10.3. SCALE Nuclear Data Covariance Library
A. Holcomb, D. Wiarda, M. L. Williams, G. Arbanas, and B. L. Broadhead
ABSTRACT
An updated cross section covariance library has been created for use with the sensitivity and uncertainty modules in SCALE 6.3. The data have been assembled from a variety sources, including highfidelity covariance evaluations from ENDF/BVIII.0 as well as approximate uncertainties obtained from a collaborative project performed by Brookhaven National Laboratory, Los Alamos National Laboratory, and Oak Ridge National Laboratory. This document describes the assumptions in generating the data, the library contents, and processing procedure for the SCALE 56group and 252group covariance libraries. The ENDF/BVII.1 covariance libraries provided with SCALE 6.3 are identical to the libraries released with SCALE 6.2. The SCALE 44group covariance library distributed with SCALE 6.0 and SCALE 6.1 is retained for backwards compatibility.
ACKNOWLEDGMENT
We gratefully acknowledge the sponsorship of the US Department of Energy Nuclear Criticality Safety Program in the development of the SCALE 6.3 covariance libraries.
10.3.1. Introduction
The SCALE 6.3 covariance library suite contains covariance libraries based on ENDF/BVIII.0, ENDF/BVII.1, and preENDF/BVII.0. For each ENDF release, if uncertainty information is not available for all neutron targets, then the corresponding SCALE covariance library is patched such that each library has some estimate of the uncertainty data for every neutron target in the library. The ENDF/BVIII.0 covariance library [XSLibDAB18] contains at least some covariance data for 252 nuclides and the ENDF/BVII.1 library [COVLIBCHO+11] has data for 187 nuclides. Both the ENDF/BVIII.0 and ENDF/BVII.1 covariance libraries have been supplemented by the previous SCALE 6.1 covariance data for the ~305 nuclides missing covariance data in ENDF/BVIII.0 and ~215 nuclides missing covariance data in ENDF/BVII.1. The ENDF/BVII.1 uncertainties were modified for a few nuclides, as described in Sect. 10.3.2.3. The ENDF/BVIII.0 covariance data are available in a 56group format, and the ENDF/BVII.1 covariance library is in both a 56group and 252group format. These covariance libraries were generated for compatibility with the ENDF/BVII.1 cross section libraries distributed with SCALE 6.3, and they may also be applied for the 238group ENDF/BVII.0 library provided with SCALE 6.2. The previous SCALE 6.0 and SCALE 6.1 44group library (44groupcov) was based on older covariance data and is retained in SCALE 6.3 for backwards compatibility. However, the 56 and 252group covariance libraries (56groupcov7.1 and 252groupcov7.1) are now recommended for all applications. The 56group librarywhich is default for SCALE uncertainty analysisand the 252 finegroup library generally produce similar results, except for some threshold reactions such as (n,2n). The 252group library may be used to improve uncertainty estimates from these types of data, but it takes more execution time than the default 56group library. Because the 56 and 252group covariance data in many cases are based on newer uncertainty evaluations than the previous 44group library, some differences will occur between these sets of results.
The covariance data correspond to relative uncertainties assembled from a variety of sources, including evaluations from ENDF/BVIII.0, ENDF/BVII.1, ENDF/BVI, and approximated uncertainties from a collaborative project performed by Brookhaven National Laboratory (BNL), Los Alamos National Laboratory (LANL), and Oak Ridge National Laboratory (ORNL). Because SCALE uncertainty data come from several different sources, the application of a single generic covariance library to all multigroup cross section libraries raises questions about consistency with any given data evaluation. In reality, much of the approximate uncertainty data in the library is based on simplifying approximations that do not depend on specific ENDF evaluations and thus can be applied to all cross section libraries within the limitations of the assumed methodology. In other cases in which a covariance evaluation has been taken from a specific nuclear data file (e.g., ENDF/BVIII.,ENDF/BVII.1, ENDF/BVI, or JENDL), it is assumed that the same relative (rather than absolute) uncertainties can be applied to all cross section libraries, even if these are not strictly consistent with the nuclear data evaluations. The assumption is partially justified by the fact that different evaluations often use many of the same experimental measurements since there is a limited amount of this information available. In some cases, older data evaluations have been carried over into the newer ENDF versions. Also, because many important nuclear data are now known rather well, newer evaluations in many instances correspond to rather modest variations from previous ones and are expected to lie within the earlier uncertainties.
No inherently “true” uncertainty can be defined for nuclear data. For example, in theory, two independent evaluations could produce similar nuclear data with very different uncertainties. Differences in nuclear data evaluations directly impact calculations that can be affirmed by comparisons with benchmark experiments; but there is no established procedure to quantify the reliability of uncertainty estimates. In general, the SCALE covariance library should be viewed as a bestestimate assessment of data uncertainties based upon the specific methodology described in the following section. While this methodology is not unique and other approaches could have been used, the SCALE covariance library is a reasonable representation of the nuclear data uncertainties for most applications given the current lack of information. Furthermore, it is the only available comprehensive library that has been created in a welldefined, systematic manner.
10.3.2. Covariance Data Description
10.3.2.1. Evaluated covariances from nuclear data files
A rigorous, modern evaluation of nuclear data typically uses a regression algorithm that adjusts parameters in a nuclear physics model (e.g., ReichMoore resonance formula, optical model, etc.), to fit a set of differential experimental measurements that have various sources of statistical and systematic uncertainties [COVLIBLLD+06]. Information from the regression analysis of the model parameters can be propagated to uncertainties and correlations in the evaluated differential data. In this manner, the differential nuclear data and covariances are consistent and are coupled together by evaluation processes. Unfortunately, only a limited number of cross section evaluations have produced highfidelity covariances in this rigorous manner. All other nuclear data uncertainties must be estimated from approximations in which the uncertainty assessment is decoupled from the original evaluation procedure.
The SCALE covariance library is based on several different uncertainty approximations with varying degrees of fidelity relative to the actual nuclear data evaluation. The library includes highfidelity evaluated covariances obtained from the latest ENDF releases whenever available. As discussed in Sect. 10.3.1, it is assumed that covariances taken from one data evaluation, such as ENDF/BVII.1, can also be applied to other evaluations of the same data, such as ENDF/BVIII.0. If this is done judiciously for cases in which the nuclear data evaluations are similar, then the covariances taken from one source should be a reasonable representation of uncertainties for the other evaluations.
10.3.2.2. Approximate covariance data
At the other end of the spectrum from high fidelity data, lowfidelity (lofi) covariances are defined to be those estimated independently of a specific data evaluation. The approximate covariance data in SCALE are based on results from a collaborative project funded by the US Department of Energy Nuclear Criticality Safety Program to generate lofi covariances over the energy range from 10^{5} eV to 20 MeV for materials without covariances in ENDF/BVII.1. Nuclear data experts at BNL, LANL, and ORNL devised simple procedures to estimate data uncertainties in the absence of high fidelity covariance evaluations. The result of this project is a set of covariance data in ENDF/B file 33 format that can be processed into multigroup covariances [COVLIBLKH+08]. Some of these data were later revised and included in ENDF/BVII.1, while others were carried over from SCALE 6.1 to the SCALE 6.3 library. In this documentation, these data are known as BLO (BNLLANLORNL) uncertainty data, which were generated as described below.
ORNL used uncertainties in integral experiment measurements of thermal cross sections, resonance integrals, and potential cross sections to approximate the standard deviations of capture, fission, and elastic scattering reactions for the thermal (<0.5 eV) and resonance ranges (0.5 eV 5 keV). Full energy correlation was assumed for the covariances within each of these respective ranges [COVLIBWBDR07, COVLIBWR08] This procedure was originally introduced for the approximate uncertainty data in SCALE 5.1. However, the current version includes updated integral measurement uncertainties, using the more recent values tabulated by Mughabghab in the Atlas of Neutron Resonances [COVLIBMug06]. The lofi relative uncertainty is computed as the absolute uncertainty in the integral parameter (i.e., thermal cross section or resonance integral) taken from the Atlas, divided by the average of the measured parameter and the calculated value computed from ENDF/BVII differential data:
where:
U is the relative lofi uncertainty included in SCALE,
\(\Delta\)_{I} is the absolute uncertainty in the integral measurement (obtained from Mughabghab), and
X_{I} and X_{D} are the measured and computed (from ENDF/B differential data) integral parameter values, respectively.
In some cases the integral measurement value from the Mughabghab Atlas^{6} and the corresponding value computed from the ENDF/BVII differential evaluation are inconsistentdefined here as having a difference greater than two standard deviations in the measured and computed integral parameters. In these cases, the lofi relative standard deviation is defined as half the difference relative to the average of the measured and calculated values:
In some instances this expression may exceed 100%. For these cases, a 100% uncertainty was assigned. Also, the Atlas does not include uncertainties in integral measurements for several isotopes, which typically are not of great interest for most applications. In this case the integral uncertainty was defined as a +/5 in the least significant digit for these materials; e.g., 1.23 is assign an uncertainty of +/ 5E3.
BNL and LANL provided estimates in the fast energy range from 5 keV to 20 MeV for covariances of capture, fission, elastic, inelastic, (n,2n) cross sections, and prompt nubar. BNL used optical model calculations with estimated uncertainties in model parameters to compute covariances in the fast range for about 300 structural isotopes, fission products, and nonfissionable heavy nuclei. Estimated uncertainties in model parameters were based on previous work and expert judgment [COVLIBPHO09]. Covariances for 14 actinide isotopes were obtained from earlier work performed by BNL for Subgroup26 (SG26) [COVLIBRHOM07]. The SG26 actinide covariances cover the full energy range, including thermal, resonance, and fast regions. If the thermal data uncertainties estimated by the SG26 approach exceed the thermal uncertainty given in reference 6, the thermal data covariances are represented by ORNL’s integral uncertainty technique.
LANL produced covariances in the fast range for an additional 47 actinide materials. The LANL actinide covariances were based on empirical estimates of nuclear reaction models [COVLIBKTY+08]. Full energy range covariances were also produced by LANL for 16 light isotopes ranging from hydrogen to fluorine [COVLIBHal08]. These included high fidelity covariances from Rmatrix analyses for ^{1}H, ^{6}Li, and ^{10}B, along with lofi uncertainties for the other materials, based on approximations such as leastsquares fitting to experimental data, statistical model calculations at higher energies, or sometimes simply bestjudgment estimation [COVLIBLKH+08].
10.3.2.3. Modifications to covariance data
In generating earlier covariance libraries, some omissions or inconsistencies were identified and corrected in the current covariance library:
If the absolute correlation is larger than 1, it is set to 1.
If a relative uncertainty is larger than 1, it is set to 1.
If cross section data exist but covariance data do not span the entire range, then the diagonal element for the higher energy groups is repeated for the lower energy groups.
If total inelastic scattering covariance is not supplied, it is calculated from the uncertainties in the discrete level inelastic data.
If total nubar covariance is not supplied, it is calculated from the the prompt and delayed nubar uncertainties
A few inconsistencies were found in the ENDF/BVII.1 uncertainty data, and these were modified for the SCALE 6.3 covariance library [COVLIBWIMR14]. The corrections were also conveyed to the National Nuclear Data Center, where they were added to the ENDF/A file for possible inclusion in the future release of ENDF/BVIII.1. These modifications are summarized below:
^{235}U thermal nubar: standard deviation was decreased from 0.7% to 0.3% in energy range from 0.0 to 0.5 eV, consistent with JENDL3.3.
^{239}Pu thermal nubar: standard deviation was increased from 0.01% to 0.15% in energy range from 0.0 to 0.01 eV, consistent with ENDF/BVII.1 uncertainty at 0.01 eV.
H thermal capture: standard deviation reduced from 2.5% to 0.2%, consistent with Williams and Rearden 2008 [COVLIBWR08],
(d) ^{103}Rh thermal capture: reduced from ~4% to 1.04%, consistent with Williams and Rearden 2008 [COVLIBWR08].
(e) ^{151}Sm thermal capture: modified to ~1.8%, consistent with Williams and Rearden 2008 [COVLIBWR08].
(f) ^{147}Pm: standard deviation was reduced from 24% to 5% in the energy range 0.5–5000 eV, consistent with the quoted resonance integral uncertainty in Williams and Rearden 2008 [COVLIBWR08].
Several modifications were also made to the uncertainties obtained from the original BLO data used in SCALE 6.1. The energy boundary between the thermal and resonance covariance blocks was modified from 0.5 to 0.625 eV in order to coincide with a 56group boundary. The BLO lofi data do not include thermal or resonance range uncertainties for isotope reactions that do not have integral uncertainties given in the Mughabghab text [COVLIBMug06]. These occur mainly for relatively unimportant data such as elastic cross sections of several fission products. Therefore in these cases the uncertainties were estimated using different approaches. For example, the thermal data uncertainty was sometimes used to represent the epithermal uncertainty if it was not available in the Mughabghab tabulation, and sometimes the highenergy uncertainty was extended to lower energies. The uncertainty in the ^{149}Sm resonance capture integral is not provided in the 2006 edition of Mughabghab’s text, so it was set to the value of 5.7%, which was obtained from an earlier tabulation by Mughabghab [COVLIBMug03].
10.3.2.4. Covariance data for fission spectra
As of ENDF/BVII.1, covariance matrices are now provided for the fission exit energy distribution. The data are given as a function of incident energy. The incident energy grid is very broad, and the exit energy distribution is constant over a given incident energy group. Since the COVERX library file only allows one multigroup fission spectrum (\(\chi\)) covariance matrix per nuclide, the exit energy spectrum is used for the average energy of fission. If \(\nu\) is nubar, f is fission, and w is the appropriate flux, then the average energy of fission is calculated as:
where the sum is over all groups and E_{g1} and E_{g2} are the group boundaries for group g. ENDF/BVII.1 provides covariance data for exit energy distributions for 64 nuclides. This includes all nuclides for which fission spectrum (\(\chi\)) covariance matrices where provided in the previous covariance library. Some additional \(\chi\)covariance matrices were taken from JENDL4.0. The new 56group and 252group fission spectrum covariances are more complete and significantly improved compared to the earlier 44group chi uncertainty data, which were based on the Watt fission spectrum in ENDF/BV. (see Sect. 10.3.5).
10.3.3. Multigroup Covariance Processing
Covariance data were processed with the AMPX code PUFFIV [COVLIBWD06]. PUFFIV has major improvements in the treatment of the resolved and unresolved resonance parameter uncertainties over previous code versions [COVLIBWALD08]. All nuclides with resonance parameter uncertainty files were processed with the full sensitivity option in PUFFIV.
10.3.4. Contents of the SCALE 6.3 Covariance Library
The SCALE covariance library provides uncertainty data in 56 and 252group formats for a total of 456 materials in ENDF/BVII.1 and 587 materials in ENDF/BVIII.0, including some duplication for materials with multiple thermal scattering kernels. Table 10.3.1 describes the contents of the library using the following nomenclature:
ENDF/BVII.1: evaluated covariance data released with ENDF/BVII.1
ENDF/BVII.2prelim: recently evaluated data proposed for future release of ENDF/BVII.2
ENDF/BVI: evaluated covariance data released with ENDF/BVI
BLO approximate data: lofi covariances from BLO project
SG26: approximate covariances from WPEC Subgroup26
JENDL4.0: evaluated covariance data released with JENDL4.0
Several covariance evaluations include cross correlations between reactions. These are summarized in Table 10.3.2.
SCALE name 
SCALE ID 
Data source 
Comment 

