The paper presents a preliminary uncertainty analysis related to potential uncertainties on the fission spectrum data. Consistent results are shown for a reference fast reactor design configuration and for experimental thermal configurations. However the results obtained indicate the need for further analysis, in particular in terms of fission spectrum uncertainty data assessment

Aliberti, G.

Kodeli, I.

Palmiotti, G.

Salvatores, M.

UNT Digital Library

This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint should not be cited or reproduced without permission of the author. This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the United States Government or the sponsoring agency. INL/CON-07-13354PREPRINTFission Spectrum Related Uncertainties 4th Workshop on Neutron Measurements, Evaluations and Applications -- Nuclear Data Needs for Generation IV and Accelerator-Driven SystemsG. Aliberti I. Kodeli G. Palmiotti M. Salvatores October 2007 Fission Spectrum Related Uncertainties G. Aliberti1), I. Kodeli2), G. Palmiotti3) and M.Salvatores1,3,4)1)  Argonne National Laboratory, NE Division, Argonne, IL 60439 (USA) 2)  OECD/NEA, Paris, France 3) Idaho National Laboratory, NSE Division, 2525 Fremont Ave. P.O. Box 1625, Idaho Falls, ID 83415-3855 (USA) 4) CEA-Cadarache, 13108 St-Paul-Lez-Durance, France aliberti@anl.gov Abstract: The paper presents a preliminary uncertainty analysis related to potential uncertainties on the fission spectrum data. Consistent results are shown for a reference fast reactor design configuration and for experimental thermal configurations. However the results obtained indicate the need for further analysis, in particular in terms of fission spectrum uncertainty data assessment. IntroductionSensitivity coefficients for the multiplication factor associated to the fission spectrum are calculated according to the formula: > @> @ > @domaindgroupenergy'g,gisotopei'gf'g,ii'g'g,id,'gfd,'g,idd,gd,g,id,g,i),(kdrdrS'g,id,'g,ieff   F)6Qu)F)6Qu)F ³¦³, (1) where dfdfd,g,id,g,idd,i)6Q)6QF F , > @  denotes the integration over the energy (summation over the groups g’), while  denotes the integration over energy and space. After computing the sensitivity coefficients, the fission spectrum related uncertainties are successively determined using the classical formula )(k)(k20 effeff DSSR FF ' , where D is the dispersion matrix containing the covariance data. Sensitivity coefficient results The following sensitivity coefficients have been calculated for the ABTR [1] multiplication factor with the ERANOS code system [2]. Table 1 gives the breakdown by energy group for Pu-239 and the total values by isotope. The sensitivity coefficients shown in the tables are the total over the reactor. It can be observed that, as expected, the total isotope sensitivity for the fission spectrum has the same value of Ȟ; the distribution by energy group is however different for each isotope (see case of Pu-239). Additionally, the overall keff sensitivity to the fission spectrum (and to Ȟ) is practically 100% (Table 1 gives ǻk/k2 sensitivities and for the ABTR under study keff = 1.034472). Table 1. ǻk/k2: Sensitivity Coefficients for ABTR   Pu-239: Breakdown by Energy Group  Total Sensitivity - Breakdown by Isotope Gr. Energy (a) ıcapt ıel Ȟ ıinel ıfiss Ȥ Total Isotope ıcapt ıel Ȟ ıinel ıfiss ın.2n Ȥ Total1 19.6 MeV 0.00 0.00 0.45 -0.01 0.30 3.24 3.98 U235 -0.04 0.00 0.56 -0.01 0.37 0.00 0.56 1.44 2 6.07 MeV -0.01 0.01 4.51 -0.13 3.03 29.49 36.90 U238 -13.84 2.72 12.22 -4.20 7.42 0.08 12.08 16.503 2.23 MeV -0.03 0.02 4.62 -0.08 3.08 18.80 26.41 Pu238 -0.01 0.00 0.16 0.00 0.11 0.00 0.16 0.42 4 1.35 MeV -0.21 0.09 15.02 -0.05 10.42 20.08 45.36 Pu239 -3.80 0.47 79.20 -0.29 56.24 0.00 79.35 211.175 