Compilation of Multigroup Cross-Section Covariance Matrices ...

v I (J)' ! (? tf* ' ORNu-5318 r* (ENDF-225)

Compilation of Multigroup Cross-Section Covariance Matrices for Several Important

Reactor Materials

J. D. Drischler C R. Weisbin

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ORNL-5318 Distribution Category UC-79d (ENDF-235)

Contract No. W-7405-sng-26

Neutron Physics Division

COMPILATION OF MULTIGROUP CROSS-SECTION COVARIANCE MATRICES FOR SEVERAL IMPORTANT REACTOR MATERIALS

J. D. Drischler and C. R. Weisbin

Date Published: October 1977

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OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

for the ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

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DISTRIBUTION or TMIS DOCUM':: ti>

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This report was prepared as an account of work sponsored by the United States Government Neither the United States nor the Energy Research and Development Administration/United States Nuclear Regulatory Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights

iii

TABLE OF CONTENTS Page No.

ORGANIZATION OF STANDARD DEVIATION AND CORRELATION MATRIX LIBRARY DATA v LIST OF FIGURES vii LIST OF TABLES ix ACKNOWLEDGEMENTS x ABSTRACT xi

I. DESCRIPTION OF CROSS-SECTION COVARIANCE MATRIX GENERATION 1.1-1 1. Background 1.1-1 2. Evaluated Covarlance Formulation 1.2-1 3. Computation of Multigroup Covariance Matrices i.r-1 4. Results for Processed Uncertainty Files 1.4-1

II. SPECIFIC EXAMPLES 11.7-1 1. Evaluated Covariance Files II.1-1 2. Multiqrcjp Covariance Files II.2-1

A. Fission Spectrum Covariance Matrix Library II.2A-1 B. LMFBR Core Physics Covariance Matrix Library IL2B-1 C. LMFBR Shielding Covariance Matrix Library II.2C-1

III. CONCLUSIONS III-l REFERENC tS R-l

App. A. COVERX FORMAT A-1

App. B. SAMPLE DATA SET IN COVERX FORMAT B-; App. C. EVALUATORS' COMMENTS ON THE CONSTRUCTION OF THE

UNCERTAINTY FILES - C-l App. D. EDITED TABULATION C7 ThT FISSION SPECTRA COVARIANCE n^l

MATRIX LIBRARY -T App. E. EDITED TABULATION OF THE LMFBR CORE PHYSICS COVARIANCE

MATRIX LIBRARY - E-l App. F. EDITED TABULATPN OF THE LMFBR SHIELDING COVARIANCE

MATRIX LIBRARY F-l

V

Organization of Standard Deviation and Correlation Matrix Library Data

Page No. 1 Page

No. Page

No.

Fission Spectrin Covari ance Matrix ! ibrary 1 see App. D) 2 3 5 U(n»f ) D-3 2 3 8 U(n ,n \2nd) 0-5 2 3 * u ( n , Y ) D-7 2 3 5 u Q D-3 2 3 8 U ( n , n \ 3 r d ) D-5 2-°Pu(v) D-8 2 3 5 U ( n > T ) D-3 2 3 8 U ( n , n \ 4 t h ) D-6 2*°Pu(n,Y) D-8 2 3 8 U ( n , f ) D-5 2 3 8 U ( n , Y ) 0-6 2 - iPu(n, f ) D-9 2 38 U (7) D-5 2 3 * u ( n , f ) D-7 2-lp u(V) D-9 2 3 8 U ( n , n \ l s t ) D-5 2 3 * u { ^ D-7 2 , f l Pu(n,Y) D-9

LMFBR Core Physics Cova riance Matrix Library (see i *PP. E) 2 3 5 U(n ,v ) E-3 2 3 * u ( n , Y ) E-7 1 , f N(elastic) E-ll 2 3 5 U ( ^ ) E-3 2"°Pu(7) E-8 1 £ f N(n,n') E-12 2 3 5 U ( n , Y ) E-3 2 M , P u ( n , Y ) E-9 " H ( n > Y ) E-l? 2 3 8 U ( n , f ) E-4 2 ^Pu(n , f ) E-9 "Ndi.p) E-12 2 3 8 U(v ) E-5 ^Pu^T) E-9 l l t N(n,a) E-12 2 3 8 U ( n , n , , l s t ) E-5 2 1 f l Pu(n , Y ) E-10 1 6 0 ( to ta l ) E-14 2 3 8 U(n,n' ,2nd) E-5 1 2 C(tota l ) E-10 1 6 0(e last ic ) E-34 2 3 8 U(n f n' ,3rd) E-5 1 2 C(n ,n ' , ls t ) E-10 1 6 0(n ,n ' ) E-15 2 3 8 U(n ,n , , 4 th ) E-6 1 2 C(n,n \cont . ) E-10 1 6 0(n,p) E-l 5 2 3 8 U(n,y ) E-6 1 2 C(n , Y ) E-ll 1 6 0(n ,a ) E-15 2 3 * u ( n , f ) E-7 1 2 C(n,a) E-ll 2 3 * u ( v ) E-7 ^Nftotal ) E-ll

LMFBR Shielding Covaria nee Matrix Library (see App . F)

Na(total) F-3 i 2 C(tota l ) F-9 "Htn.y) F-13 Na(elastic) F-3 1 2 C(n ,n \1s t ) F-9 ^ ( n . p ) F-13 Na(non-el astic) F-4 1 2 C(n,n' ,cont.) F-10 J*N(n,o) F- l* Na(n,Y) F-4 1 2 C ( n f Y ) F-10 1 6 0( to ta l ) F-l? Fe(total) F-6 1 2 C(n,a) F-ll 1 6 0(elast ic) F-2) Fe(elastic) F-6 ^Nftotal ) F-11 ! 1 6 0(n,n' ) ?-'<) Fe(non-elastic) F-7 ^ ( e l a s t i c ) F-12 1 6 0(r„p) F-2

Fe(n,y) F-7 ^ ( n . n ' ) F-12 ! I 6 0(n,a) F-2:

vn

LIST OF FIGURES Page No.

Fig. A-l. Fission Spectrum Covariance Matrix Library (GOOIVA Weighting). II.2A-3

Fig. A-2. Standard Deviation and Correlation Matrix of the 2 3 5U(n,f) Cross Sections. II.2A-8

Fig. A-3. Standard Deviation and Correlation Matrix of the 2 3 5U(n,T) Cross Sections. II.2A-8

Fig. A-4. Standard Deviation and Correlation Matrix of the 2 3 ^(v) Cross Sections. IJ.2A-9

Fig. A-5. Standard Deviation and Correlation Matrix of the 2 3 8U(n,f) Cross Sections. II.2A-9

Fig. A-6. Standard Deviation and Correlation Matrix of the 2 3 8U(n,Y) Cross Sections. II.2A-10

Fig. A-7. Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,f) Cross Sections. II.2A-10

Fig. A-8. Standard Deviation and Correlation Matrix of the 2 , 9Pu(n,y) Cross Sections. II.2A-11

Fig. A-9. Standard Deviation and Correlation Matrix of the 2 3 9Pu(v) Cross Sections. II - kj

Fig. B-l. LMFBR Core Physics Covariance Matrix Library (ZPR-6/7 Weighting). II.2B-3

Fig. B-2. Standard Deviation and Correlation Matrix of the 2 3 SU(n,f) Cross Sections. II.2B-7

Fig. B-3. Standard Deviation and Correlation Matrix of the 2 38U(n,f) Cross Sections. II.2B-7

F1g. B-4. Standard Deviation and Correlation Matrix of the 2 3 8 U ( n , Y ) Cross Sections. II.2B-8

F1g. B-5. Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,f) Cross Sections. II.2B-8

Fig. B-6, Standard Deviation and Correlation rtatrlx of the 239Pu(.n,Y) Cross Sections. — II.2B-9

F1g. B-7, Standard Deviation and Correlation Matrix of the 2 3 9Puft) Cross Section. „-T - — - II.2B-9

V111

LIST OF FIGURES (Cont'd) Page No.

Fig. B-8. Correlation Subaatrlx Between the 2 3 9Pu(n,f) and 2 3 9 / u ( n , T ) Cross Sections. II.2B-10

Fig. B-9. Standard Deviation and Correlation Matrix of the 2 , | 0Pu(n,Y) Cross Sections. II.2B-10

Fig. B-10. Standard Deviation and Correlation Matrix of the 2 l > 1Pu(n,f) Cross Sections. II.2B-11

F1g. C-l. LMFBR Shielding Covariance Matrix Library (1/E Weighting). II.2C-2

Fig. C-2. StanJard Deviation and Correlation Matrix of the Na Elastic Cross Sections. II.2C-4

F1g. C-3. Standard Deviation and Correlation Matrix of the Na Non-Elastlc Cross Sections. II.2C-4

F1g. C-4. Correlation Submatrix Between the Na Elastic and Na Non-Elastic Cross Sections. II.2C-5

F1g. C-5. Standard Deviation and Correlation Matrix of the Fe Elastic Cross Sections II.2C-5

Fig. C-6. Standard Deviation and Correlation Matrix of the Fe Non-Elastlc Cross Sections. II.2C-6

Fig. C-7. Correlation Submatrix Between the F» Elastic and Fe Non-Elastic Cross Sections. II.2C-6

IX

Table I Table II

Table III

Table IV

Table V

Table VI

Table VII

Table VIII Table IX

Table X

Table XI

Table XII

Table XIII

Table XIV

•J

LIST OF TABLES Page No.