ac225 
89225 
ENDF/BVII.1 

ac226 
89226 
ENDF/BVII.1 

ac227 
89227 
ENDF/BVII.1 

ag107 
47107 
BLO approximation data 

ag109 
47109 
ENDF/BVII.1 

ag110m 
1047110 
BLO approximation data 

ag111 
47111 
BLO approximation data 

al27 
13027 
ENDF/BVII.1 

albound 
1013027 
ENDF/BVII.1 
Duplicate of al27 
am240 
95240 
ENDF/BVII.1 

am241 
95241 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

am242 
95242 
SG26 \(\chi\) covariance JENDL4.0 
Thermal uncertainty replaced by Mughabghab value 
am242m 
1095242 
ENDF/BVII.1 

am243 
95243 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

am244 
95244 
BLO approximation data \(\chi\) covariance JENDL4.0 

am244m 
1095244 
BLO approximation data 

ar36 
18036 
BLO approximation data 

ar38 
18038 
BLO approximation data 

ar40 
18040 
BLO approximation data 

as74 
33074 
BLO approximation data 

as75 
33075 
BLO approximation data 

au197 
79197 
ENDF/BVII.1 

b10 
5010 
ENDF/BVII.1 

b11 
5011 
ENDF/BVII.1 

ba130 
56130 
BLO approximation data 

ba132 
56132 
BLO approximation data 

ba133 
56133 
BLO approximation data 

ba134 
56134 
BLO approximation data 

ba135 
56135 
BLO approximation data 

ba136 
56136 
BLO approximation data 

ba137 
56137 
BLO approximation data 

ba138 
56138 
BLO approximation data 

ba140 
56140 
BLO approximation data 

be7 
4007 
BLO approximation data 

be9 
4009 
ENDF/BVII.1 

bebeo 
5004009 
ENDF/BVII.1 
Duplicate of be9 
bebound 
3004009 
ENDF/BVII.1 
Duplicate of be9 
bi209 
83209 
ENDF/BVII.1 