498 keV -0.58 0.17 20.32 -0.01 14.31 6.01 40.22 Pu240 -0.62 0.07 2.65 -0.05 1.80 0.00 2.65 6.51 6 183 keV -0.74 0.13 16.15 -0.02 11.68 1.37 28.57 Pu241 -0.07 0.01 1.51 0.00 1.09 0.00 1.51 4.04 7 67.4 keV -0.55 0.03 8.00 -0.01 5.99 0.28 13.75 Pu242 -0.03 0.00 0.10 0.00 0.07 0.00 0.10 0.24 8 24.8 keV -0.59 0.02 5.32 0.01 4.04 0.06 8.87 Np237 -0.08 0.00 0.10 0.00 0.07 0.00 0.10 0.18 9 9.12 keV -0.34 0.00 1.67 0.00 1.24 0.02 2.58 Am241 -0.12 0.00 0.11 0.00 0.08 0.00 0.10 0.17 10 2.03 keV -0.51 0.00 2.19 0.00 1.56 0.00 3.24 Am242m 0.00 0.00 0.02 0.00 0.02 0.00 0.02 0.07 11 454 eV -0.21 0.00 0.79 0.00 0.49 0.00 1.06 Am243 -0.02 0.00 0.02 0.00 0.01 0.00 0.01 0.02 12 22.6 eV -0.03 0.00 0.11 0.00 0.06 0.00 0.14 Cm242 0.00 0.00 0.01 0.00 0.01 0.00 0.01 0.02 13 4 eV 0.00 0.00 0.04 0.00 0.03 0.00 0.07 Cm244 0.00 0.00 0.01 0.00 0.01 0.00 0.01 0.02 14 0.54 eV 0.00 0.00 0.01 0.00 0.00 0.00 0.01 Cm245 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 15 0.1 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Fe56 -1.38 5.18 0.00 -1.59 0.00 0.00 0.00 2.22 Total -3.80 0.47 79.20 -0.29 56.24 79.35 211.17 Cr52 -0.17 1.25 0.00 -0.17 0.00 0.07 0.00 0.98 (a) Upper energy boundary Ni58 -0.05 0.12 0.00 -0.01 0.00 0.00 0.00 0.06         Zr90 -0.14 0.49 0.00 -0.21 0.00 0.00 0.00 0.14         Na23 -0.12 2.03 0.00 -0.42 0.00 0.00 0.00 1.49         B10 -0.52 0.01 0.00 0.00 0.00 0.00 0.00 -0.52        Total -21.01 12.37 96.66 -6.96 67.29 0.16 96.66 245.18Fission spectra covariance matrices The information on the fission spectra covariance matrices is available in the DOSCOV package [3] and in the JENDL-3.2 and -3.3 [4,5] evaluations. In the DOSCOV package, dating back to ~1980, the covariance data for the U-235 fission spectrum were obtained assuming the standard deviations of 1.2% and 5.9% for the Watt spectrum parameters a and b, respectively, and the correlation of -0.21 between them. For the purpose of these studies the covariance matrices were converted from the DOSCOV 24-group structure to those needed using the ANGELO code [6]. More recently, the covariance matrices for several isotopes, including U-235, U-238, Pu-239, were prepared in the JENDL-3.2 and -3.3 [2,3] evaluations. The data were processed using the ERROR-J 2.3 code [7]. The JENDL3.3 fission spectrum covariance matrix for Pu-239 is presented in Table 2 in a 15 energy group structure. Table 2. Pu-239 JENDL3.3 Variance/Covariance Data (ABTR)    Covariances   Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Variances(%) Gr. Energy (a) 19.6 MeV6.07 MeV2.23 MeV1.35MeV498keV 183keV 67.4keV 24.8keV 9.12keV 2.03keV 454eV22.6 eV4eV0.54eV0.1 eV9.58 1 19.6 MeV 1.000 0.787 -0.323 -0.905 -0.665 -0.608 -0.592 -0.589 -0.589 -0.590 -0.594 -0.595 -0.595 -0.596 -0.5967.12 2 6.07 MeV 0.787 1.000 0.329 -0.975 -0.984 -0.968 -0.963 -0.962 -0.962 -0.963 -0.964 -0.964 -0.964 -0.964 -0.9641.03 3 2.23 MeV -0.323 0.329 1.000 -0.110 -0.491 -0.554 -0.571 -0.574 -0.574 -0.574 -0.569 -0.568 -0.568 -0.568 -0.5685.03 4 1.35 MeV -0.905 -0.975 -0.110 1.000 0.919 0.888 0.879 0.877 0.877 0.877 0.880 0.880 0.881 0.881 0.8816.62 5 498 keV -0.665 -0.984 -0.491 0.919 1.000 0.997 0.996 0.995 0.995 0.995 0.996 0.996 0.996 0.996 0.9968.92 6 183 keV -0.608 -0.968 -0.554 0.888 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0008.21 7 67.4 keV -0.592 -0.963 -0.571 0.879 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0007.30 8 24.8 keV -0.589 -0.962 -0.574 0.877 0.995 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.00012.59 9 9.12 keV -0.589 -0.962 -0.574 0.877 0.995 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.00012.16 10 2.03 keV -0.590 -0.963 -0.574 0.877 0.995 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.00025.09 11 454 eV -0.594 -0.964 -0.569 0.880 