Calculated Volune Averaged Flux Spectrum in GODIVA II.2A-2 Standard Deviation and Correlation Matrix of the 2 ? 5U(n,f) Cross Sections II.2A-5 Standard Deviation and Correlation Matrix of the 2 3 5U(n, Y) Cross Sections II.2A-5 Standard Deviation and Correlation Matrix of the 2 3 8U(n,f) Cross Sections II.2A-5 Standard Deviation and Correlation Matrix cf the 2 3 8U(n, Y) Cross Sections II.2A-6 Standard Deviation and Correlation Matrv< of the 2 3 9Pu(n,f) Cross Sections II.2A-6 Standard Deviation and Correlation Matrix of the 239Pu("v) Cross Sections — II.2A-6 Calculated Central Flux Spectrum in ZPR-6/7 II.2B-2 Relative Standard Deviation and Correlation Matrix of the 2 3 8U(n,f) Cross Sections II.2B-5 Relative Standard Deviation and Correlation Matrix of the 2 3 8U(n,y) Cross Sections II.2B-5 Relative Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,f) Cross Sections II.2B-5 Relative Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,y) Cross Sections II.2B-6 Correlation Submatrlx Between the 2 3 9Pu(n,f) and 2 3 9Pu(n,y) Cross Sections II.2B-6 Relative Standard Deviation and Correlation Matrix of the 2 3 9Pu(77) Cross Sections II.2B-6

X

ACKNOWLEDGEMENTS

The authors wish to thank R. U. Peelle and F. S. Perey for their guidance and encouragement In the course of this work. Much of the information and Important feedback was obtained through discussion with G. de Saussure, R. Gwln, L. H. Weston, F. Difilippo, R. W. Peelle, F. G. Perey, E. N. Oblow, C. Y. Fu, R. B. Perez and D. C. Larson. The authors gratefully acknowledge the Inportant contribution of J. L. Lucius for organizing and creating the COVERX format, and of J. E. White and R. Q. Wright ft" guidance In cross-section preparation. Finally we owe our deep gratitude to Lorraine S. Abbott, Jan Gentry, Ann Houston, LaHanda Klobe. and Cathy Oldham for preparinq this report in its final form,

XI

Abstract

This report presents multigroup cross-section covariance matrices for fission in 2 3 5 U , 2 3"U, 2 3 9 P u , and 2 l f lPu; capture in 2 3 5 U , 2 3 8 U , 2 3 9 P u , 2*°Pu, and 2 , f lPu; fission neutron yield Q for 2 3 5 U , 2 3 8 U , 2 3 9 P u , and 2t*°Pu; elastic scattering for Na and Fe; non-elastic reactions for Na and Fe; first-level inelastic scattering for 2 3 8 U ; and all reactions pro­vided in the ENDF/B-IV covariance description of N, 0, and C. Other data files generated are included for reference but have not yet been tested. The report presents the multigroup data in six, ten, and fifteen energy group forms corresponding to weighting of the covariance data witn fission (G00IVA), LMFBR (ZPR-6/7) and l/E spectra, respectively. The data are illustrated and tabulated in an edited form for convenience. The multigroup covariance files are currently available from RSIC and NNCSC in the COVERX format, a computer retrievable format designed for data uncertainty analysis and described herein. As new covariance files become available with subsequent Issues of ENDF/B, this report will be added to or revised by the issuance of dated pages that can be incorporated in the report.

1.1-1

I. DESCRIPTION OF CROSS-SECTION COVARIANCE MATRIX GENERATION

1. Background

Only recently have standard formats and procedures been established within the ENOF/B system 1* 2 for the processing of evaluated and corre­lated energy-dependent uncertainty Information Into a multlgroup covarl-ance matrix formulation. The covarlance matrices were established3 to permit systematic sensitivity Investigations to propagate uncertainties in radiation transport calculations and thereby to determine, in a credible fashion, what cross-section measurements, evaluations, or processing methods roost need further refinement for specific applications. Multlaroup covari-ance matrices have been processed from ENDF/B-IV and from evaluations in­ternally generated at ORNL. Libraries of multlgroup matrices in COVERX format are currently available through the Radiation Shielding Information Center (RSIC) at Oak Ridge National Laboratory and the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory. The COVERX format is described 1n Appendix A. Auxiliary routines for reading and writing these data are also available. A sample COVERX data file is tabulated in Appendix B and a comprehensive, more readable tabulation 1s presented 1n Appendices D, E, and F.

1.2-1

2. Evaluated Covarlance Formulation

The types of covariance representations permitted in ENDF/B-IV include1:

16=0 Absolute components correlated only within each energy (E.) inter­val (LB=0 as defined in the ENDF/B-IV format) cov(x . ,Y . )=y:p] : ] ;F X V J c ( 1 )

k

LB=1 Fractional components correlated only within each E. interval

Cov(X rY.) . £ p!j* F X Y > k X.Y. (2) k

LB=2 Fractional components fully correlated over all E. intervals (one

table F„Y . a s a function of energy) Cov(X r Y. )=y ; p ] * F X V ) k F X Y k , X.Y. (3)

k,k'

LB=3 Fractional components correlated between F. and E intervals

C o v ^ . Y . ) ^ fj j j F X > k fy, t Vo ««>

where X^ and Y. represent cress sections X arid Y evaluated at energies 1 and j, respectively, the F's (F X Y k, F A Y k,, F x k, and F y ) represent uncertainty components, taken directly from the ENDF/B file describing the covarlances of cross sections X and Y for specific energy intervals. These components are defined assuming a multivariate normal distribution of cross-section uncertainties; furthermore, multiple sections (e.g.,

1.2-2

F? Y .) nay be provided corresponding to specific types of experimental un­certainties associated with the compete covarlance matrix. The F X Y k

and Fwy u* *re taken from a single table of energy-aependent covarlance In­formation for reactions X and Y. The F„ . and Fy , are defined such that the covarlance data Unking cross sections for these reactions are taken

1-k from two Independent tables, one for X and one for Y. The ?-*.v, 1s zero J ,K except for the case when energy 1 Is contained within.energy Interval k and energy j Is contained within energy Interval k'. Cov(Xj,Y.) Is then the covarlance of cross section X at energy 1 and cross section Y at energy j. Thpr« 1s a fifth law (LB-4), but since It can be described a? combinations of tha first four, no data have yet beer cast 1n this form for ENDF/B-IV.

1.3-1

3. Computation of Multigroup Covarlance Matrices

The type of formulation described in the previous section (sums of quantities separable in X and Y) has the very desirable characteristic that, if one assumes a flux model uncorrelated to the cross sections of interest, the multigroup covarlance matrices are reduced to combinations of single integrals Involving group fluxes and cross sections which can be calculated easily. In particular, for

LB=0, v ^ v ^ F" *n *n

L . L , hXY,k *G,k *H,k Cov(X r,Y H) = n keG'" (5)

LB=1 • E Z F*Y-k * G » k X^k *"'k Y"'k

Cov(Xp,Y„) = n k e G' H — (6)

YJCL FXY.k *G,k XG,k) I L FXY,k' •H,k' YH,k') Cov(Xr,Yu) - JLAfe§ JLklH /

G H (7)

LB=3,

E ( E F**k *G,k x ^ k ) ( Z F "» k ' *"» k ' Y "» k ' j Co V(x r,Y H) » -sASfiS / \fc'«H L (8)

G H *G *H

In general, the covarlance Matrix will be a sum of terms from any of the LB descriptions. The derivation of Eqs. (5-8) has been described previously;1 thi notation used here is:

1.3-2

Cov(Xg,YH) - Multi group covarlance of reaction X,group 6, and reaction Y, group H.

•6 = Nultlgroup flux for user group G. Xg . = Nultlgroup cross section for reaction X for a super-group

(G,k) constructed from the union of energy bounds for Inter­val k (taken from subsection n) and those which *»w» user Input. •? . Is the flux for this group.

Note that this formalism Is appropriate for Infinitely dilute cross sec­tions; uncertainties In resonance parameters are not addressed. The as­sumption Is that uncertainties In the Infinitely dilute cross sections are more severe than those 1n the self-shielding factor which itself Is a ratio.

1.4-1

4. Results for Processed Uncertainty Files

Several quantities related to uncertainties in multlgroup cross sections are processed from the polntwlse ENDF/B data covarlance file using the PUFF covarlance file processing code.* Clearly of Interest Is the covarlance matrix

Cov(X G,Y H) = <(X G - 7 G ) (Y H - Y H)> (9)

the covarlance of reaction X, group G, and reaction Y, group H. (Angle brackets represent expectation values In this section.) The associated quantity, the relative covarlance matrix,1s defined:

Rel Cov(X 6,Y H) = Cov(X G,Y H)/X GY H (10)

In this notation, the standard deviation Is given by: Std. Dev(XQ) = ^CovUg.Xg) (11)

and the analogous relative quantity, the relative standard deviation, Is Std. Dev(Xr)

Rel Std. Dev(Xr) = = 2- (12)

V. 1s reasonable to expect that 1n many cases the covariance matrix of energy-dependent cross sections 1s strongly diagonal; i.e., the magni­tude of the matrix elements tend to be small for groups G and H widely displaced from each other In energy.

The correlation matrix 1s a quantity constructed by dividing the co-variance matrix for X g and Y„ by the respective standard deviations:

((X f i- XJ(Y - Y )>

V v v w <<vv2> < 1 3 >

1.4-2

The correlation matrix Is bounded by unity, I.e.,

iCorrtXg.Y^} < 1 (14)

When Corr(Xg,YH) * 0, the group cross sections are said to be totally uncorrelated; when |Corr(Xg,YH)| • 1, the group cross sections are termed fully correlated (or antlcorrelated).

II.1-1

II. SPECIFIC EXAMPLES

1. Evaluated Covariance FiUs

In the cases cf nitrogen, oxygen, and carbon, covariance files Mere available from the ENUF/B-IV evaluated data. However, in all ot.ier cases

considered here, the covariance files Mere obtained by private communi­cation from evaluators at ORNL. 5" 1 5

Multigroup covariance matrices Mere processed for fission in ?- 3 5U, 2 3 8 U , 2 3 9 P u , and 2«»lPu; capture in 2 3 5 U , 2 3 8 U , 2 3 9 P u , 2 l f 0Pu, and 2 , , 1Pu; fission neutron yield N ) for 2 3 5 U , 2 3 8 U , 2 3 9 P u , ^^Pu. and 2 , , IPu; elastic scattering for Na and Fe; norvelastic reactions for Ka and Fe; and first-level inelastic scattering for 2 3 8 U .