bk245 
97245 
ENDF/BVII.1 

bk246 
97246 
ENDF/BVII.1 

bk247 
97247 
ENDF/BVII.1 

bk248 
97248 
ENDF/BVII.1 

bk249 
97249 
ENDF/BVII.1 

bk250 
97250 
ENDF/BVII.1 

br79 
35079 
BLO approximation data 

br81 
35081 
BLO approximation data 

c 
6000 
ENDF/BVII.1 

ca 
20000 
BLO approximation dataca 

ca40 
20040 
BLO approximation data 

ca42 
20042 
BLO approximation data 

ca43 
20043 
BLO approximation data 

ca44 
20044 
BLO approximation data 

ca46 
20046 
BLO approximation data 

ca48 
20048 
BLO approximation data 

cd 
48000 
BLO approximation data 

cd106 
48106 
BLO approximation data 

cd108 
48108 
BLO approximation data 

cd110 
48110 
BLO approximation data 

cd111 
48111 
BLO approximation data 

cd112 
48112 
BLO approximation data 

cd113 
48113 
BLO approximation data 

cd114 
48114 
BLO approximation data 

cd115m 
1048115 
BLO approximation data 

cd116 
48116 
BLO approximation data 

ce136 
58136 
BLO approximation data 

ce138 
58138 
BLO approximation data 

ce139 
58139 
BLO approximation data 

ce140 
58140 
BLO approximation data 

ce141 
58141 
ENDF/BVII.1 

ce142 
58142 
BLO approximation data 

ce143 
58143 
BLO approximation data 

ce144 
58144 
BLO approximation data 

cf246 
98246 
ENDF/BVII.1 

cf248 
98248 
ENDF/BVII.1 

cf249 
98249 
ENDF/BVII.1 

cf250 
98250 
ENDF/BVII.1 

cf251 
98251 
ENDF/BVII.1 

cf252 
98252 
ENDF/BVII.1 

cf253 
98253 
ENDF/BVII.1 

cf254 
98254 
ENDF/BVII.1 

cl 
17000 
BLO approximation data 

cl35 
17035 
ENDF/BVII.1 

cl37 
17037 
ENDF/BVII.1 

cm240 
96240 
ENDF/BVII.1 

cm241 
96241 
ENDF/BVII.1 

cm242 
96242 
ENDF/BVII.1 

cm243 
96243 
ENDF/BVII.1 

cm244 
96244 
ENDF/BVII.1 

cm245 
96245 
ENDF/BVII.1 

cm246 
96246 
ENDF/BVII.1 

cm247 
96247 
ENDF/BVII.1 

cm248 
96248 
ENDF/BVII.1 

cm249 
96249 
ENDF/BVII.1 

cm250 
96250 
ENDF/BVII.1 

co58 
27058 
BLO approximation data 

co58m 
1027058 
BLO approximation data 

co59 
27059 
ENDF/BVII.1 

cr50 
24050 
ENDF/BVII.1 

cr52 
24052 
ENDF/BVII.1 

cr53 
24053 
ENDF/BVII.1 

cr54 
24054 
ENDF/BVII.1 

cs133 
55133 
ENDF/BVII.1 

cs134 
55134 
BLO approximation data 

cs135 
55135 
ENDF/BVII.1 

cs136 
55136 
BLO approximation data 

cs137 
55137 
BLO approximation data 

cu63 
29063 
ENDF/BVI 

cu65 
29065 
ENDF/BVI 

d 
1002 
ENDF/BVII.1 
Duplicate of h2 
dcryo_ortho 
4001002 
ENDF/BVII.1 
Duplicate of h2 
dcryo_para 
5001002 
ENDF/BVII.1 
Duplicate of h2 
dfreegas 
8001002 
ENDF/BVII.1 

dy156 
66156 
BLO approximation data 

dy158 
66158 
BLO approximation data 

dy160 
66160 
BLO approximation data 

dy161 
66161 
BLO approximation data 

dy162 
66162 
BLO approximation data 

dy163 
66163 
BLO approximation data 

dy164 
66164 
BLO approximation data 

er162 
68162 
BLO approximation data 

er164 
68164 
BLO approximation data 

er166 
68166 
ENDF/BVII.1 

er167 
68167 
ENDF/BVII.1 

er168 
68168 
ENDF/BVII.1 

er170 
68170 
ENDF/BVII.1 

es251 
99251 
ENDF/BVII.1 

es252 
99252 
ENDF/BVII.1 

es253 
99253 
ENDF/BVII.1 

es254 
99254 
ENDF/BVII.1 

es254m 
1099254 
ENDF/BVII.1 

es255 
99255 
ENDF/BVII.1 

eu151 
63151 
BLO approximation data 

eu152 
63152 
BLO approximation data 

eu153 
63153 
ENDF/BVII.1 

eu154 
63154 
BLO approximation data 

eu155 
63155 
ENDF/BVII.1 
Uses ENDF/BVII.1 data uncertainty in the thermal range for MT=102 
eu156 
63156 
BLO approximation data 

eu157 
63157 
BLO approximation data 

f19 
9019 
ENDF/BVII.1 

fe54 
26054 
ENDF/BVII.1 

fe56 
26056 
ENDF/BVII.1 

fe57 
26057 
ENDF/BVII.1 

fe58 
26058 
ENDF/BVI 

febound 
1026000 
ENDF/BVII.1 
Duplicate of fe56 
fm255 
100255 
ENDF/BVII.1 

ga 
31000 
BLO approximation data 

ga69 
31069 
BLO approximation data 

ga71 
31071 
BLO approximation data 

gd152 
64152 
ENDF/BVII.1 

gd153 
64153 
ENDF/BVII.1 

gd154 
64154 
ENDF/BVII.1 

gd155 
64155 
ENDF/BVII.1 

gd156 
64156 
ENDF/BVII.1 

gd157 
64157 
ENDF/BVII.1 

gd158 
64158 
ENDF/BVII.1 

gd160 
64160 
ENDF/BVII.1 

ge70 
32070 
BLO approximation data 

ge72 
32072 
BLO approximation data 

ge73 
32073 
BLO approximation data 

ge74 
32074 
BLO approximation data 

ge76 
32076 
BLO approximation data 

graphite 
3006000 
ENDF/BVII.1 
Duplicate of c 
h 
1001 
ENDF/BVII.2 prelim 
Duplicate of h1 
h3 
1003 
BLO approximation data 

hbenzene 
6001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hbenzene 
5006000 
ENDF/BVII.1 
Duplicate of c 
hcryo_ortho 
4001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hcryo_para 
5001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hliquid_ch4 
1001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hpoly 
9001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hsolid_ch4 
2001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
hzrh2 
7001001 
ENDF/BVII.2 prelim 
Duplicate of h1 
he3 
2003 
BLO approximation data 