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0000.61 12 22.6 eV -0.595 -0.964 -0.568 0.880 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0000.05 13 4 eV -0.595 -0.964 -0.568 0.881 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0000.00 14 0.54 eV -0.596 -0.964 -0.568 0.881 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0000.00 15 0.1 eV -0.596 -0.964 -0.568 0.881 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000(a) Upper energy boundary          The DOSCOV fission spectrum covariance matrix is presented in Table 3 for U-235 in a 15 energy group structure. In the present study, as demonstrative example, the same matrix has been used for Pu-239. Table 3. U-235 DOSCOV Variance/Covariance Data (ABTR)    Covariances   Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Variances(%) Gr. Energy (a) 19.6 MeV6.07 MeV2.23 MeV1.35MeV498keV 183keV 67.4keV 24.8keV 9.12keV 2.03keV 454eV22.6 eV4eV0.54eV0.1 eV11.33 1 19.6 MeV 1.000 1.002 -0.674 -1.011 -1.002 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.9912.85 2 6.07 MeV 0.969 1.000 -0.590 -1.012 -1.003 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.991 -0.9910.31 3 2.23 MeV -0.770 -0.620 1.000 0.649 0.616 0.618 0.614 0.613 0.612 0.612 0.612 0.612 0.612 0.612 0.6121.93 4 1.35 MeV -0.992 -1.000 0.596 1.000 1.002 1.010 1.010 1.010 1.010 1.010 1.010 1.010 1.010 1.010 1.0102.98 5 498 keV -0.974 -0.999 0.564 0.998 1.000 1.009 1.009 1.009 1.009 1.009 1.009 1.009 1.009 1.009 1.0093.46 6 183 keV -0.952 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.64 7 67.4 keV -0.950 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.71 8 24.8 keV -0.950 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.73 9 9.12 keV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 10 2.03 keV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 11 454 eV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 12 22.6 eV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 13 4 eV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 14 0.54 eV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.0003.74 15 0.1 eV -0.949 -0.990 0.559 0.990 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000(a) Upper energy boundary          Uncertainty results Table 4 shows the breakdown of the calculated uncertainty coefficients by energy group for Pu-239 and the total uncertainties by isotope. Results for the fission spectrum are obtained with the JENDL3.3 covariance data (only U-235 and Pu-239 matrices were available), while for other cross-sections the BOLNA dispersion matrix [8] is used. It is observed that the total uncertainty associated with the fission spectrum is dramatically important, an order of magnitude higher than the Ȟ total contribution. Consequently, the overall uncertainty on the multiplication factor significantly increases (from 0.92% to 4.01%) becoming desperately out of the required accuracies (0.3%). Table 4. ǻk/k2: Uncertainty Coefficients (ABTR)   Pu-239: Breakdown by Energy Group  Total Uncertainty - Breakdown by Isotope Gr. Energy (a) ıcapt ıel Ȟ ıinel ıfiss Ȥ Total Isotope ıcapt ıel Ȟ ıinel ıfiss ın.2n Ȥ Total1 19.6 MeV 0.00 0.00 0.00 0.01 0.01 1.01 1.01 U235 0.01 0.00 0.00 0.00 0.00 0.00 0.02 0.022 6.07 MeV 0.02 0.01 0.01 0.04 0.05 2.87 2.87 U238 0.26 0.20 0.14 0.69 0.04 0.00 0.00 0.773 2.23 MeV 0.03 0.01 0.01 0.03 0.05 0.34 0.35 Pu238 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.024 1.35 MeV 0.06 0.02 0.02 0.03 0.10 1.96 1.97 Pu239 0.23 0.03 0.13 0.06 0.24 0.00 3.90 3.925 498 keV 0.11 0.02 0.05 0.01 0.13 1.21 1.22 Pu240 0.06 0.00 0.08 0.01 0.09 0.00 0.00 0.136 183 keV 0.11 0.01 0.09 0.01 0.13 0.66 0.69 Pu241 0.01 0.00 0.00 0.00 0.12 0.00 0.00 0.127 67.4 keV 0.09 0.00 0.06 0.01 0.08 0.29 0.32 Pu242 