentials of Padé approximants , 1975 .

[49]  G. D'Agostini,et al.  On the use of the covariance matrix to fit correlated data , 1994 .

[50]  L. E. Sherman,et al.  A measurement of the capture cross sections of 238U and 232Th for 5–200 keV neutrons☆ , 1964 .

[51]  R. W. Peelle,et al.  Evaluating nuclear data uncertainty: Progress, pitfalls, and prospects , 1986 .

[52]  V. G. Pronyaev,et al.  Neutron capture cross section measurements for 197Au from 3.5 to 84 keV at GELINA , 2014, The European Physical Journal A.

[53]  H. Padé Sur la représentation approchée d'une fonction par des fractions rationnelles , 1892 .

[54]  Octavian Sima,et al.  Uncertainties in gamma-ray spectrometry , 2015 .

[55]  Diane E. Vaughan,et al.  Physical Uncertainty Bounds (PUB) , 2015 .

[56]  Ralph A. Johnson,et al.  Statistical analysis in chemistry and the chemical industry , 1955 .

[57]  B. Pritychenko,et al.  Towards a More Complete and Accurate Experimental Nuclear Reaction Data Library (EXFOR): International Collaboration Between Nuclear Reaction Data Centres (NRDC) , 2014, 2002.07114.

[58]  Satoshi Chiba,et al.  A suggested procedure for resolving an anomaly in least-squares data analysis known as Peelle's Pertinent Puzzle'' and the general implications for nuclear data evaluation , 1991 .

[59]  J. Heyse,et al.  Determination of Resonance Parameters and their Covariances from Neutron Induced Reaction Cross Section Data , 2012 .

[60]  Michael Heil,et al.  Measurement of the stellar Ni 58 (n,γ) Ni 59 cross section with accelerator mass spectrometry , 2017 .

[61]  Guohui Zhang,et al.  Differential Cross-Section Measurement for the 10B(n,α)7Li Reaction , 2002 .

[62]  M. R. Bhat Evaluation methods for neutron cross section standards , 1980 .

[63]  R. Macfarlane,et al.  The NJOY Nuclear Data Processing System , 2008 .

[64]  Alexander B Laptev,et al.  Fast Neutron-Induced Fission Cross Sections of , 2014 .

[65]  Richard R. Spencer,et al.  New Maxwellian averaged neutron capture cross sections for Cl-35,Cl-37 , 2002 .

[66]  Roberto Capote,et al.  Impact of model defect and experimental uncertainties on evaluated output , 2013 .

[67]  C Michotte,et al.  Uncertainty of combined activity estimations , 2015 .

[68]  R. B. Perez,et al.  Measurement of the Uranium-238 to Uranium-235 Fission Cross-Section Ratio for Neutron Energies Between 0.1 and 25 MeV , 1978 .

[69]  R. A. Forster,et al.  MCNP - a general Monte Carlo code for neutron and photon transport , 1985 .

[70]  Georg Schnabel,et al.  Fitting and Analysis Technique for Inconsistent Nuclear Data , 2018, 1803.00960.

[71]  Gowri Srinivasan,et al.  Validating nuclear data uncertainties obtained from a statistical analysis of experimental data with the “Physical Uncertainty Bounds” method , 2020, EPJ Nuclear Sciences & Technologies.

[72]  A. R. de L. Musgrove,et al.  Resonant neutron capture in 40Ca , 1976 .

[73]  Dorothea Wiarda,et al.  Astrophysical reaction rates for Ni-58,Ni-60(n,gamma) from new neutron capture cross section measurements , 2010 .

[74]  Arjan J. Koning,et al.  Covariance Data in the Fast Neutron Region , 2011 .

[75]  B. C. Diven,et al.  Numbers of prompt neutrons per fission for U 233 , U 235 , Pu 239 , and Cf 252 , 1962 .

[76]  Stephen L.R.Ellison An outlier-resistant indicator of anomalies among inter-laboratory comparison data with associated uncertainty , 2018 .