he4 
2004 
ENDF/BVII.1 

hf 
72000 
BLO approximation data 

hf174 
72174 
BLO approximation data 

hf176 
72176 
BLO approximation data 

hf177 
72177 
BLO approximation data 

hf178 
72178 
BLO approximation data 

hf179 
72179 
BLO approximation data 

hf180 
72180 
BLO approximation data 

hfreegas 
8001001 
ENDF/BVII.2 prelim 

hg196 
80196 
BLO approximation data 

hg198 
80198 
BLO approximation data 

hg199 
80199 
BLO approximation data 

hg200 
80200 
BLO approximation data 

hg201 
80201 
BLO approximation data 

hg202 
80202 
BLO approximation data 

hg204 
80204 
BLO approximation data 

ho165 
67165 
BLO approximation data 

ho166m 
1067166 
BLO approximation data 

i127 
53127 
ENDF/BVII.1 

i129 
53129 
ENDF/BVII.1 

i130 
53130 
BLO approximation data 

i131 
53131 
BLO approximation data 

i135 
53135 
BLO approximation data 

in 
49000 
ENDF/BVI 

in113 
49113 
BLO approximation data 

in115 
49115 
BLO approximation data 

ir191 
77191 
ENDF/BVII.1 

ir193 
77193 
ENDF/BVII.1 

k 
19000 
BLO approximation data 

k39 
19039 
ENDF/BVII.1 

k40 
19040 
BLO approximation data 

k41 
19041 
ENDF/BVII.1 

kr78 
36078 
BLO approximation data 

kr80 
36080 
BLO approximation data 

kr82 
36082 
BLO approximation data 

kr83 
36083 
BLO approximation data 

kr84 
36084 
BLO approximation data 

kr85 
36085 
BLO approximation data 

kr86 
36086 
BLO approximation data 

la138 
57138 
BLO approximation data 

la139 
57139 
ENDF/BVII.1 

la140 
57140 
BLO approximation data 

li6 
3006 
ENDF/BVII.1 

li7 
3007 
ENDF/BVII.1 

lu175 
71175 
BLO approximation data 

lu176 
71176 
BLO approximation data 

mg 
12000 
BLO approximation data 

mg24 
12024 
ENDF/BVII.1 

mg25 
12025 
ENDF/BVII.1 

mg26 
12026 
ENDF/BVII.1 

mn55 
25055 
ENDF/BVII.1 

mo 
42000 
BLO approximation data 

mo100 
42100 
ENDF/BVII.1 

mo92 
42092 
ENDF/BVII.1 

mo94 
42094 
ENDF/BVII.1 

mo95 
42095 
ENDF/BVII.1 

mo96 
42096 
ENDF/BVII.1 

mo97 
42097 
ENDF/BVII.1 

mo98 
42098 
ENDF/BVII.1 

mo99 
42099 
BLO approximation data 

n14 
7014 
BLO approximation data 

n15 
7015 
ENDF/BVII.1 

na23 
11023 
ENDF/BVII.1 

nb93 
41093 
ENDF/BVI 

nb94 
41094 
BLO approximation data 

nb95 
41095 
ENDF/BVII.1 

nd142 
60142 
BLO approximation data 

nd143 
60143 
ENDF/BVII.1 

nd144 
60144 
BLO approximation data 

nd145 
60145 
ENDF/BVII.1 

nd146 
60146 
ENDF/BVII.1 

nd147 
60147 
BLO approximation data 

nd148 
60148 
ENDF/BVII.1 

nd148 
60148 
BLO approximation data 

nd150 
60150 
BLO approximation data 

ni58 
28058 
ENDF/BVII.1 

ni59 
28059 
BLO approximation data 

ni60 
28060 
ENDF/BVII.1 

ni61 
28061 
ENDF/BVI 

ni62 
28062 
ENDF/BVI 

ni64 
28064 
ENDF/BVI 

np234 
93234 
ENDF/BVII.1 

np235 
93235 
ENDF/BVII.1 

np236 
93236 
ENDF/BVII.1 

np237 
93237 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

np238 
93238 
ENDF/BVII.1 

np239 
93239 
ENDF/BVII.1 

o16 
8016 
ENDF/BVII.1 

o17 
8017 
BLO approximation data 

obeo 
5008016 
ENDF/BVII.1 
Duplicate of o16 
ouo2 
1008016 
ENDF/BVII.1 
Duplicate of o16 
p31 
15031 
BLO approximation data 

pa229 
91229 
ENDF/BVII.1 

pa230 
91230 
ENDF/BVII.1 

pa231 
91231 
BLO approximation data \(\chi\) covariance JENDL4.0 

pa232 
91232 
ENDF/BVII.1 

pa233 
91233 
BLO approximation data \(\chi\) covariance JENDL4.0 

pb204 
82204 
ENDF/BVII.1 

pb206 
82206 
ENDF/BVII.1 

pb207 
82207 
ENDF/BVII.1 

pb208 
82208 
ENDF/BVII.1 

pd102 
46102 
BLO approximation data 

pd104 
46104 
BLO approximation data 

pd105 
46105 
ENDF/BVII.1 

pd106 
46106 
ENDF/BVII.1 

pd107 
46107 
ENDF/BVII.1 

pd108 
46108 
ENDF/BVII.1 

pd110 
46110 
BLO approximation data 

pm147 
61147 
ENDF/BVII.1 
Thermal and resonance range uncertainty values from Mughabghab 
pm148 
61148 
BLO approximation data 

pm148m 
1061148 
BLO approximation data 

pm149 
61149 
BLO approximation data 

pm151 
61151 
BLO approximation data 

pr141 
59141 
ENDF/BVII.1 

pr142 
59142 
BLO approximation data 

pr143 
59143 
BLO approximation data 

pu236 
94236 
ENDF/BVII.1 

pu237 
94237 
ENDF/BVII.1 

pu238 
94238 
ENDF/BVII.1 

pu239 
94239 
ENDF/BVII.2 prelim 

pu240 
94240 
ENDF/BVII.1 

pu241 
94241 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

pu242 
94242 
ENDF/BVII.1 

pu243 
94243 
BLO approximation data 

pu244 
94244 
ENDF/BVII.1 

pu246 
94246 
ENDF/BVII.1 

rb85 
37085 
BLO approximation data 

rb86 
37086 
BLO approximation data 

rb87 
37087 
BLO approximation data 

re185 
75185 
ENDF/BVI 

re187 
75187 
ENDF/BVI 

rh103 
45103 
ENDF/BVII.1 
Uses ENDF/BVII.1 data uncertainty in the thermal range for MT=102 
rh105 
45105 
BLO approximation data 

ru100 
44100 
BLO approximation data 

ru101 
44101 
ENDF/BVII.1 

ru102 
44102 
ENDF/BVII.1 

ru103 
44103 
ENDF/BVII.1 

ru104 
44104 
ENDF/BVII.1 

ru105 
44105 
BLO approximation data 

ru106 
44106 
ENDF/BVII.1 

ru96 
44096 
BLO approximation data 

ru98 
44098 
BLO approximation data 

ru99 
44099 
BLO approximation data 

s 
16000 
BLO approximation data 

s32 
16032 
BLO approximation data 

s33 
16033 
BLO approximation data 

s34 
16034 
BLO approximation data 

s36 
16036 
BLO approximation data 

sb121 
51121 
BLO approximation data 

sb123 
51123 
BLO approximation data 

sb124 
51124 
BLO approximation data 

sb125 
51125 
BLO approximation data 

sb126 
51126 
BLO approximation data 

sc45 
21045 
ENDF/BVI 

se74 
34074 
BLO approximation data 

se76 
34076 
BLO approximation data 

se77 
34077 
BLO approximation data 

se78 
34078 
BLO approximation data 

se79 
34079 
BLO approximation data 

se80 
34080 
BLO approximation data 

se82 
34082 
BLO approximation data 

si 
14000 
ENDF/BVI 

si28 
14028 
ENDF/BVII.1 

si29 
14029 
ENDF/BVII.1 

si30 
14030 
ENDF/BVII.1 

si28 in SiO_{2} 
14728 
ENDF/BVII.1 
Duplicate of si28 
si29 in SiO_{2} 
14729 
ENDF/B0VII.1 
Duplicate of si29 
si30 in SiO_{2} 
14730 
ENDF/BVII.1 
Duplicate of si30 
sm144 
62144 
BLO approximation data 

sm147 
62147 
BLO approximation data 

sm148 
62148 
BLO approximation data 

sm149 
62149 
ENDF/BVII.1 
Uses ENDF/BVII.1 data uncertainty in the thermal range for MT=102 
sm149 
62149 
BLO approximation data 

sm150 
62150 
BLO approximation data 

sm151 
62151 
ENDF/BVII.1 
Uses ENDF/BVII.1 data uncertainty in the thermal range for MT=102 
sm152 
62152 
ENDF/BVII.1 