For the Fission Spectrum Covariance Matrix Library the 2 3 9 P u and 2 3 8 U fission reactions were deduced from evaluated covarlances on the 219PU/235U a n d 238IJ/235U f i s s i o n ratios coupled Mith uncertainty esti­mates for the 2 3 5 U fission cross section. The "polntMise" covariance fUas were represented on convenient energy t,rids believed to be adequate­ly fine to faithfully reproduce the broad range behavior important for estimation of uncertainties 1n integral quantities. The evaluations Mere based primarily on "external" methods of analysis which examine the scat­ter among existing data sets. 1 6 These sets are assumed to represent fair­ly the statistical ensemble of hypothetical sets of measurements which could have been obtained 1n the experiments which form our present data base. In cases for which only a few uata sets exist or could be compiled, the ensemble variances were statistically poorly determined by the smell sample; however, variance fluctuations over small energy regions may be

II.1-2

unimportant after averaging over the assembly spectrum. It 1s alec im­portant to recognize that such "external" covarlance evaluation irenhous do not Include any systematic bias; for example, the possibility that the 2 3 9 P u half life is now off by two percent could systematically affect all "absolute" 2 3 9 P u measurements requiring exact foil wights.

The source of data for the 2 8a^/ 2 5a. ( and ** 9o f/ 2 5o. was the recent compilation prepared by Poenltz. 1 7 In the method used by Peelle,9 weights were assigned to each experiment which were to reflect the reciprocal vari­ance of a typical point from the data set. Since uncertainties In most sets are a function of energy, an overall judgment was used. The evalu­ated ratio for 2 6 c * / 2 5 o . was taken to be the proposed evaluated fission ratio for ENDF/B-V 1 8; I.e., the ratio was used which, when multiplied by the 2 3 5 U fission cross section for ENDF/B-V, gives the proposed 2 3 8 U fission cross section for ENDF/B-V. For the "* 9o./ 2 5o- fission ratio, the ENDF/B-V evaluateu ratio was not available early enough so that the evalu­ated ratio had to be taken from the ENDF/B-IV. For these fission ratios, a distinction was made between the ensemble of hypothetical measurements and the ensemble of evaluations based upon these measurements. This ap­parently straightforward difference Introduced added complexities because of the varied pattern of measurements made by Individual authors and be­cause of the unequal weights assigned.

II.2-1

^) 2. Multigroup Covarlance Files

The differential covarlance files developed in the preceding sections were put into ENDF/B-IV format1 and processed with the PUFF covariance file processing code.1* Three nultlgroup covariance libraries were de­veloped corresponding to the Fission Spectrum Covariance Matrix Library (GOOIVA 1 9* 2 0 weighting), the LMFBR Core Physics Covariance Matrix Library (ZPR-6/7 2 1 weighting), and the LMFBR Shielding Covarlance Matrix Library (1/E weighting). (Note the name Fission Spectrum Covariance Matrix Library is meant to characterize covarlance files weighted with a GOOIVA type fission spectrum.) These data sets have been used to assess

uncertainties in clean-geometry fast integral data, 2 2 1n large LMFBR reactor analysis, 2 3, 2 1* and in analysis of deep-penetration shielding

, experiments.25

J

II.2A-1

A. Fission Spectrum Covarlance Matrix Library. Our existing Fission Spectrum Covarlance Matrix Library [weighted with a calculated SODIVA spectrum (Table 1)1 1s Illustrated In Fig. A-1. This figure represents a square matrix Including all reactions for which uncertain­ty Information was developed In the six-group structure for analysis of GOOIVA. Each Individual box 1s Itself a square matrix with sfx energy groups on a side. The total number of elements in the full ma­trix Is 11664. However, most of these are null elements Indicating no correlation. The boxes along the major diagonal refer to the covarlance of a specific reaction as a function of energy. The off-diagonal boxes reflect correlations between reaction types which were developed largely through evaluation of ratio measurements related to a common standard; e.g., 2 3 9Pu(n,f) and 2 3 8U(n,f) were both measured relative to 2 3 5U(n,f). Other sources of correlation between reaction types Include evaluations of capture/fission measurements (a). For example, If one assumes that the 2 3 9 P u fission cross section was measured relative to 2 3 5 U (^a. s

r 25o„r being the 239py/235u fission ratio) and the 2 3 9 P u capture cross section was measured relative to the 2 3 9 P u fission data (I.e., '•V. - a k9Of'* <* Is the Pu capture/fission ratio), then It follows that: (1) The relative covarlance for 2 3 9 P u fission 1s the sum of the relative

covarlances of r and 2 5<j f. (2) The relative covarlance between 2 3 9 P u fission and capture 1s the

sum of the relative covarlances of r and 2 5o^.

(3) The relative covarlance between 2 3 9 P u fission and 2 3 5 U fission 1s the relative covarlance for 25<r^.

v:.~SL,

BLANK PAGE

y

. # - ^ '

II.2A-2

Table I. Calculated Volwe Averaged Flux Spectra in GODIVA*

Group Group Mdpoir.t Flux/Unit Energy Group Group Midpoint Mux/Unit Energy Group Energy (cV) (n/ca 2-sec-eV) Group Energy (eV) (n/cn)2-sec-ev)

1 1.0 0002-0 5 1.00002-20 65 1.87902*05 3 .77702-06 2 5 .0000E-02 1.00002-20 66 1.97502*05 3.84302-06 3 2 .57001 -01 3 .7140E-11 67 2 .07602*05 3 .90*02 -06 * 7 .69702-01 1 .8*602-10 68 2.18302*05 3.98302-06 5 1.75402*00 8 . *2502 -10 69 2.35502*05 4 . 0*702-06 6 3 .71302*00 1.72002-09 70 2.60202*05 4 .06802-06 7 7 .86002*00 1.26302-09 71 2.90202*05 4 .09902-06 0 1 .66*02*01 2 .09102-09 72 2.90902*05 4 .13702-06 9 2 .99302*01 2 .75302-09 73 2.95902*05 3 .77*02 -05

10 4 .25602*01 3 . 3 * * 0 2 - 0 9 7* 2 .97902*05 4 .17602-06 11 5 .46502*01 2 .62302-09 75 3.00202*05 4 .23102-06 12 8 .13702*01 9 .62202-09 76 3.17902*05 4 . 16602-06 13 1.34208*02 1 .46502-08 77 3.51302*05 4 .16802-06 1 * 1.90702*02 1.80302-08 78 3.88202*05 4 .11702-06 15 2.4490E*C2 1.61002-08 79 * . 29102*05 4 . 02002-06 16 3 .64702*02 2 .62702-03 80 • . 7 * 2 0 2 * 0 5 3.89202-06 17 6 .01302*02 3. 53402-09 81 5.10602*05 3.78302-06 18 8 .54801*02 « .73802-08 82 5.36802*05 3 .70502-06 19 1.0980E»03 5 .57102-08 83 5.64302*05 3.61802-06 20 1.*090E*03 7 .11302-08 8* 5 .93302*05 3.«9302-06 21 1.81002*03 8 .6 *002 -08 R5 6.23702*05 3 .37802-06 22 2 .1 *208*03 1.06802-07 8b 6.55702*05 3 .2 *002-06 23 2 .36702*03 1.069OE-O7 87 6 .8 )302*05 3 .12502-06 2* 2 .5 *902*03 1.16102-07 88 7 .24602*05 3.0290Z-06 25 2 .68002*03 1.?6102-07 89 7.61802*05 2 .92602-06 26 2 .89102*03 1.31202-07 90 8.00802*05 2 .83002-06 27 3 .19502*03 1.39902-07 91 8.41902*05 2 . 72 702-06 28 3 .53102*03 1.62002-07 92 8.85102*05 2.62202-06 29 4 .00702*03 1.81002-07 93 9 .34*02*05 2 .51402-06 30 • . 9 1 9 0 2 * 0 3 2 .25702-07 9* 9.8210fc»05 2 .«1002-06 31 6 .31608*03 2 .85802-07 95 1.05502*06 2 .28 302-06 32 8.1100E»03 3.6170E-C7 96 1.13602*06 2 .1 *202 -06 33 1.04102*04 4 .46802-07 97 1.19502*06 2 .05102-06 34 1 .33702*0* 5 .77802-07 98 1.25602*06 1.97 302-06 35 1 .71702*0* 7 .59602-07 33 1.32002*06 1.87802-06 36 2 . 0 5 9 0 2 * 0 * 8 .38302-07 100 1.39802*06 1.79002-06 37 2 .27302*0 * 8 .65302-07 101 1.45902*06 1.70202-06 38 2 . 9 1 8 0 2 * 0 * 8 .3340S-07 102 1.53*02*06 1. ' .1502-06 39 2 .5 *202*04 1 .27*02-06 103 1.61302*06 1.53002-06 • 0 2 . 6 5 3 0 2 * 0 * 1.03802-06 10* 1.69502*06 1 .4*502-06 • 1 2 . 7 7 5 0 2 * 0 * 1 . 10602-06 105 1.78202*06 1.36202-06 42 3 . 0 1 6 0 2 * 0 * 1.21802-06 106 1.87*02*06 1.27702-06 43 3 . 3 0 7 0 2 * 0 * 1.35608-06 107 1.97002*06 1.19902-06 »• 3 . 7 5 9 0 2 * 0 * 1.52902-06 108 2.07102*06 1.12002-06 45 * . 3 5 9 0 2 * 0 * 1.71202-06 109 2.17702*06 1 .0*502-06 •6 • - 93902*00 1 .93*02-06 110 2.26902*06 9 . 8 * ; 0 2 - T 7 •7 5 .45202*0 * 2 .00302-06 111 2.33602*06 9 . * 1 9 0 2 - 0 7 48 6 .19702*0 * 2 .17302-06 112 2.37502*06 9 .17602-07 • 9 6 . 9 6 9 0 2 * 0 * 2 . 3 * 1 0 2 - 0 6 113 2 . » 26 02* 06 8 .88302-07 SO 7 .57502*0 * 2.47~,02-06 1 1 * 2 .52902*06 8 .29502-07 51 8 .10002*0 * 2 .62302-06 115 2.65902*06 7. 59902-07 52 8.<<5102*0« 2 .77 *02 -06 116 2.79502*06 6 .92002-07 53 9 .22802*0* 2.8140E-06 117 2 .9 )802*06 6 .27502-07 54 1 .0*602*05 2 .93702-06 118 3.08902*06 5 .67702-07 55 1.1J90f.*05 3 .07702-06 119 l .«2302*06 4 .57802-07 56 1 .19802*0* 3. 1530E-06 120 «.08602*06 2 .96002-07 57 1.25902*05 3. 23002-06 121 ».¥9102*0ft 1.63002-07 58 1 .32*05*05 3. 3020B-06 122 5.77702*06 9 .69702-08 59 1.39202*05 3 .38102-06 123 6 .38*02*06 6 .60502-08 60 1.«6302*05 3. «««02-06 12* 7 .4*502*06 3 .38402-08 61 1.53802*05 3 .52202-06 125 9 .09*02*06 1.11102-08 62 1.61702*05 3. 59502-06 126 1.11102*07 2 .80108-09 63 1.70002*05 3. 65 902-C6 127 1.*7702*07 2 .93202-10 64 1.78702*05 3.7130E-06 128 2 .00002*07 1.46602-10

'Two energy points Mere added to the 126 group library 2 6 to extend the energy mesh to Include 10*5 e v to 20 MeV.