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.018 24.8 keV 0.09 0.00 0.04 0.01i 0.06 0.13 0.17 Np237 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.019 9.12 keV 0.07 0.00 0.02 0.00 0.02 0.09 0.12 Am241 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.0110 2.03 keV 0.01 0.00 0.00 0.00 0.02 0.03 0.04 Fe56 0.07 0.08 0.00 0.24 0.00 0.00 0.00 0.2711 454 eV 0.00 0.00 0.00 0.00 0.01 0.01 0.02 Cr52 0.01 0.06 0.00 0.00 0.00 0.01 0.00 0.0612 22.6 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Zr90 0.01 0.01 0.00 0.03 0.00 0.00 0.00 0.0413 4 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Na23 0.02 0.05 0.00 0.07 0.00 0.00 0.00 0.0814 0.54 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 B10 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.0415 0.1 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total 0.36 0.23 0.20 0.73 0.29 0.01 3.90 4.01Total 0.23 0.03 0.13 0.06 0.24 3.90 3.92         (a) Upper energy boundary          Table 5 shows the results with the DOSCOV covariance matrix for the fission spectrum (only U-235 and Pu-239 matrices were available). The fission spectrum related uncertainties are lower than in the previous case but still very high. Table 5. ǻk/k2: Uncertainty Coefficients (ABTR)   Pu-239: Breakdown by Energy Group  Total Uncertainty - Breakdown by Isotope Gr. Energy (a) ıcapt ıel Ȟ ıinel ıfiss Ȥ Total Isotope ıcapt ıel Ȟ ıinel ıfiss ın.2n Ȥ Total1 19.6 MeV 0.00 0.00 0.00 0.01 0.01 0.83 0.83 U235 0.01 0.00 0.00 0.00 0.00 0.00 0.01 0.022 6.07 MeV 0.02 0.01 0.01 0.04 0.05 1.26 1.26 U238 0.26 0.20 0.14 0.69 0.04 0.00 0.00 0.773 2.23 MeV 0.03 0.01 0.01 0.03 0.05 0.26 0.27 Pu238 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.024 1.35 MeV 0.06 0.02 0.02 0.03 0.10 0.86 0.86 Pu239 0.23 0.03 0.13 0.06 0.24 0.00 1.87 1.915 498 keV 0.11 0.02 0.05 0.01 0.13 0.58 0.60 Pu240 0.06 0.00 0.08 0.01 0.09 0.00 0.00 0.136 183 keV 0.11 0.01 0.09 0.01 0.13 0.30 0.36 Pu241 0.01 0.00 0.00 0.00 0.12 0.00 0.00 0.127 67.4 keV 0.09 0.00 0.06 0.01 0.08 0.14 0.19 Pu242 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.018 24.8 keV 0.09 0.00 0.04 0.01i 0.06 0.07 0.13 Np237 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.019 9.12 keV 0.07 0.00 0.02 0.00 0.02 0.03 0.08 Am241 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.0110 2.03 keV 0.01 0.00 0.00 0.00 0.02 0.01 0.02 Fe56 0.07 0.08 0.00 0.24 0.00 0.00 0.00 0.2711 454 eV 0.00 0.00 0.00 0.00 0.01 0.00 0.01 Cr52 0.01 0.06 0.00 0.00 0.00 0.01 0.00 0.0612 22.6 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Zr90 0.01 0.01 0.00 0.03 0.00 0.00 0.00 0.0413 4 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Na23 0.02 0.05 0.00 0.07 0.00 0.00 0.00 0.0814 0.54 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 B10 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.0415 0.1 eV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total 0.36 0.23 0.20 0.73 0.29 0.01 1.87 2.09Total 0.23 0.03 0.13 0.06 0.24 1.87 1.91         (a) Upper energy boundary          KRITZ critical light water benchmark analysis Cross-section sensitivity and uncertainty analyses of several KRITZ UO2 and MOX critical configurations [9] were performed in the scope of the OECD international benchmark exercise. These studies, based on the SUSD3D [10] cross-section sensitivity and uncertainty package, addressed among other sources of uncertainty also those linked to the fission spectra [11]. The calculated uncertainties in keff due to the uncertainties in the fission spectra of U-235, U-238 and Pu-239 are presented in Table 6. It can be observed that the uncertainties vary only slightly between different KRITZ configurations. Subsequently it seems that the discrepancy between the calculated and measured keff, largely varying with