sm153 
62153 
BLO approximation data 

sm154 
62154 
BLO approximation data 

sn112 
50112 
BLO approximation data 

sn113 
50113 
BLO approximation data 

sn114 
50114 
BLO approximation data 

sn115 
50115 
BLO approximation data 

sn116 
50116 
BLO approximation data 

sn117 
50117 
BLO approximation data 

sn118 
50118 
BLO approximation data 

sn119 
50119 
BLO approximation data 

sn120 
50120 
BLO approximation data 

sn122 
50122 
BLO approximation data 

sn123 
50123 
BLO approximation data 

sn124 
50124 
BLO approximation data 

sn125 
50125 
BLO approximation data 

sn126 
50126 
BLO approximation data 

sr84 
38084 
BLO approximation data 

sr86 
38086 
BLO approximation data 

sr87 
38087 
BLO approximation data 

sr88 
38088 
BLO approximation data 

sr89 
38089 
BLO approximation data 

sr90 
38090 
BLO approximation data 

ta181 
73181 
BLO approximation data 

ta182 
73182 
BLO approximation data 

tb159 
65159 
BLO approximation data 

tb160 
65160 
BLO approximation data 

tc99 
43099 
ENDF/BVII.1 

te120 
52120 
BLO approximation data 

te122 
52122 
BLO approximation data 

te123 
52123 
BLO approximation data 

te124 
52124 
BLO approximation data 

te125 
52125 
BLO approximation data 

te126 
52126 
BLO approximation data 

te127m 
1052127 
BLO approximation data 

te128 
52128 
BLO approximation data 

te129m 
1052129 
BLO approximation data 

te130 
52130 
BLO approximation data 

te132 
52132 
BLO approximation data 

th227 
90227 
ENDF/BVII.1 

th228 
90228 
ENDF/BVII.1 

th229 
90229 
ENDF/BVII.1 

th230 
90230 
ENDF/BVII.1 

th231 
90231 
ENDF/BVII.1 

th232 
90232 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

th233 
90233 
ENDF/BVII.1 

th234 
90234 
ENDF/BVII.1 

ti 
22000 
BLO approximation data 

ti46 
22046 
ENDF/BVII.1 

ti47 
22047 
ENDF/BVII.1 

ti48 
22048 
ENDF/BVII.1 

ti49 
22049 
ENDF/BVII.1 

ti50 
22050 
ENDF/BVII.1 

tl203 
81203 
ENDF/BVII.1 

tl205 
81205 
ENDF/BVII.1 

tm169 
69169 
ENDF/BVII.1 

tm170 
69170 
ENDF/BVII.1 

u230 
92230 
ENDF/BVII.1 

u231 
92231 
ENDF/BVII.1 

u232 
92232 
ENDF/BVII.1 

u233 
92233 
ENDF/BVII.1 \(\chi\) covariance JENDL4.0 

u234 
92234 
ENDF/BVII.1 

u235 
92235 
ENDF/BVII.2 prelim 

u236 
92236 
ENDF/BVII.1 

u237 
92237 
BLO approximation data 

u238 
92238 
ENDF/BVII.1 

u239 
92239 
BLO approximation data 

u240 
92240 
BLO approximation data 

u241 
92241 
BLO approximation data 

uuo2 
1092235 
ENDF/BVII.1 
Duplicate of u235 
v 
23000 
BLO approximation data 

v50 
23050 
BLO approximation data 
Duplicate of v 
v51 
23051 
BLO approximation data 
Duplicate of v 
w 
74000 
BLO approximation data 

w180 
74180 
ENDF/BVII.1 

w182 
74182 
ENDF/BVII.1 

w183 
74183 
ENDF/BVII.1 

w184 
74184 
ENDF/BVII.1 

w186 
74186 
ENDF/BVII.1 

xe123 
54123 
BLO approximation data 

xe124 
54124 
BLO approximation data 

xe126 
54126 
BLO approximation data 

xe128 
54128 
BLO approximation data 

xe129 
54129 
BLO approximation data 

xe130 
54130 
BLO approximation data 

xe131 
54131 
ENDF/BVII.1 

xe132 
54132 
ENDF/BVII.1 

xe133 
54133 
BLO approximation data 

xe134 
54134 
ENDF/BVII.1 

xe135 
54135 
BLO approximation data 

xe136 
54136 
BLO approximation data 

y89 
39089 
ENDF/BVII.1 

y90 
39090 
BLO approximation data 

y91 
39091 
BLO approximation data 

zr 
40000 
BLO approximation data 

zr90 
40090 
ENDF/BVII.1 

zr91 
40091 
ENDF/BVII.1 

zr92 
40092 
ENDF/BVII.1 

zr93 
40093 
ENDF/BVII.1 

zr94 
40094 
ENDF/BVII.1 

zr95 
40095 
ENDF/BVII.1 

zr96 
40096 
ENDF/BVII.1 

zr90zr5h8 
1040090 
ENDF/BVII.1 
Duplicate of zr90 
zr91zr5h8 
1040091 
ENDF/BVII.1 
Duplicate of zr91 
zr92zr5h8 
1040092 
ENDF/BVII.1 
Duplicate of zr92 
zr93zr5h8 
1040093 
ENDF/BVII.1 
Duplicate of zr93 
zr94zr5h8 
1040094 
ENDF/BVII.1 
Duplicate of zr94 
zr95zr5h8 
1040095 
ENDF/BVII.1 
Duplicate of zr95 
zr96zr5h8 
1040096 
ENDF/BVII.1 
Duplicate of zr96 
Nuclide 1 
Reaction 1 
Nuclide 2 
Reaction 2 

^{239}Pu 
Fission 
^{6}Li 
Triton production 
^{239}Pu 
Fission 
^{197}Au 
Capture 
^{239}Pu 
Fission 
^{235}U 
Fission 
^{239}Pu 
Fission 
^{238}U 
Fission 
^{235}U 
Fission 
^{197}Au 
Capture 
^{235}U 
Fission 
^{6}Li 
Triton production 
^{238}U 
Capture 
^{197}Au 
Capture 
^{238}U 
Capture 
^{235}U 
Fission 
10.3.5. SCALE 6.1 44group covariance library
The older 44group covariance library distributed with SCALE 6.0 and SCALE 6.1 is included with this distribution for backwards compatibility. The 44group covariance library provides uncertainty data for a total of 401 materials, including some duplication for materials with multiple thermal scattering kernels. However, the 44group library was created prior to the official release of ENDF/BVII.1. Therefore, it is recommended that the 56 or 252group covariances be used rather than the 44group. As discussed in Sect. 10.3.1, it is assumed that covariances taken from one data evaluation such as ENDF/BVI or JENDL3.3 can also be applied to other evaluations of the same data, such as ENDF/BVII. If this is done judiciously for cases in which the nuclear data evaluations are similar, then the covariances taken from one source should be a reasonable representation of uncertainties for the other evaluations. Among the materials in the SCALE 44group library with covariances taken from highfidelity nuclear data evaluations are the following:
a) ENDF/BVII evaluations (includes both VII.0 and prerelease covariances proposed for VII.1, but no official ENDF/BVII.1):
Au, ^{209}Bi, ^{59}Co, ^{152,154,155,156}Gd, ^{191,193}I, ^{7}Li, ^{23}Na, ^{93}Nb, ^{58}Ni, ^{99}Tc,^{232}Th, ^{48}Ti, ^{239}Pu, ^{233,235,238}U,V
ENDF/BVI evaluations:
Al, ^{241}Am, ^{10}B, ^{12}C, ^{50,52,53,54}Cr, ^{63,65}Cu, ^{54,56,57}Fe, In, ^{55}Mn, ^{60,61,62,64}Ni, ^{206,207,208}Pb, ^{242}Pu, ^{28,29}Si
JENDL3.3 evaluations:
^{11}B, ^{1}H, ^{16}O, ^{240,241}Pu
Two modifications were also made to the ENDF/BVII evaluated nubar covariances. These nubar uncertainties are believed to be more realistic. The ENDF/BVII.0 ^{235}U thermal nubar uncertainty of 0.71% was revised to the JENDL3.3 value of 0.31%. In addition, the thermal nubar certainty in the prereleased ENDF/BVII.1 ^{233}U evaluation was modified to the value in a recent ORNL data evaluation [COVLIBLWRD08]. This ORNL ^{233}U cross section evaluation also provided the thermal and resonance cross sections for the prereleased ENDF/BVII.1 data. The ENDF/BVII.1 prerelease nubar data for ^{239}Pu was incomplete when the 44group covariance library was generated, so ^{239}Pu nubar data are included from ENDF/BV, the most current data available at that time. This value is much higher than the current estimated uncertainty in ^{239}Pu nubar. The basic ENDF/B uncertainty files that were changed are described in Table 10.3.3.
Several modifications were also made to the uncertainties obtained from the BLO data. The BLO thermal uncertainties for ^{1}H capture and elastic and for ^{16}O elastic were modified to the JENDL3.3 values of 0.5% and 0.1%, respectively. Similarly, the uncertainty in the ^{10}B (n,alpha) thermal cross section was modified to the ENDF/BVI value of about 0.2%, since this is more consistent with the Mughabghab integral uncertainty. The uncertainty in the ^{149}Sm resonance capture integral is not provided in the 2006 edition of Mughabghab’s text; therefore it was set to the value of 5.7% which was obtained from an earlier tabulation by Mughabghab [COVLIBMug03].
ENDF/BVII.1 prerelease ^{239}Pu 
Data were incomplete at time of library generation, so ENDF/BV data were used for nubar. 