II.2A-3

•> -o TI r m C i- •!-»

r - N O *

l> c | •> c c c c \> \> \>

( / ^ L O m c D C O C O C O C O C O C O C A C A C A O O ^ ^ ^* *"•

2 3 5 U(n, f ) 2 3 5 U(7) 2 3 5 U(n, Y ) 2 3 8 U(n,f ) 2 3 8 u f r ) 2 3 8 U(n,n ' , 1st) 2 3 8 U(n,n ' , 2nd) 2 3 8 U(n,n ' , 3rd) 2 3 8 U(n,n ' , 4th) 2 3 8 U(n , Y ) 2 3 9 Pu(n,f) 2 3 9Pu(V) 2 3 9 Pu(n, Y ) 2«»0pu(-) 2-°Pu(n, Y) 2 , t lPu(n,f) 2 , t lPu(v) 2 , t JPu(n, Y)

CM CO CM

en CM

CO CM

CO CM

CO CM

CO CM

en CM

CO CM

m CM

CO CM

CO CM

J-CM CM CM CM

J-CM

0 o 0 A A A A A o 0 0

A A A A • A

•

•

• A

0 o o o A A A A • o o A A A A •

A A

• • • * * A

1. Each box contains a 6x6 energy group covariance matrix. The blank boxes contain null elements.

22 2. A Indicates the evaluation has been used In the analysis. 3. OIndicates the evaluation has been used in the analysis, 2 2 and is in

some way dependent upon 2 3 5 U . 4. ^Covariance matrices exist in COVERX format, but have not yet been

used in analysis.

Fig. A-1. Fission Spectrum Covariance Matrix Library (GODIVA Weighting)

II.2A-4

(4) The relative covarlance of 2 3 9 P u capture 1s the sum of the relative covarlances for o, r, and 2 5 o . .

(5) The relative covarlance between 2 3 9 P u capture and 2 3 5 U fission Is the relative covariance for 2 5a^. Similarly arguments can be made to deduce relative covariance ma­

trices between 2 3 8U fission and 2 3 5 U fission and between 2 3 8 U fission and 2 3 9 P u capture cross sectior.s. Perey has shown 2 that when the covarlance matrix for a cross section is to be determined from the covarlance matri­ces of ratios and other cross sections, it is necessary in the reduction to group form to weight the error files with the cross section whose co-variance is being determined. This was implemented properly in this work for the matrices which required only one reaction for weighting. However, off-diagonal group matrices (e.g. \ 2 3 9Pu(n,y), 2 3 9Pu(n,f))) for which the 2 3 5 U covarlance file should have been weighted bilinearly (e.g. by the 2 3 9Pu(n,f) cross section at one energy and by the 2 3 9Pu(n,y) cross section at the other) were approximated by weighting with the 2 3 5 U cross section itself. This approximation was found to be unsatisfactory in the case of the correlation matrices of the 2 3 5U(n,f) and of the 2 3 9Pu(n,y), as well as the correlation matrices of the 2 3 8U(n,f) and of the 2 3 9Pu(n,y). Work 1s 1n progress (7/77) to correct this deficiency, however, and these files will be Included in our library at a later time. Additional off-diagonal components are Introduced due to the uncertainty in 2 l 2 C f V affecting other \T evaluations.

Tables II through VII present several of the Important covarlance files of the Fission Spectrum CovaHance Matrix library 1n the form of

relative standard deviations and correlation matrices (matrix elements

II.2A-5

v j Table I I . Standard Deviation and Correlation Matrix of the 2 3 5 U ( n , f )

Cross Sections

ENERGY RANGE (EV) % REL GPCUP 1 2.0OOE*07— 3.679E + 06— 1.3S3E»06— 4.979E+05— 1.832E*05— 4.087E + 04—

3.679E+06 1. 353E*C6 4. 979E+C5 1.832E»05 4. 087E+04 1.000E-05

STD-DfV 3 . 1 2 . J 2 .7 2 . 8 2 . 7 3 .3

1 2 3 4 5 6

1C0O 546 184 50 10 0

1000 517 24 3 72

0

1000 7«9 311

0

100O 516 282

1000 610 1000

Table I I I . Standard Deviation and Correlation Matrix of the 2 3 5 U(n ,y ) Cross Sections

vJ ENERGY RANGE (EV) \ REL GROUP 1

2 . 0 0 0 E * 0 7 - -3 .679E*06— 1.353E*06— 4.979E*05— 1.832E*05— 4.087E + 04—

STD-DEV 3.679E*06 61 .8 1 1000 1. 353E»C6 60.0 2 730 1000 4.97^E*05 39.7 3 593 763 1000 1.832E*05 24 .1 4 358 417 728 4.087E*C4 10.9 5 149 19 3 292 1.000E-05 8.4 6 97 100 150

1000 502 248

1000 633 1Q00

Table IV. Standard Deviation and Correlation Matrix of the 2 3 8 U ( n , f ) Cross Sections

ENERGY RANGE (EV) % REL GROUP 1 STD-DIV

2 .000E*07— 3.679E*06 3 . 1 3.679E*06— 1.353E*06 2 .5 1.353B*06-- 4.979E*05 2 .6 4 .979E+05-- 1.832E*05 3 .1 1.832E*05— 4. 087E*04 7 .8 4 .087E*04- - 1.000E-05107.1

1 2 3 4 5 6

1CC0 5U2 272

53 -2 0

1000 621 241 32

0

1000 ?52

40 0

1000 475

7 1000

8 1000

II.2A-6

Table V. Standard Deviation and Correlation Matrix of the 2~8U(n,Y) Cross Sections

EMEBGT RANGE (E¥) % BEL GROUP 1 2 3 STD-DE?

2 .000E*07— 3 .679E*06 5 1 . 8 1 1000 3 . 6 7 9 E * 0 6 ~ 1 .353E*06 1 7 . 8 2 922 1000 1.3S3E*06— 4 .979E*05 1 9 . 8 3 449 611 1000 4 .979E»05— 1.832E*05 1 2 . 7 * 402 547 857 1 .832E*05— 4 .087E*04 7 . 6 5 327 427 618 4 .087E*04— 1 .000E-05 9 . 6 6 68 150 402

1000 769 400

1000 500 1000

Table VI. Standard Deviation and Correlation Matrix of the 2 3 , P u ( n , f ) Cross Sections

ENERGY RANGE (g?) 1 BEL GfiCOP 1

2.000E+07— 3.679E*06— 1.353E»06— 4.979E*05— 1 . 8 3 2 E * 0 5 -4 . 0 8 7 £ * 0 4 ~

3.679E + 06 1. 353E*06 «!. 979E*05 1.832E + 05 4.087£*04 ;. OOOE-05

SID-DE? 3 . 1 2 . 4 2 . 7 2 . 8 2 . 8 3 . 4

1 2 3 4 5 6

1000 544 184

51 9 0

1000 511 242 74 - 1

Table VII. Standard Deviation and Correlation Matrix of the 2 3 9?uCv) Cross Sections

ENERGY RANGE (EV) % BEL GROUP 1

2 .000E*07— 3.679E*06— 1.353E + 06 - -4 . 9 7 9 E * 0 5 ~ 1.832E»05— 4.087E*04—

3 . 679E*06 1.353E*06 4 .979E*05 1. 832E»0r> 4 .087E*04 1 .000E-05

STD-DIV 1 .3 0 . 7 0 . 5 0 . 8 0 . 8 0 . 8

1C00 892 1000

-278 58 - 6 6 5 -458 - 6 6 5 - 4 5 8 -665 - 4 5 8

1000 748 1000 310 509

1 271 1000 570 1000

1000 793 1000 793 1000 1000 793 1000 1000 1000

II.2A-7

multiplied by 1000 for ease in reading) 1n the six-group structure se­lected for analysis. 2 2 Figures A-2 through A-9 illustrate corresponding correlation plots In six-group processed form. The GOOIVA spectrum (Table I) was used as the weighting function. Note that the energy-dependent correlation matrix for a specific reaction Is symmetric. The complete covarlance file with GOOIVA weighting is shown In tabular form In Appendix D.

II.2A-8

O

Fig. A-2. Standaru Deviation and Correlation Matrix of the 2 3 5 I K ^ f) Cross Sections.

Fig. A-3. Standard Deviation and Correlation Matrix of the 235U(ri,y) Cross Sections.

II.2A-9

*-CT"rj

Fig. A-4. Standard Deviation and Correlation Matrix of the 2 3 SU(\T) Cross Sections.

**"09*> "^-conj

Fig. A-5. Standard Deviation and Correlation Matrix of the 2 3 8U(n,f) Cross Sections.

II.2A-10

U

' • " * * • *

' * * • * ^

r«««r i y

Fig. A-6. Standard Deviation and Correlation Matrix of the 2 3 8U(n ty) Cross Sections.

pig. A-7. Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,f) Cross Sections.

II.2A-11

*-<z»r,

Fig. A-8. Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,y) Cross Sections.

(NOTE: Where uncertainties in this and the following figures are shown as dotted lines, values have been extrapolated into regions where covariance files have not yet been obtained.)