[77]  Alan D. Martin,et al.  Review of Particle Physics , 2014 .

[78]  G.E. Moore,et al.  Cramming More Components Onto Integrated Circuits , 1998, Proceedings of the IEEE.

[79]  Patrick Talou,et al.  Evaluation of the 239 Pu prompt fission neutron spectrum induced by neutrons of 500 keV and associated covariances , 2015 .

[80]  Soo-Youl Oh,et al.  International Evaluation of Neutron Cross Section Standards , 2009 .

[81]  F. Gunsing,et al.  The Use of C6D6 Detectors for Neutron Induced Capture Cross-Section Measurements in the Resonance Region , 2007 .

[82]  Peter Steier,et al.  Precise measurement of the thermal and stellar Fe 54 (n,γ) Fe 55 cross sections via accelerator mass spectrometry , 2017 .

[83]  Roberto Capote,et al.  Nuclear data evaluation methodology including estimates of covariances , 2010 .

[84]  W. Kutschera,et al.  Determination of the stellar (n,?) cross section of Ca40 with accelerator mass spectrometry , 2009 .

[85]  Isabel S. Gonçalves,et al.  Neutron capture cross section of Th-232 measured at the n_TOF facility at CERN in the unresolved resonance region up to 1-MeV , 2006 .

[86]  D. R. Weaver,et al.  The use of the normalized residual in averaging experimental data and in treating outliers , 1992 .

[87]  J. Terrell,et al.  PROMPT NEUTRONS FROM FISSION , 1964 .

[88]  Francesca Pennecchi,et al.  The generalized weighted mean of correlated quantities , 2006 .

[89]  D. M. Hetrick,et al.  GLUCS: a generalized least-squares program for updating cross section evaluations with correlated data sets. [In FORTRAN IV for PDP-10] , 1980 .

[90]  Massimo Salvatores,et al.  Needs and Issues of Covariance Data Application , 2008 .

[91]  E. Bauge,et al.  Evaluation of the Covariance Matrix of 239Pu Neutronic Cross Sections in the Continuum Using the Backward-Forward Monte-Carlo Method , 2011 .

[92]  Andrea Favalli,et al.  A review of the prompt neutron nu-bar value for 252Cf spontaneous fission , 2020 .

[93]  E. V. Gai Some Algorithms for Evaluating Nuclear Data and Generating Uncertainty Covariance Matrices , 2018 .

[94]  E. Iso,et al.  Measurement Uncertainty and Probability: Guide to the Expression of Uncertainty in Measurement , 1995 .

[95]  J. W. Boldeman,et al.  Odd-even effects in radiative neutron capture by 42Ca, 43Ca and 44Ca , 1977 .

[96]  Nien Fan Zhang,et al.  The uncertainty associated with the weighted mean of measurement data , 2006 .

[97]  Alexander B Laptev,et al.  Fast Neutron–Induced Fission Cross Sections of 233, 234, 236, 238U up to 200 MeV , 2014 .

[98]  M. Ishikawa,et al.  CIELO Collaboration Summary Results: International Evaluations of Neutron Reactions on Uranium, Plutonium, Iron, Oxygen and Hydrogen , 2018 .

[99]  Patrick Talou,et al.  Evaluation and Uncertainty Quantification of Prompt Fission Neutron Spectra of Uranium and Plutonium Isotopes , 2013 .

[100]  S. Kailas,et al.  Neutron capture gross section of th-232 , 1986 .

[101]  Diane E. Vaughan,et al.  Template for estimating uncertainties of measured neutron-induced fission cross-sections , 2018 .

[102]  Liu Tingjin,et al.  Evaluated Nuclear Data for Nuclides within the Thorium-Uranium Fuel Cycle , 2010 .

[103]  R. W. Peelle,et al.  The ENDFB-VI neutron cross section measurement standards , 1993 .

[104]  M. Divadeenam,et al.  A least-squares fit of thermal data for fissile nuclei , 1984 .