ENDF/BVII ^{235}U 
Thermal nubar modified to JENDL3.3 value 
ENDF/BVII ^{233}U 
Thermal nubar modified to value from ORNL internal evaluation 
ENDF/BVI ^{241}Am 
Thermal uncertainties were added to total cross section (set equal to capture uncertainties) 
ENDF/BVI ^{28}Si, ^{29}Si, ^{30}Si, ^{206}Pb, ^{57}Fe 
In elastic scatter uncertainty, corrected cross reference to MT=102 from original value of MT=1.02 
ENDF/BVI ^{208}Pb, ^{207}Pb 
Removed MT=3 due to inconsistency with other MT values, resulting in very large uncertainty predictions 
At the time of the preparation of the 44group covariance library, ENDF/B did not provide fission spectra uncertainty estimates. The methodology used to construct these data for the 44group covariance library is described in Broadhead and Wagschal [COVLIBBW04]. In this approach, the fission spectrum is represented as either a Watt or Maxwellian distribution. These energy distributions are widely used to represent fission spectra and have been commonly employed in many ENDF/B evaluations. For example, Watt and Maxwellian expressions were used almost exclusively to describe fission spectra in ENDF/BV and also for many ENDF/BVI evaluations. More recent evaluations for some important fissionable nuclides have replaced the simple Watt and Maxwellian analytical expressions by distributions such as the MadlandNix spectrum obtained from more phenomenological nuclear fission models. However, it is assumed here that uncertainties based on an appropriate Watt or Maxwellian representation of the fission spectrum can be transferred to the actual fission spectra contained in the different multigroup cross section libraries.
The methodology in Broadhead and Wagschal [COVLIBBW04] determines energydependent covariances from uncertainties and correlations in the a and b parameters for the Watt spectrum or the T parameter for a Maxwellian spectrum, appearing the analytical expressions given below:
Watt Spectrum: \(\chi(\mathrm{E})=\frac{\mathrm{e}^{\mathrm{E} / \mathrm{a}}}{\mathrm{I}} \sinh (\sqrt{\mathrm{bE}})\)
Maxwellian Spectrum: \(\chi(\mathrm{E})=\frac{\sqrt{\mathrm{E}} \mathrm{e}^{\mathrm{E} / \mathrm{T}}}{\mathrm{I}}\)
In these expressions, the parameter “I” is the normalization factor required to normalize the integrated spectrum to unity. The value of “I” is fixed by the values of the other parameters. Due to the normalization constraint, the fission spectrum covariance includes anticorrelations. The assumed fission spectra parameters and uncertainties are given in Maerker, Marable, and Wagschal 1980 [COVLIBMMW80] and in Howerton and Doyas 1971 [COVLIBHD71].
Table 10.3.4 shows that fission spectra covariances are not provided for all fissionable materials in the SCALE multigroup cross sections. Table 10.3.5 lists the fissionable nuclides without fission spectra covariances on the 44group covariance library.
Watt spectrum 
a or T 
b 
Source of parameters 
\(\sigma_a\) or \(\sigma_T\) (%) 
\(\sigma_b\) (%) 
Source of uncertainty 

^{235}U 
0.988 
2.249 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
^{238}U 
0.881 
3.401 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
^{233}U 
0.977 
2.546 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
^{239}Pu 
0.966 
2.842 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
^{232}Th 
1.0888 
1.6871 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
^{252}Cf 
1.025 
2.926 
ENDF/BV 
1.2 
5.9 
TANS^{16} 
Maxwellian Spectrum 

^{238}Pu 
1.330 
 
ENDF/BV 
3.01 
 
NSE^{17} 
^{240}Pu 
1.346 
 
ENDF/BV 
2.97 
 
NSE^{17} 
^{241}Pu 
1.3597 
 
ENDF/BV 
2.50 
 
NSE^{17} 
^{242}Pu 
1.337 
 
ENDF/BV 
5.24 
 
NSE^{17} 
^{241}Am 
^{244}Cm 
^{238}Pu 

^{242}Am 
^{245}Cm 
^{243}Pu 
^{243}Am 
^{246}Cm 
^{244}Pu 
^{249}Bk 
^{247}Cm 
^{230}Th 
^{249}Cf 
^{248}Cm 
^{232}U 
^{250}Cf 
^{237}Np 
^{234}U 
^{251}Cf 
^{238}Np 
^{236}U 
^{253}Cf 
^{239}Np 
^{237}U 
^{242}Cm 
^{231}Pa 

^{243}Cm 
^{233}Pa 
Table 10.3.6 describes the contents of the library using the following nomenclature:
ENDF/BVII.0: evaluated covariance data released with ENDF/BVII.0
ENDF/BVIIp: recently evaluated data proposed for future release of ENDF/BVII.1
ENDF/BVI: evaluated covariance data released with ENDF/BVI
JENDL3.3: evaluated covariance data in JENDL3.3
BLO approximate data: lofi covariances from BLO project
BLO LANL evaluation: LANL Rmatrix evaluation from BLO project
SG26: approximate covariances from WPEC Subgroup26
SCALE name 
Data source 
Comments 
ac225 
BLO approximate data 

ac226 
BLO approximate data 

ac227 
BLO approximate data 

ag107 
BLO approximate data 

ag109 
BLO approximate data 

ag110m 
BLO approximate data 

ag111 
BLO approximate data 

al27 
ENDF/BVI 

am241 
ENDF/BVI 
MT=452 added corrections for total and elastic) 
am242 
SG26 
Thermal uncertainty replaced by Mughabghab value 
am242m 
SG26 
Thermal uncertainty replaced by Mughabghab value 
am243 
BLO approximate data 

am244 
BLO approximate data 

am244m 
BLO approximate data 

ar36 
BLO approximate data 

ar38 
BLO approximate data 

ar40 
BLO approximate data 

as74 
BLO approximate data 

as75 
BLO approximate data 

au197 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
b10 
BLO LANL evaluation +ENDF/BVI 
LANL highfidelity covariance, with ENDF/BVI for thermal 
b11 
JENDL 3.3 

ba130 
BLO approximate data 

ba132 
BLO approximate data 

ba133 
BLO approximate data 

ba135 
BLO approximate data 

ba136 
BLO approximate data 

ba137 
BLO approximate data 

ba138 
BLO approximate data 

ba140 
BLO approximate data 

be7 
BLO approximate data 

be9 
BLO approximate data 

Bebound 
BLO approximate data 
Duplicate of ^{9}Be 
bi209 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
bk249 
BLO approximate data 

bk250 
BLO approximate data 

br79 
BLO approximate data 

br81 
BLO approximate data 

C 
ENDF/BVI 

Cgraphite 
ENDF/BVI 
Duplicate of carbon 
Ca 
BLO approximate data 

ca40 
BLO approximate data 

ca42 
BLO approximate data 

ca43 
BLO approximate data 

ca44 
BLO approximate data 

ca46 
BLO approximate data 

ca48 
BLO approximate data 

Cd 
BLO approximate data 

cd106 
BLO approximate data 

cd108 
BLO approximate data 

cd110 
BLO approximate data 

cd111 
BLO approximate data 

cd112 
BLO approximate data 

cd113 
BLO approximate data 

cd114 
BLO approximate data 

cd115m 
BLO approximate data 

cd116 
BLO approximate data 

cd136 
BLO approximate data 

cd138 
BLO approximate data 

cd139 
BLO approximate data 

cd140 
BLO approximate data 

cd141 
BLO approximate data 

cd142 
BLO approximate data 

ce143 
BLO approximate data 

ce144 
BLO approximate data 

cf249 
BLO approximate data 

cf250 
BLO approximate data 

cf251 
BLO approximate data 

cf252 
BLO approximate data 

cf253 
BLO approximate data 

cf254 
BLO approximate data 

Cl 
BLO approximate data 

cl35 
BLO approximate data 

cl37 
BLO approximate data 

cm241 
BLO approximate data 
Thermal uncertainty 
cm242 
SG26 
Mughabghab value 
cm243 
SG26 
Thermal uncertainty replaced by Mughabghab value 
cm244 
SG26 
Thermal uncertainty replaced by Mughabghab value 
cm245 
SG26 
Thermal uncertainty replaced by Mughabghab value 
cm246 
BLO approximate data 

cm247 
BLO approximate data 

cm248 
BLO approximate data 

cm249 
BLO approximate data 

cm250 
BLO approximate data 

co58 co58m co59 
BLO approximate data BLO approximate data ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
cr50 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
cr52 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
cr53 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
cr54 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
cs133 
BLO approximate data 

cs134 
BLO approximate data 

cs135 
BLO approximate data 

cs136 
BLO approximate data 

cs137 
BLO approximate data 

cu63 
ENDF/BVI 

cu65 
ENDF/BVI 

dy156 
BLO approximate data 

dy158 
BLO approximate data 

dy160 
BLO approximate data 

dy161 
BLO approximate data 

dy162 
BLO approximate data 

dy163 
BLO approximate data 

dy164 
BLO approximate data 

er162 
BLO approximate data 

er164 
BLO approximate data 

er166 
BLO approximate data 

er167 
BLO approximate data 

er168 
BLO approximate data 

er170 
BLO approximate data 

es253 
BLO approximate data 

es254 
BLO approximate data 

es255 
BLO approximate data 

eu151 
BLO approximate data 

eu152 
BLO approximate data 

eu153 
BLO approximate data 

eu154 
BLO approximate data 

eu155 eu156 eu157 
BLO approximate data BLO approximate data BLO approximate data 

f19 
BLO approximate data 

fe54 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
fe56 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
fe57 
ENDF/BVI 
Error in file corrected LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
fe58 fm255 
ENDF/BVI BLO approximate data 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. New material not in previous SCALE 5.1 covariance libraries. 
Ga ga69 ga71 
BLO approximate data BLO approximate data BLO approximate data 

gd152 gd153 
ENDF/BVII.0 BLO approximate data 

gd154 
ENDF/BVII.0 

gd155 
ENDF/BVII.0 

gd156 
ENDF/BVII.0 

gd157 
ENDF/BVII.0 

gd158 
ENDF/BVII.0 

gd160 
ENDF/BVII.0 

ge70 
BLO approximate data 

ge72 
BLO approximate data 

ge73 
BLO approximate data 

ge74 
BLO approximate data 

ge76 
BLO approximate data 

h1 
BLO LANL evaluation +JENDL 3.3 
LANL covariance above 5 keV; JENDL values below 5 keV 
hZrH 
BLO LANL evaluation +JENDL 3. 
Duplicate of ^{1}H 
hpoly 
BLO LANL evaluation +JENDL 3. 
Duplicate of ^{1}H 
Hfreegas 
BLO LANL evaluation +JENDL 3. 
Duplicate of ^{1}H 
h2 
BLO approximate data 