Fig. A-9. Standard Deviation and Correlation Matrix Cross Sections.

of the 2 3 5Pu(7)

II.2B-1

B. LMFBR Core Physics Covarlance Matrix Library. Our existing LMFBR Core Physics Covar1ar.ce Matrix Library (weighted with a calculated ZPR-6/7 spectrum (Table VIII)) 1s Illustrated In Fig. B-l. (The ZPR-6/7 flux/energy 1s similar to a 1/E shape joined to a fission spectrum at approximately 800 keV.) This figure represents a square matrix Including all reactions for which uncertainty Information was developed 1n the ten-group structure for analysis of ZPR-6/7. Each individual box 1s itself a square matrix with ten energy groups on a side. The total number of elements in the full matrix 1s 115600. However, clearly most of these are null elements Indicating no correlation. The boxes along the diagonal refer to the covarlance of a specific reaction as a function of energy. Off-diagonal boxes reflect correlations between reaction types. For example, elements reflecting correlations between the 2 3 9Pu(n,y) and the 2 3 9Pu(n,f) cross sections take Into account that many of the existing experiments are actually ratio measurements (a). The relative covarlance matrix elements linking "v values for ewery pair of fissionable materials was taken as 1.33 x 10~ 5 because all \T measurements above the thermal energy region have been measured relative to v p ( 2 5 2 C f ) , and (1.33 x 10" s)

was the relative standard error assigned to " v f 2 5 ^ ) for ENDF/B-IV. The covarlance evaluations for N, C, and 0 were taken directly from the ENDF/B-IV. Only the Independently evaluated covarlance files for carbon were processed; multlgroup covarlance files for other reaction types are easily derived. The covarlance description of 2 3 8U(n,f) and 2 3 9Pu(n,f) does not Include the more recent evaluation of Peelle9 which considers the correlations through standards (e.g. 2 3 5U(n,f)); this 1nformailon 1s Included 1n the Fission Spectrum Covarlance Matrix Library of the previous section, which reports later work.

BLANK PAGE

II.2B-2

Table V I I I . Calculated Central Flux Spectna in ZPR-6/7 a

nun Group Midpoint Flux/Unit Energy Group Group Midpoint Flux/Unit Energy w a j Energy ( t f ) (n/cn^-sec-eV) Group Energy (eV) (n/o*-sec-ev)

1 1 .00008-05 1.00008-20 65 1.87908*05 1 .47508-10 2 5 .00008-02 1.00008-20 66 1.97508*05 1 .20808-10 3 2 .5700E-01 6 . 0 5 1 0 8 - 1 * 67 2 .07608*05 1 .13508-10 « 7 .69708-01 1 .9*708-13 68 2 .18308*05 1 .19808-10 5 1 .75*08*00 2 .36108-12 69 2 .35508*05 1 .10608-10 6 3 .71308*00 5 .8 *008 -12 70 2 .60208*05 1 .02308-10 7 7 .86008*00 6 .68508-12 71 2 .80208*05 8 . 8 8 7 0 8 - 1 1 8 1.66408*01 2 .75908-11 72 2 .90908*05 9 .05808 -11 9 2 .99308*01 1.19508-13 73 2 .95908*05 9 .80608-11

10 * .2560E«01 1.38808-10 7* 2 .97908*05 9 .06208 -11 11 5 .46508*01 2 .58908-10 75 3 .00208*05 8 .52408 -11 12 8 .13708*01 4 .78708-10 76 3 .17908*05 8 .58308-11 13 1 .3*208*02 8 .01008-10 77 3 .51308*05 6 .96908 -11 1 * 1 .90708*02 1.40208-09 78 3 .88208*05 6 .79208-11 IS 2.««90B*02 1.61608-09 79 « .29108*05 3 .64408-11 16 3 .6 *708*02 2 .07808-09 80 * . 7 * 2 0 8 * 0 5 4 .52308 -11 17 6 .01308*02 2 .61 *08 -09 81 5 .10608*05 5 . 6 3 3 0 8 - 1 1 18 8 .5 *808*02 2 .89208-09 82 5 .36808*05 5 .15808-11 1 * 1 .098)8*03 2 .92208-09 83 5 .6 *308*05 4 .54108 -11 20 1.«090E*03 2 .85308-09 8* 5 .93308*05 4 .23508-11 21 1.81001*03 2.«730B-09 85 6 .23708*05 3 .91008-11 22 2 .1 *208*0 3 1 .63508-09 86 6 .55708*05 3 .45308-11 23 2 .3670E*03 8 .66108-10 87 6 .89308*05 2 .88408 -11 2 * 2 . 5 * 9 0 8 * 0 3 • . 3 2 8 0 8 - 1 0 88 7 . 2 * 6 0 8 * 0 5 2 .70008 -11 25 2 .68008*03 2 .33508-10 89 7 .61808*05 2 .55108-11 26 2 .89108*03 1.36208-10 90 6 .00808*05 2 .26808-11 27 3 .19508*03 2 .99208-10 91 8 .41908*05 2 .12808-11 28 3 .53108*03 6 .03708-10 92 8 .85108*05 1 .57708-11 29 • . 0 0 7 0 8 * 0 3 8 .30308-10 93 9 . 3 4 * 0 8 * 0 5 1 .35508-11 30 • . 9 1 9 0 8 * 0 3 9 . •9808-10 9* 9 .32108*05 1 .09308-11 31 6 .31608*03 9 . 5 7 * 0 8 - 1 0 95 1 .05508*06 9 .70608-12 32 8 .11008*03 8 .28 *08 -10 96 1.13608*06 1 .43508-11 33 1 .0 *108*0 * 9 . 3 5 * 0 8 - 1 0 97 1.19508*06 1 .31908-11 3* 1 .33708*0* 8 .83008-10 98 1 .25608*06 1 .20*08-11 35 1 .71708*0* 7 .01008-10 99 1.32008*06 7 .76108-12 36 2 . 0 5 9 0 8 * 0 * 8 .40908-10 100 1.38808*06 8 .88508-12 37 2 . 2 7 3 0 8 * 0 * 7 .88708-10 101 1.«590B*06 7 .97508-12 38 2 .«1608»0* 8 .36208-10 102 1 .53*08*06 7 .10908-12 39 2 . 5 * 2 0 8 * 0 * 1.15108-09 103 1.61308*06 6 .21708-12 •0 2 . 6 5 3 0 8 * 0 * 8 .12308-10 109 1 .69508*06 6 .22808-12 • 1 2 .7750E*0* 2 .30908-10 105 1.78208*06 5 .79808-12 •2 3 . 0 1 6 0 8 * 0 * 2 .49508-10 106 1 .87*08*06 4 .87608-12 •3 3 .30708*0* • . 5 0 2 0 8 - 1 0 107 1.97008*06 4 .38408-12 M 3 . 7 5 9 0 8 * 0 * • . 5 9 1 0 8 - 1 0 108 2 .07108*06 3 .93508-12 • 5 « . 3 5 9 0 8 * 0 * • . 7 6 0 0 8 - 1 0 109 2 .17708*06 3 .89008-12 •6 • . 9 3 9 0 8 * 0 * • . 2 1 7 0 8 - 1 0 110 2 .26908*06 4 .12308-12 •7 5 . * 5 2 0 E * 0 * 2 . « 5 * 0 8 - 1 0 1 " 2.33608*06 4 .24308-12 •8 6 .19708*0 * 3 . 6 0 * 0 8 - 1 0 112 2 .37508*06 4 .19508-12 •9 6 . 9 6 9 0 8 * 0 * 3 .88*08 -10 113 2 . *2608*06 3 .51201-12 50 7 .57508*0 * 2 .81208-10 1 1 * 2 .52908*06 3 .16108-12 51 8 . 1 0 0 0 8 * 0 * « .28708-10 115 2 .65908*06 2 .99008-12 52 8 . * S 1 0 8 * 0 * 1.99708-10 m 2.79508*06 2 .49808-12 53 9 . 2 2 8 0 8 * 0 * 2 . 5700* -10 117 2 .93808*06 2 .21408-12 5« 1 .0*608*05 2 .11608-10 118 3 .08908*06 2 .01008-12 55 1.13908*05 2 .22508-10 119 3.«2308*06 1 .32508-12 56 1.19808*05 2 . 3 * 1 0 8 - 1 0 120 * . 0 8 6 0 8 * 0 6 8 .30708-13 57 1.25908*05 2 . 2 * 1 0 8 - 1 0 W l • . 9 9 1 0 8 * 0 6 4 .81008 -13 58 1 .32*08*05 2 .16008-10 122 5 .77708*06 2 .75308-13 59 1.39208*05 2 .09108-10 123 6 . 3 6 * 0 8 * 0 6 1 .91608-13 60 1.*6308»05

1.53808*05 1.36108-10 1i"» 7.44508*06 9 .49408-14

61 1.*6308»05 1.53808*05 1.65108-10 125 9 .09408*06 3 .21508-14

62 1.61708*05 1.68008-10 126 1.11108*07 6 .47308-15 63 1.70008*05 1.51908-10 127 1.47708*07 9 .96308-16 6* 1.7«708*05 1 .8*608-10 128 2 .00008*07 « .98108-16

•Two energy points were added to the 126 group 1* 10-5 eV to ?0 MeV,

brary?* to extend the tntrgy ntsh to Include

added to the 126 group 1* 10-5 eV to ?0 MeV, , , , i i i

II.2B-3

v j ** "O -O JZ vt c t - * * — <v m «-

r? c r> C f > C * *

#?#rrrf#H**##*"*l£5SsH? * * J- .» * V V V V V * * * J- o o o o .-* M (»*

Ht) 2nd) 3rt)

2 5 H j ( n . f ) 2 ! 5 U H ) 2 J i U(n . t5 2 l a U ( " . f ) 2 3 d U Q < i S U ( n , n \ i 3 * U ( r . n \ 2 3 » U { i i , n \ ^'ufn.n". 4th)

- 3 *U( !V, ) : : ' *Pu(«. f ) ; >*Pu(7) •-'*Pu(n.T; '"'PutT) "• ; Pu(rv,} •''•'uln.f) - WT) ' * * u ( " , r ) - ^ ( t o u i ) "C(n,n". 1st) u C(n ,n" , cont.J U C ( n . t ) , 2C(n.„) '"Nl toUl)

"•H(el»sttc) '"mn.n') !*!»(n.-,) "iKn.p) "(Kn.c) I 6 0( to t i l ) u 0 ( e l a s t i c ) "O(n.n') I 60(n.p) 1 6 0(n . a )

• i • • • • •

• ^ 1

A • • J • ^^

• •

• •

A A A

# • , A • • ... — A A

... —

i * m j | i • • • - r

I 1 j • — - - r -

I I • — - - r -

• • i # • • i ! t ; • J i • i t

• • 1 • 1 1

* ; :

1

• i f • • • 1 i « • t • •

f • •

! ., • • t i • • • i

• • • •

CEGKJ • • C G 4 • •

, _ _ _J 1 i _ 1 + •

1. Each box represents a 10 x 10 group covariance matrix. The blank boxes contain null elements.

2. A indicates that the evaluation used in the analysis is described in the FORSS 2 3 report.

3. £ Covariance matrices exist in COVERX format, but were not used in analysis.