the configuration and the temperature, cannot be explained by the fission spectra uncertainties. Furthermore, compared to the observed discrepancies between the calculations and experiments, of the order of ~0.5 %, these uncertainties seem largely overestimated, indicating either some error compensation effects, or too-conservative covariance matrix estimations. Table 6. Fission Spectra Related Uncertainties for the KRITZ benchmarks. Impact of fission spectra uncertainty    [%] KRITZ-2.1c KRITZ-2.1h KRITZ-2.13c KRITZ-2.13h KRITZ-2.19c U235 (DOSCOV) 1.59 1.58 1.62 1.61 0.09 U235 (JENDL3.3) 4.06 4.03 4.14 4.11 0.24 U238 (JENDL3.3) 0.61 0.71 0.48 0.53 0.19 Pu239 (JENDL3.3) - - - - 3.68 Total (JENDL3.3) 4.10 4.09 4.16 4.14 3.70 ConclusionsThe impact of the uncertainties in the fission spectra was evaluated for an actinide burner Na-cooled fast reactor (ABTR) as well as for several KRITZ critical benchmark configurations. The information on the fission spectra covariance matrices was taken from the JENDL-3.3 [4,5] evaluation and the DOSCOV package [3]. Large differences were observed between the two with the uncertainties in keff as high as 1.5 – 4 %. The results show rather small differences between different reactor systems (fast, light water) and different configurations (UO2, MOX). Furthermore, compared to the observed discrepancies between the calculations and experiments for KRITZ, of the order of ~0.5 %, these uncertainties seem largely overestimated, indicating either some error compensation effects (due to cross-section adjustments involving nu-bar, absorption etc.), or too-conservative covariance matrix estimations.  Possible inconsistencies in correlation matrix were observed. References [1] Y. I. Chang, P. J. Finck, C. Grandy, “Advanced Burner Reactor Preconceptual Design Report”, ANL-ABR-1 (Argonne National Laboratory, September 2006). [2] G. Rimpault, et al., “The ERANOS Code and Data System for Fast Reactor Neutronic Analyses,” in Proc. of PHYSOR 2002 Conference, Seoul, South Korea, (October 2002). [3] R.E. Maerker, J.J. Wagschal and B.L. Broadhead, “Development and Demonstration of an Advanced Methodology for LWR Dosimetry Applications. (Section 7)”, EPRI NP-2188 (December 1981), report available in “ZZ DOSCOV, 24-Group Covariance Data Library from ENDF/B-V for Dosimetry Calculation”, DLC-0090 package of NEA Data Bank collection(http://www.nea.fr/abs/html/dlc-0090.html). [4] K. Shibata et al., JENDL-3.2 Covariance File, Proc. Nuclear Data Covariance Workshop, BNL, April 22-23, 1999, ORNL/TM-2000/19. [5] T. Kawano, K. Shibata, “Evaluation of Covariances for Resolved Resonance Parameters of 235U, 238U and 239Pu in JENDL-3.2”, JAERI-Research 2003-001, Feb. 2003. [6] I. Kodeli, Manual for ANGELO2 and LAMBDA codes, NEA-1264/05 package (2003). [7] G. Chiba: ERRORJ Manual, JNC TN9520 2003-008, Sept. 2003. [8] M. Salvatores et al., “Nuclear Data Needs for Advanced Reactor Systems. A NEA Nuclear Science Committee Initiative,” Proc. Int. Conf. ND-2007, Nice, France (April 2007). [9] I. Remec, J.C. Gehin, R.J. Ellis, "KRITZ-2 and KRITZ-1 Experiments on Regular H2O/Fuel Pin Lattices with Low Enriched Uranium Fuel at Temperatures up to 245 C", ORNL, Sept. 2000. [10] I. Kodeli, “Multidimensional Deterministic Nuclear Data Sensitivity and Uncertainty Code System, Method and Application,” Nucl. Sci. Eng., 138, 45-66 (2001). [11] I. Kodeli, Sensitivity and Uncertainty Analysis of The Kritz-2 Benchmarks, in “Benchmark on the KRITZ-2 LEU and MOX Critical Experiments, Final Report”, NEA/NSC/DOC(2005)24, OCDE 2006. 

Fission Spectrum Related Uncertainties

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Fission Spectrum Related Uncertainties

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