Dfreegas 
BLO approximate data 
Duplicate of ^{2}H 
h3 
BLO approximate data 

he3 
BLO approximate data 

he4 
BLO approximate data 

Hf 
BLO approximate data 

hf174 
BLO approximate data 

hf176 
BLO approximate data 

fh177 
BLO approximate data 

hf178 
BLO approximate data 

hf179 
BLO approximate data 

hf180 
BLO approximate data 

hg196 
BLO approximate data 

hg198 
BLO approximate data 

hg199 
BLO approximate data 

hg200 
BLO approximate data 

hg201 
BLO approximate data 

hg202 
BLO approximate data 

hg204 
BLO approximate data 

ho165 
BLO approximate data 

i127 
BLO approximate data 

i129 
BLO approximate data 

i130 
BLO approximate data 

i131 
BLO approximate data 

i135 
BLO approximate data 

In 
ENDF/BVI 

in113 in115 
BLO approximate data BLO approximate data 

ir191 
ENDF/BVII.0 

ir193 
ENDF/BVII.0 

K 
BLO approximate data 

k39 
BLO approximate data 

k40 
BLO approximate data 

k41 
BLO approximate data 

kr78 
BLO approximate data 

kr80 
BLO approximate data 

kr82 
BLO approximate data 

kr83 
BLO approximate data 

kr84 
BLO approximate data 

kr85 
BLO approximate data 

kr86 
BLO approximate data 

la138 la139 
BLO approximate data BLO approximate data 

la140 
BLO approximate data 

li6 
BLOLANL evaluation 

li7 
ENDF/BVII.0 

lu175 
BLO approximate data 

lu176 
BLO approximate data 

Mg 
BLO approximate data 

mg24 
BLO approximate data 

mg25 
BLO approximate data 

mg26 
BLO approximate data 

mn55 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
Mo 
BLO approximate data 

mo92 
BLO approximate data 

mo94 
BLO approximate data 

mo95 
BLO approximate data 

mo96 
BLO approximate data 

mo97 
BLO approximate data 

mo98 mo99 mo100 
BLO approximate data BLO approximate data BLO approximate data 

n14 
BLO approximate data 

n15 
BLO approximate data 

na23 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
nb93 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
nb94 
BLO approximate data 

nb95 
BLO approximate data 

nd142 
BLO approximate data 

nd143 
BLO approximate data 

nd144 
BLO approximate data 

nd145 
BLO approximate data 

nd146 
BLO approximate data 

nd147 
BLO approximate data 

nd148 
BLO approximate data 

nd150 
BLO approximate data 

ni58 ni59 
ENDF/BVIIp BLO approximate data 
Prereleased evaluation proposed for ENDF/BVII.1 
ni60 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
ni61 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
ni62 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
ni64 
ENDF/BVI 
LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
np235 np236 np237 
BLO approximate data BLO approximate data SG26 
Thermal uncertainty replaced by Mughabghab value 
np238 
BLO approximate data 

np239 
BLO approximate data 

o16 
JENDL 3.3+BLO 
BLO covariances from LANL used above 5 keV 
o17 
BLO approximate data 

p31 
BLO approximate data 

pa231 pa232 
BLO approximate data BLO approximate data 

pa233 
BLO approximate data 

pb204 pb206 
BLO approximate data ENDF/BVI 
Error in file corrected 
pb207 
ENDF/BVI 
MT=3 removed, Error in file corrected 
bp208 
ENDF/BVI 
MT=3 removed, Error in file corrected 
pd102 
BLO approximate data 

pd104 
BLO approximate data 

pd105 
BLO approximate data 

pd106 
BLO approximate data 

pd107 
BLO approximate data 

pd108 
BLO approximate data 

pd110 
BLO approximate data 

pm147 
BLO approximate data 

pm148 
BLO approximate data 

pm148m 
BLO approximate data 

pm149 
BLO approximate data 

pm151 
BLO approximate data 

pr141 
BLO approximate data 

pr142 
BLO approximate data 

pr143 
BLO approximate data 

pu236 pu237 pu238 
BLO approximate data BLO approximate data SG26 
Thermal uncertainty replaced by Mughabghab value 
pu239 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1; nubar data from ENDF/BV Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide Table 10.3.2 
pu240 
JENDL 3.3 
Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide (Table 10.3.2 
pu241 
JENDL 3.3 
Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide (Table 10.3.2) 
pu242 
ENDF/BVI 

pu243 
BLO approximate data 

pu244 
BLO approximate data 

pu246 
BLO approximate data 

rb85 
BLO approximate data 

rb86 
BLO approximate data 

rb87 
BLO approximate data 

re185 
ENDF/BVI 
MT=2 added from Mughabghab. LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
re187 
ENDF/BVI 
MT=2 added from Mughabghab. LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
rh103 
BLO approximate data 

rh105 
BLO approximate data 

ru96 
BLO approximate data 

ru98 
BLO approximate data 

ru103 
BLO approximate data 

ru99 
BLO approximate data 

ru100 
BLO approximate data 

ru101 
BLO approximate data 

ru102 
BLO approximate data 

ru104 
BLO approximate data 

ru105 
BLO approximate data 

ru106 
BLO approximate data 

S 
BLO approximate data 

s32 
BLO approximate data 

s33 
BLO approximate data 

s34 
BLO approximate data 

s36 
BLO approximate data 

sb123 
BLO approximate data 

sb124 
BLO approximate data 

sb125 
BLO approximate data 

sb126 
BLO approximate data 

sc45 
ENDF/BVI 

se74 
BLO approximate data 

se76 
BLO approximate data 

se77 
BLO approximate data 

se78 se79 
BLO approximate data BLO approximate data 

se80 
BLO approximate data 

se82 
BLO approximate data 

Si 
ENDF/BVI 

si28 
ENDF/BVI 
Error in file corrected LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
si29 
ENDF/BVI 
Error in file corrected LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
si30 
ENDF/BVI 
Error in file corrected LB=8 representation caused problematic representation of cross section uncertainty due to use of fine energy group structure. Tests were performed to determine how to handle this problem. LB=8 data were removed in the final results. 
sm144 
BLO approximate data 

sm147 
BLO approximate data 

sm148 
BLO approximate data 

sm149 
BLO approximate data 
Resonance range uncertainty from Kawano 2008 
sm150 
BLO approximate data 

sm151 
BLO approximate data 

sm152 
BLO approximate data 

sm153 
BLO approximate data 

sm154 
BLO approximate data 

sn112 
BLO approximate data 

sn113 
BLO approximate data 

sn114 
BLO approximate data 

sn115 
BLO approximate data 

sn116 
BLO approximate data 

sn117 
BLO approximate data 

sn118 
BLO approximate data 

sn119 
BLO approximate data 

sn120 
BLO approximate data 

sn122 
BLO approximate data 

sn123 
BLO approximate data 

sn124 
BLO approximate data 

sn125 
BLO approximate data 

sr84 
BLO approximate data 

sr86 
BLO approximate data 

sr87 
BLO approximate data 

sr88 
BLO approximate data 

sr89 
BLO approximate data 

sr90 
BLO approximate data 

ta181 
BLO approximate data 

ta182 
BLO approximate data 

tb159 
BLO approximate data 

tb160 
BLO approximate data 

tc99 
ENDF/BVII.0 

te120 
BLO approximate data 

te122 
BLO approximate data 

te123 
BLO approximate data 

te124 
BLO approximate data 

te125 
BLO approximate data 

te126 
BLO approximate data 

te127m 
BLO approximate data 

te128 
BLO approximate data 

te129m 
BLO approximate data 

te130 
BLO approximate data 

th227 
BLO approximate data 

th228 
BLO approximate data 

th229 
BLO approximate data 

th230 
BLO approximate data 

th232 th233 th234 Ti ti46 ti47 ti48 
ENDF/BVII.0 BLO approximate data BLO approximate data BLO approximate data BLO approximate data BLO approximate data ENDF/BVIIp 
Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide (Table 10.3.2) Prereleased evaluation proposed for ENDF/BVII.1 
ti49 
BLO approximate data 