Fig. B-l. LMFBR Core Physics Covariance Matrix Library (ZPR-6/7 Weighting).

II.2B-4

Tables IX-XIV present several of the Important processed covarlance files of the present LMFBR Core Physics Covarlance Matrix Library 1n the fora of relative standard deviations and correlation Matrices (matrix elements Multiplied by 1000 for ease In reading) In the ten-group struc­ture selected for analysis.23*2"1 Figures B-2 throughB-10 Illustrate so«e of the Interesting correlation plots In the ten-group processed form. These figures clearly represent only a small portion of the total covarl­ance library described 1n F1g.B-l. The ZPR-6/7 spectrum (Table VIII) was used as the weighting function. The complete LMFBR Core Physics Co-variance Matrix Library with ZPR-6/7 weighting Is shown In tabular fori in Appendix E.

u II.2B-5

Table IX. Relative Standard Deviation and Correlation Matrix of the 2 3 8Uln,f) Cross Sections

EBEB6T BftRGE (BT) I BEL GBOOP 1 2 3 * 5 6 7 8 9 10 STD-DET

1 . 7 3 3 E * 0 7 ~ 1.3538*06 2 . 2 1 1000 1 .353E*06— 9.9798*05 10 .9 2 203 1000 9 . 9 7 9 B * 0 5 ~ 1.832E*0S 0 . 0 3 0 0 0 1 .832E*05- - 1.1118*05 0 . 0 * 0 0 0 0 1 . 1 1 1 8 * 0 5 - - 6.738E*09 0 . 0 5 0 0 0 0 0 6 .738E*09— 9.087B*0* 0 .0 8 0 0 0 0 0 0 9 . 0 8 7 8 * 0 9 — 2 .979E*0* 0 . 0 7 0 0 0 0 0 0 0 2 .979E*09— 9.1198*03 0 . 0 8 0 0 0 0 0 0 0 0 9 .119E*03— 1.23*E*03 0 .0 9 0 0 0 0 0 0 0 0 0 1.239E*03— 1. 0008-05 0 . 0 10 0 0 0 0 0 0 0 0 0

u

Table X. Relative Standard Deviation and Correlation Matrix of the 2 3 8U(n,Y) Cross Sections

8BBRGY BBRGE (ET) * BEL GBOOP 1 8 10 5TD-DET

1 .7338*07— 1.3538*06 18.8 1 1000 1 .3538*06— 4.979E*05 13.7 2 585 1000 « .979E*05— 1.832E*05 12 .9 3 518 834 1000 1.8328*05— 1.1118*05 10.3 4 • 5« 615 830 1000 U111E*05— 6.7388*04 8 .7 5 291 973 469 569 1000 6 . 73 SB* 09— 4 .0878*04 « .8 6 178 310 395 355 710 1000 9 .0878*09— 2.4798*09 10 .1 7 115 276 299 279 510 792 1000 2 . 4 7 9 8 * 0 9 - - 9.119E*03 12.3 8 158 414 382 308 9 97 926 668 1000 9 .119E*03— 1.2398*03 9 .6 9 119 966 3*0 202 397 339 358 580 1000 1 .2398*03 - - 1.000E-05 7 .3 10 0 51 31 15 127 216 201 189 500 1000

Table XI. Relative Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,f) Cross Sections

SRBRGT BARGE (BT) % BEL CBOOP 1 2 3 9 5 6 7 8 9 STD-DE?

1.7338*07— 1.3538*06 6 .0 1 1000 1 .3538*06— 9.9798*05 5 .7 2 792 9^9798*05— 1.8326*05 10.9 3 3 13 1.832E*05— 1.1118*05 1 9 . } 9 193 1 .1118*05— 6.7388*04 12.9 5 209 6 . 7 3 8 8 * 0 9 - - 4 .0878*04 6 ,7 6 382 4 :0878*04— 2.9798*09 3 .2 7 564 2 * 9 7 9 8 * 0 9 - - 9 .1198*03 3.8 8 929 9 f 1118*03— 1.2398*03 5 .1 9 329 1 .2398*03— 1.000E-05 3.9 10 279

10

1000 502 265 257 951 799 957 395 292

1000 589 675 329 422 238 180 152

1000 879 179 229 139 102

86

1000 373 271 192 108 91

1000 529 297 107 158

1000 699 1000 393 496 1000 320 206 720 1000

u

II.2B-6

Table XII. Relative Standard Deviation and Correlation Matrix of the Pu(n.y) Cross Sections

BBB8GY M I C E (ET)

1.7338*07— 1.3538*06— 8 . 9 7 9 8 * 0 5 - -1 . 8328*05— 1.1118*05— 6 . 7 3 8 8 * 0 * - -* . 0 8 7 8 * 0 * — 2 . * 7 9 B * 8 « - -9 . 1 1 9 8 * 0 3 - -1 .23*8*03—

% » E l GiOUP 1 STD-DBT

1.3538*06 0 .0 1 1000 • . 9 7 9 1 * 0 5 1 9 . 1 2 0 1.8328*05 11 .5 3 0 1.1118*05 2 3 . 2 • 0 8 . 7 3 8 8 * 0 * 13.3 5 0

12 .2 6 0 7 . 9 7 0 8 .5 8 0

12 .0 9 0 9 . 5 10 0

10

«. 0878*0 * 2 . * 7 9 B * 0 * 9 .1198*03 1.23*8*03 1.0008-05

1000 99 1000

352 538 1000 -199 58C 35* 1000 - 3 * 0 113 - 3 9 1 579

223 155 1*9 38 98 19

188 85 18* 87 55 82

1000 38 3 * 1000 77 109 5*3 1000 87 - 1 8 2 «19 «1« 1000 17 - 5 3 152 95 881 1000

Table XIII. Correlation Submatrix Between the 2 3 9 P u (n.f) and the 2 3 9Pu(n,y) Cross Sections

BBEB6T «»BCB (ET) GIOOP 10

1 .7338*07— 1.3538*06 1 0 0 0 0 0 0 0 0 0 0 1 .3538*06— • . 9 7 9 8 * 0 5 ; I 0 1000 502 265 257 • 5 1 7*4 •57 3*5 292 • • 9 7 9 8 * 0 5 — 1.8328*05 3 1 0 502 1000 589 675 323 • 22 238 180 152 1 . 8328*05— 1.1118*05 I 1 0 265 589 1000 8 7 * 179 22« 13* 102 86 1.1118*05— 6 . 7 3 8 8 * 0 * • i 0 257 675 87* 1000 373 271 1«2 108 91 6 . 7 3 8 8 * 0 * - - « .0878*0* ( » 0 •51 329 179 373 1000 52« 2«7 187 158 * . 0 8 7 E * 0 * ~ 2 . * 798*0* 1 0 7*« 922 2 2 * 271 5 2 * 1000 699 393 320 2 . * 7 9 B * 0 * — 9.1198*03 ( » 0 •57 238 13* 1*2 2«7 699 1000 896 206 9 .1198*03— 1.23*8*03 < > 0 3*5 180 102 108 187 393 • 9 6 1000 720 1 .23*8*03— 1.0008-05 1( > 0 292 152 86 91 158 320 206 720 1900

Table XIV. Relative Standard Deviation and Correlation Matrix of the 2 3 9Pu(vr) Cross Sections

B8EB6T BBBCE (ET) X I EL GROUP 1 10

1.7338*07— 1.3538*06— • . 9 7 9 8 * 0 5 — 1.8328*05— 1.1118*05— 6 . 7 3 8 8 * 0 * — * . 0 8 7 B * 0 « — 2 . * 7 9 B * 0 * ~ 9 .1198*03—

1.3538*06 « .9798*05 1.8328*05 1.1118*05 6 .7388*0 * « .0878*0* 2. • 79E*0 * 9. 1198*03 1 .23*2*03

STO-OBT 0 .8 0 . 5 0 .8 0 .8 0 . 8 0 .8 0 .8 0 .8 0 .8

1 1000 2 -95 1000 3 - 5 2 3 8*1 1000

8*1 1000 1000 8*1

• -523 5 -523 6 -523 7 -523 3 -523 * -523

1000 1000 1000 8*1 1300 1000 1000 1000 8*1 1000 1000 1000 1000 1000 8*1 1000 1900 1000 1000 1000 1000 8*1 1000 1000 1O00 1000 1000 1000 1000

1 .23*8*03— 1.C»0*-05 0 .8 10 - 5 2 3 8*1 1000 1000 1000 1000 1000 1000 1000 1000

11.28-7

sj

^3*^7

//^G5*ry

Fig. B-2. Standard Deviation and Correlation Matrix of the 2 3 5 U(n, f ) Cross Sections.

U

i /! i

y~ "**-<* ' '*>*'<>, '"*-* •"r.os £

"**. CC»T,

Fig. B-3. Standard Deviation and Correlation Matrix of the 2 3 8 U(n,f ) Cross Sections.

(NOTE: Wh^re uncertainties in thfs and the following figures art shown as dotted lines, values have been extrapolated into regions whsre covariance files have not yet been obtained,)

II.2B-8

' • » - »

f-a»n Fig. B-4. Standard Deviation and Correlation Matrix of the 2 3 8 U(n,Y)

Cross Sections. (NOTE: The saaple Mans for the sets of aeasureaents used to obtain this uncertainty aetrix were not close to the EMiF/B-IV evaluated cross section over the Major portion of the energy spectru*. so the ras uncertainties for this case reflect pr1a«rily the real discrepancy between the saaple aean and the eval­uated cross sections. That i s , for the considerable saaple of ansureaeni data selected for this parti­cular covariance analysis, the ENOF/B-IV evaluated cross section falls -JH below the inferred enseable average over the iaportant energy region froa 10-300 keV. A consistent evaluation based solely upon differential aeasureaents nouTJ exacerbate the central 2 , c / " * f discrepancy for ZPR-6/7. Proper handling of tnis difficulty is presently a aajor challenge to the reliabil ity of the uncertainty analyses row aide by FORSS (or any Sucn systea) i f one assuaes that adjustaents to alcroscopic aeasureaents aay har* already been irxluded in EHOF/B-IV.)

'•me.* £

'-'** £•?

Fig. B-5. Standard Deviation and Correlation Matrix of the 2 3 9 Pu(n , f ) Cross Sections.

II.2B-9

vj

Fig. B-6. Standard Deviation and Correlation Matrix of the 2 3 9Pu(n,y) Cross Sections.

Fig. B-7. Standard Deviation and Correlation Matrix of the 2 3 9Pu(v) Cross Sections.

11.28-10

Fig. B-8. Correlation Submatrix Between the 2 3 9Pu(n,f) and 2 3 9Pu(n,y) Cross Sections. Note that except in the highest energy group the shape of the correlation matrix is the same as that, shown in Fig. B-5 for the 2 3 9Pu(n,f) reaction.

Fig. B-9. Standard Deviation and Correlation Matrix of the 2 l , 0Pu(n,Y) Cross Sections.

II.2B-11

O

Fig. B-IO. Standard Deviation and Correlation Matrix of the 2l,1Pu(r.,f) Cross Sections.

O

II.2C-1

C. LHFBR Shielding Covariance Matrix Library. Our existing LMFBR Shielding Covariance Matrix Library is currently limited to ha, Fe (the latter being the major constituent of stainless steel), N, 0, and C, and is illustrated in rig. C-1. These files have been used in uncertainty analysis of steel/sodium/iron,25 air/ and fusion blanket systems. 2 7 Figure C-1 represents a square matrix including all reactions for which uncertainty information was developed in the 15-group structure. Each individual box is itself a square matrix with 15 energy groups on a side. The total number of elements 1n the full matrix Is 129600. However, clearly most of these are null elements Indicating no correlation. The evaluated covariance file for Na is described in Appendix C and Includes estimates for the total, elastic, Inelastic and capture reactions. At low energies (eV range) the total cross section Is essentially the elastic cross section; i.e. the non-elastic cross section 1s essentially zero up until the first-1 /el In­elastic (-V440 keV). The non-elastic cross section and its covariance fila 1s entirely that of capture. Above the first level, for lack of better Information, we have approximated the energy-dependent uncertainty file for non-elastic to be that of the first-level Inelastic. The error file for Na elastic, however, was only evaluated between 600 eV and 150 keV and had to be derived for energies above and below these boundaries. The error files are described similarly for Iron, the major differences from Na tefng only'the energy region where the elastic covariance file was de­rived (above 1 MeV). The derived files were deduced as follows: Neglecting ether possible reaction types (e.g. (n,2n), (n,p)), assuming no correlation between uncertainties 1n the non-elastic and total cross sections, and denoting non-elastic by (n,x),

BLANK PAGE

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II.2C-2

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k^i #

1. Each box contains a 15 x 15 energy group covariance matrix. The blank boxes contain null elements.

2. A indicates the evaluation used in the analysis. 25

3. WCovariance Matrices exist in COVERX format, but have not yet been used in analysis.

Fig. C-1. LMFBR Shielding Covariance Matrix Library (l/E Weighting).

II.2C-3

°el = a T " °n,x ( 1 5 )

then the covarlance of the elastic to itself Is

and the covariance for cross reactions is

( d ael d on.x) = -< d an,x d an,x) (17)

In a recent paper, 2 5 the Na and Fe covariance files were utilized to deduce uncertainties in calculated doses through deep penetrations cf steel, sodiun, and iron. The data used in this analysis 1s presented In tabular form in Appendix F. Several of the important covarlance files are Illus­trated 1n F1gs. C-2 through C-7.

II.2C-4

"***r,

Fig. C-2. Standard Deviation and Correlation Matrix of the Na Elastic Cross Sections.

' " * * • / / » . '-en*,

Fig. C-3. Standard Deviation and Correlation Matrix of the Na Non-Elastic Cross Sections.

J

II.2C-5

•**• < y

Fig. C-4. Correlation Submatrix Between the Na Elastic and Na Non-Elastic Cross Sections.

vJ

«***7

'-con,

Fig. C-5. Standard Deviation and Correlation Matrix of the Fe Elastic Crosi Sections.

II.2C-6

**?

' * > • ' * * . ~*t*rj

Fig. C-6. Standard Deviation and Correlation Matrix of the Fe Non-Elastic Cross Sections.

"**<* eg

Fig. C-7. Correlation Submatnx Between the Fe Elastic and Fe Non-Elastic Cross Sections.

III-l

III. CONCLUSIONS

The covariance files described in this report represent a first at­tempt to report important uncertainty information which has heretofore been undocumented. The files are our current best estimates which will obviously be refined with feedback from the measurement, evaluation and analysis communities. Under the auspices of the Cross Section Evaluation Working Group (CSEWG), it is anticipated that beginning with ENOF/B Version V, many of the required covariance files will be generated and reviewed more systematically. The current effort represents our attempt to fill the gap until this information appears, to provide initial esti­mates which can be factored into the ENOF/B evaluators' considerations, and to lend insight as to how these files are to be processed and used in application.

The report represents multigroup covariance matrices including fis­sion in 2 3 5 U , 2 3 8 U , 2 3 9 P u , and 2 l t lPu; capture in 2 3 5 U , 2 3 8 U , 2 3 9 P u , 2 l , 0Pu, and 2 , t lPu; fission neutron yield (^ for 2 3 5 U , 2 3 8 U , 2 3 9 P u , 2 , f 0Pu and 2 l f lPu; elastic scattering for Na and Fe; non-elastic reactions for Na and Fe; and the first four inelastic levels for 2 3 8 U ; 1n addition to all reactions provided in the ENDF/B-IV covariance description of N, 0, and C. Other data files generated are included for reference but have not yet been tested. The report presents the multigroup data in six, ten, and fifteen energy group form corresponding to weighting of selected co-variance data with fission spectrum (GODIVA), LMFBR (ZPR-6/7) and 1/E, respectively. The data are Illustrated and tabulated 1n an edited form for convenience.

The multigroup covariance files are currently available from RSIC

III-2

and NNCSC in the COVERX format, a computer retrievable format desiqned for data uncertainty analysis and described herein. It Is the authors Intent to update this report as new covarlance files become available with subsequent Issues of ENDF/B.

p.-l

REFERENCES

F. Perey, Format Modifications 73~7, minutes of the CSEWG Meeting, December 1973 (Enclosures 6 and 1 2 ) , S. Pear ls te in , Editor , Brookhaven National Laboratory; see a lso, F. G. Perey, "Estimated Uncertainties in Nuclear Data - An Approach," Proceedings of a ConTerence on Nuclear Cross Section and Technology, Volume I I , edited by R. A. Schrack and C. D. Bowman, p. 842 (October 1975).

F. G. Perey, "The Data Covariance Fi les for ENDF/B-V, ORNL/TM-5938 (ENDF-249) (1977) .

F. G. Perey, "The Estimated Data Covariance Files of ENDF/B - Their Uses," Minutes of the CSEWG Meeting, June 17-79, 1974 (enclosure 10), S. Pear ls te in , Editor, Brookhaven National Laboratory.

C. R. Weisbin, E. M. Oblow, J . Ching, J . E. White, R. Q. Wright, and J . 0. Dr ischler , "Cross Section and Method Uncertainties: The Applica­t ion of Sensi t iv i ty Analysis to Study Their Relationship in Radiation Transport Benchmark Problems," ORNL/TM-4847 (ENDF-218) (August 1975); see also RSIC Code Collection PSR-93.

C. Y. Fu, "Covariance Fi les of ENDF/B-IV.Material 1192 ( I ron) for Reactor Appl icat ion," Oak Ridge National Laboratory internal memo­randum, March 3 1 , 1975 (reprinted here in Appendix C ) .

F. G. Perey, "Covariance Fi le for Sodium ENDF/B-IV," Oak Ridge National Laboratory internal memorandum, August 23, 1976 (reprinted here in Appendix c ) .

D. C. Larson, "Sodium Data Covariance F i l e for Reactor Studies," Oak Ridge National Laboratory internal memorandum, March 27, 'i975 (reprinted here i;i Appendix C ) .

R. W. Peelle, "Error Fi les for NUBAR(E)," Oak Ridge National Laboratory internal memorandum, February 3, 1976 (reprinted here in Appendix C ) .

R. W. Pee l le , "Uncertainty Fi les for Fission Ratios 2 3 8 u / 2 3 5 u and 2 3 9 P u / 2 3 5 U , " Oak Ridge National Laboratory internal memorandum, February 17, 1977 (reprinted here in Appendix C ) .

F. G. Perey, "238-U Inelast ic Data Covariance F i l e for Reactor Studies," Oak Ridge National Laboratory internal memorandum, March 3 1 , 1975 (reprinted here in Appendix C ) .

R. Gwin, "Error Fi les for the 2 3 9 P u Neutron Capture and Fission Cross Sections," Oak Ridge National Laboratory internal memorandum, July 7, 1975 (reprinted here in Appendix C ) .

R-2

u 12. F. OifiliDDO, 6 . de Saussure, and R. B. Perez, "Covariance Files for

v, o(n,f) and o(n,y) for 2 3 8 U , M Oak Ridge National Laboratory internal mevirandum, July 14, 1975 (reprinted here in Appendix C).