ti50 
BLO approximate data 

u232 
BLO approximate data 

u233 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1; nubar uncertainty from Ref. 14Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide ( 
u234 
SG26 
Thermal uncertainty replaced by Mughabghab value 
u235 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1; nubar uncertainty from JENDL3.1 Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide (Table 10.3.2). 
u236 
SG26 
Thermal uncertainty replaced by Mughabghab value 
u237 
BLO approximate data 

u238 u239 u240 u241 
ENDF/BVIIp BLO approximate data BLO approximate data BLO approximate data 
Prereleased evaluation proposed for ENDF/BVII.1 Cross nuclidetonuclide matrices present; covariances due to fission cross sections / nubar for each nuclide (Table 10.3.2). 
V 
ENDF/BVIIp 
Prereleased evaluation proposed for ENDF/BVII.1 
W 
BLO approximate data 

w182 
BLO approximate data 

w183 
BLO approximate data 

w184 
BLO approximate data 

w186 
BLO approximate data 

xe123 
BLO approximate data 

xe124 
BLO approximate data 

xe126 
BLO approximate data 

xe128 
BLO approximate data 

xe129 
BLO approximate data 

xe130 
BLO approximate data 

xe131 
BLO approximate data 

xe132 
BLO approximate data 

xe134 
BLO approximate data 

xe135 
BLO approximate data 

xe136 
BLO approximate data 

y89 
ENDF/BVI 

y90 
BLO approximate data 

y91 
BLO approximate data 

Zr 
BLO approximate data 

zr90 
BLO approximate data 

zr91 
BLO approximate data 

zr92 
BLO approximate data 

zr93 
BLO approximate data 

zr94 
BLO approximate data 

zr95 
BLO approximate data 

zr96 
BLO approximate data 
Nuclide 1 
Reaction 1 
Nuclide 2 
Reaction 2 

^{240}Pu 
Fission 
^{239}Pu 
Fission 
^{240}Pu 
Fission 
^{233}U 
Fission 
^{240}Pu 
Fission 
^{238}U 
Fission 
^{241}Pu 
Fission 
^{239}Pu 
Fission 
^{241}Pu 
Fission 
^{240}Pu 
Fission 
^{241}Pu 
Fission 
^{233}U 
Fission 
^{241}Pu 
Fission 
^{235}U 
Fission 
^{241}Pu 
Fission 
^{238}U 
Fission 
^{235}U 
Fission 
^{240}Pu 
Fission 
References
 COVLIBBW04(1,2)
Bryan L. Broadhead and J. J. Wagschal. The Fission Spectrum Uncertainty. PHYSOR 2004–The Physics of Fuel Cycles and Advanced Nuclear Systems: Global Developments, pages 25–29, 2004.
 COVLIBCHO+11
M.B. Chadwick, M. Herman, P. Obložinský, M.E. Dunn, Y. Danon, A.C. Kahler, D.L. Smith, B. Pritychenko, G. Arbanas, R. Arcilla, R. Brewer, D.A. Brown, R. Capote, A.D. Carlson, Y.S. Cho, H. Derrien, K. Guber, G.M. Hale, S. Hoblit, S. Holloway, T.D. Johnson, T. Kawano, B.C. Kiedrowski, H. Kim, S. Kunieda, N.M. Larson, L. Leal, J.P. Lestone, R.C. Little, E.A. McCutchan, R.E. MacFarlane, M. MacInnes, C.M. Mattoon, R.D. McKnight, S.F. Mughabghab, G.P.A. Nobre, G. Palmiotti, A. Palumbo, M.T. Pigni, V.G. Pronyaev, R.O. Sayer, A.A. Sonzogni, N.C. Summers, P. Talou, I.J. Thompson, A. Trkov, R.L. Vogt, S.C. van der Marck, A. Wallner, M.C. White, D. Wiarda, and P.G. Young. ENDF/BVII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data. Nuclear Data Sheets, 112(12):2887–2996, 2011. URL: https://www.sciencedirect.com/science/article/pii/S009037521100113X, doi:https://doi.org/10.1016/j.nds.2011.11.002.
 COVLIBHal08
Gerald Hale. Covariances from lightelement rmartix analyses. Technical Report, Los Alamos National Laboratory, Los Alamos, NM (USA), 2008.
 COVLIBHD71
R. J. Howerton and R. J. Doyas. Fission temperatures as a function of the average number of neutrons from fission. Nuclear Science and Engineering, 46(3):414–416, 1971. Publisher: Taylor & Francis.
 COVLIBKTY+08
T. Kawano, P. Talou, P. G. Young, G. Hale, M. B. Chadwick, and R. C. Little. Evaluation of covariances for actinides and light elements at LANL. Nuclear Data Sheets, 109(12):2817–2821, 2008.
 COVLIBLLD+06
N. M. Larson, L. C. Leal, H. Derrien, G. Arbanas, R. O. Sayer, and D. Wiarda. A systematic description of the generation of covariance matrices. In PHYSOR2006: ANS Topical Meeting on Reactor Physics, 10–14. 2006.
 COVLIBLWRD08
Luiz C. Leal, D. Wiarda, Bradley T. Rearden, and Herve Derrien. 233 U CrossSection and Covariance Data Update for SCALE 5.1 Libraries. ORNL/TM2007/115, Oak Ridge National Laboratory, Oak Ridge, Tenn, 2008.
 COVLIBLKH+08(1,2)
R. C. Little, T. Kawano, G. D. Hale, M. T. Pigni, M. Herman, P. Obložinsky, M. L. Williams, M. E. Dunn, G. Arbanas, and D. Wiarda. Lowfidelity Covariance Project. Nuclear Data Sheets, 109(12):2828–2833, 2008. Publisher: Elsevier.
 COVLIBMMW80
R. E. Maerker, J. H. Marable, and J. J. Wagschal. Estimation of the uncertainties in the ENDF/BV Uranium 235 fission spectrum. In Transactions of the American Nuclear Society, volume 35. 1980.
 COVLIBMug03(1,2)
S. F. Mughabghab. Thermal neutron capture cross sections resonance integrals and gfactors. International Atomic Energy Agency, 2003.
 COVLIBMug06(1,2)
Said F. Mughabghab. Atlas of Neutron Resonances: Resonance Parameters and Thermal Cross Sections. Z= 1100. Elsevier, 2006.
 COVLIBPHO09
M. T. Pigni, M. Herman, and P. Obložinsky. Extensive Set of CrossSection Covariance Estimates in the Fast Neutron Region. Nuclear science and engineering, 162(1):25–40, 2009. Publisher: Taylor & Francis.
 COVLIBRHOM07
D. Rochman, M. Herman, P. Oblozinsky, and S. F. Mughabghab. Preliminary crosssection covariances for WPEC Subgroup 26. Technical Report BNL774072007IR, Brookhaven National Laboratory, Upton, NY (USA), 2007.
 COVLIBWD06
D. Wiarda and M. E. Dunn. PUFFIV: A Code for Processing ENDF Uncertainty Data into Multigroup Covariance Matrices. Technical Report ORNL/TM2006/147, Oak Ridge National Laboratory, Oak Ridge, TN (USA), 10 2006.
 COVLIBWALD08
Dorothea Wiarda, Goran Arbanas, L. Leal, and Michael E. Dunn. Recent advances with the AMPX covariance processing capabilities in PUFFIV. Nuclear Data Sheets, 109(12):2791–2795, 2008. Publisher: Elsevier.
 COVLIBWBDR07
Mark L. Williams, Bryan L. Broadhead, Michael E. Dunn, and Bradley T. Rearden. Approximate Techniques for Representing Nuclear Data Uncertainties. In Eighth International Topical Meeting on Nuclear Applications and Utilization of Accelerators (AccApp'07)," Pocatello, ID (July 30Aug. 2, 2007). 7 2007.
 COVLIBWIMR14
Mark L. Williams, Germina Ilas, William J. Marshall, and Bradley T. Rearden. Applications of nuclear data covariances to criticality safety and spent fuel characterization. Nuclear Data Sheets, 118:341–345, 2014.
 COVLIBWR08(1,2,3,4,5)
Mark L. Williams and Bradley T. Rearden. SCALE6 Sensitivity/uncertainty methods and covariance data. Nuclear Data Sheets, 109(12):2796–2800, 2008.