13. E. T. Totalinson, G. de Saussure and C. R. Ueisbin, "Sensitivity Analysis of TRX-2 Lattice Parameters with Emphasis on Epithermal 2 3 8 U Capture," EPRI Research Project 612, Final Report (March 1977).

14. D. Garber, Compiler, "ENDF/B Summary Documentation," BNL-17541 (ENDF-201) Second Edition (1975).

15. L. W. Weston, "Error Files for 2 l f 0 Pu Neutron Capture and 2 1 , 1 Pu Neutron Capture and Fission Cross Sections," Oak Ridge National Laboratory internal memorandum, July 1 , 1975 (reprinted here in Appendix C).

16. F. C. Dif i l ippo, "SUR, A Program to Generate Error Covariance Files," ORNL/TW-5223 (March 1976). The data in this report were derived from discussions with G. de Saussure, R. B. Perez, R. Gwin, L. W. Weston, and R. W. Peelle; the principles behind the procedures described are discussed in F. G. Perey, G. de Saussure, and R. B. Perez, "Estimated Data Covariance Files for Evaluated Cross Sections - Examples for 2 3 5 U and 2 3 8 U , " Advanced Reactors: Physics, Design, and Economics, Edited by Kallfelz and Karam, Pergamon Press, p. 578 (1975).

17. W. P. Poenitz and A. B. Smith, Editors, "Proceedings of the NEANDC/ J NENCRP Specialists Meeting on Fast Neutron Fission Cross Sections of 233 U f 23*>u, 2 3 8 U ) a n d 239pU i.. ANL-76-90 (June 1976).

18. W. Poenitz, Argonne National Laboratory, privato communication (March 1877).

19. G. E. Hansen and H. C. Paxton, "Reevaluated Critical Specifications of Some LASL Fast Neutron Systems," LA-4208, 1969.

20. G. E. Hansen, "Status of Computational and Experimental Correlation for Los Alamos Fast Neutron Critical Assemblies," Proc. of Seminar on Physics of Fast and Intermediate Reactors, Vol. I , IAEA, Vienna, 1962.

21. C. E. T i l l , L. G. LeSage, R. A. Karam et a l . , "ZPR-6 Assemblies 6A and 7: Benchmark Specifications for the Two Large 5",ingle-Core-Zone Critical Assemblies - 2 3 5U-Fueled Assembly 6A and Plutonium-Fueled Assembly 7 - LMFBR Demonstration Reactor Benchmark Program," Applied Physics Divisior Annual Report, July : , 1970 to June 30, 1971, 86-101, ANL-7910.

22. C. R. Wei'bin and R. k. Peelle, "Propagation of Uncertainties in Fission Cross Section Standards in the Interpretation and Utilization of Critical Benchmark Measurements," Proceedings of International Specialists Symposium on Neutron Standards and Applications, National /£& Bureau of Standards, Washington, p. C., (March 28-31, 1977). * • '

R-3

J 23. C. R. Weisbin, J . H. Marable, J . L. Lucius, E. M. Oblow, F. R. Mynatt, R. W. Peelle, and F. G. Perey, "Application of FORSS Sensitivity and Uncertainty Methodology to Fast Reactor Benchmark Analysis," ORNL/TH-5563 (ENDF-236) (December 1976).

24. J. H. Marable and C. R. Weisbin, "Performance Parameter Uncertainties for a Urge LMFBR," Trans. Am. Nucl. Soc. 26, 542 (1977).

25. E. M. Oblow and C. R. Weisbin, "Fast Reactor Shield Sensitivity Studies for Steel-Sodium-Iron Systems," Fifth International Confer­ence on Reactor Shielding, Knoxville, Tenn., April 18-22, 1977.

26. C. R. Weisbin, R. W. Roussin, J . E. White, and R. Q. Wright, "Speci­fication for Pseudo-Composition Independent Fine-Group and Composi­tion-Dependent Fine- and Broad-Group LMFBR Neutron-Gamma Libraries at ORNL," ORNL-TM-5142 (ENDF-224) (December 1975).

27. R. G. Alsmiller, J r . , J . Barish, and C. R. Weisbin, "Uncertainties in Calculated Heating and Radiation Damage in the Toroidal Field Coil of a Tckamak Experimental Power Reactor Due to Neutron Cross-Section Errors," ORNL/TM-5198 (March 1976).

J

A-1

APPENDIX A COVERX Fonnat

C J

*>

A-J

C REVISED 0 9 / 3 0 / 7 6 C CE COVERX CE THIS PILE CONTAINS CROSS SECTIONS, CE STANDARD DEVIATIONS, AMD CE BT DESIGNATION EITHER COVARIANCE, CE RELATIVE COVARIAICE, CE OR CORRELATION HATRICES. C CE A FILE SUCH AS THIS IS HEEDED BT ORML - PORSS C C J . L. LHCIfJS C

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CS CS C S • * * • • • « * • • • > * » ( R E P E A T FOH ALL MATRICES) CS * "ATPIX COHTRCL ALHATS CS * BLOCK CCMTROL ALHATS CS » * * « • « « * « « « • (RtPEAT FOR ALL SLOCKS) CS • * HATPIX DATA ALHATS

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q B 8 i M e , p , « » • « 1 a o w n s o « a » -o a H o a a o a 3 M a . ? ? sa^ S) a a » o a *4 •o «> a o wt >4 to M a Ul M i» a a * M *• M O a M • M H n » w • « o re '4

re ui o o w ^ a H) r re HJ M to to r * : ^ s * : ^ s •e e M M to M to O m a >» a n « e 4 9

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A-5

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CD HATERIAL - REACTION TTPE CROSS SECTIONS CR AMD ERBCR PILES CL (CRS(J) ,J = 1,NCBOOP) ,(ERROR (J) ,J=1,IGROOP) CB 2*IGROOP C CB PORHAT(«H SD , 5 E 1 2 . V ( 6 E 1 2 . «) ) C CD CRS CROSS SECTION CD ERROR STANDARD DETIATION C

c

CB HATRIX CONTROL CL H A T 1 , H T 1 , HAT.? , R T 2 , R B L 0 K CR 5 C CB PORHAT(*H 6D , 5 I f ) C CD HAT1 MATERIAL 1 IDENTIFICATION NOHBER CD HT1 BR ACTIOS TtPE 1 IDENTIFICATION MBBER CD RAT2 RATERIAL 2 IDENTIFICATION ROBBER CD BT2 BEACTIOR TTPE 2 IDENTIFICATION AOHBER CD IBLOK IQRBEB OP BLOCKS INTO WHICH RATRIX I ? SdBDITIDED c

c

CR BLOCK CCNTKOL CL (JBAND(J) ,TJJ (J) ,J=1,RGROUP; , (LGRP(N) ,R=1 ,NBLOK) C CW 2*NGHO0P •NBLCK C CB PORHAT(«H 7D , 1 1 1 6 / ( 1 2 1 6 ) ) C CD JBAND(J) EANDHIDTH FOB GROUP J CD I J J ( J ) POSITION OP DIAGONAL ELEMENT POB GROUP J CD LGBP(N) K04BZB OP GROUPS IN BLOCK(N) c ,

c

CR 1 A T K H CATA CL (COT(K) ,K = 1,KHAX) C CC KBAX=SOH 0»eP JBAND (J) FOR ALL J IN BLOCK N CR KBAI C CB POR*AT(«H ftD ,5K12 . V (6E12 . • ) ) C C CD COT NTTPE MATRIX DATA C CCEP

B-l

APPENDIX B Saaple Data Set In COVERX Fomat

The following page tabulates the 2 3 5U(n,f) and 2 3 5U(n,y) covarlance file, processed using PUFF," weighted by the ZPR-6/7 spectrin (Table VIII), and output in the COVERX fomat described in Appendix A.

Of COTBtZ CDTBBX*OB8L - P08SS* 1 ID 10 10 0 2 2 2 13 2D 10 G800P BBLlTITE C0T8BIA8C8 8A18ICBS CIS1TED BT POPP B I T ! XPB-6/7

•BIGBTIBG 3D 0 .17338-08 0 .13538*07 0.49798*06 0 .18328*06 0 .11118*06 0.67388*05 0 .40878*05 0 .2*798*05 0 .91198*04 0 .123*8*04 0 .10008-04

40 1261 18 4 1261 102 4 5D 0 .12508*01 0 .11748*01 0 .12748*01 0 .14748*01 0.1655B*01 0 .18398*01 0 .20308*01 0 .2 *418*01 0 .46528*01 0 .11668*02 0 .22478 -01 0 .29108-01 0.278SB-01 0 .32748-01 0 .27538 -01 0 .29668-01 0 .30108 -01 0 .37628-01 0 .53358 -01 0 .31858-01

5D 0 .48238-01 0 .13698*00 0.24608*00 0 .36638*00 0 .47478*00 0.59218*00 0 .72478*00 0 .97848*00 0 .19198*01 0 .52628*01 0 .59038*00 0.39298*00 0 .22758*00 0 .15008*00 0 .94488-01 0 .10008*00 0 .87028 -01 0 .96178-01 0 .75508 -01 0 .73708-01

6D 1261 18 1261 18 1 7D 10 1 10 2 10 3 10 4 10 5 10

6 10 7 10 8 10 9 10 10 10 80 0.5050B-03 0 .27728 -03 0.12508 -03 0 .61978 - 0 * 0 .10668 -04

0.00008*00 0 .00008*00 0 .00008*00 0 .00008*00 0 .00008*00 0 .27728-03 0 .84688-03 0 .58008-03 0 .40298-03 0 .74958-04 0 .00008*00 0 .00008*00 0.00008*00 0 .00008*00 0.00008*00 0 .12508-03 0.5800E-03 0 .77578-03 0 .45408-03 0 .34208-03 0 .33418-03 0 .33418-03 0.3085E-03 0 .00008*00 0 .00008*00 0 .61978-04 0.4029E-03 0 .45408-03 0 .10728-02 0 .56338-03 0.40008-03 0 .40008-03 0 .36938-03 0 .00008*00 0.00008*00 0 .10668-04 0.74958-04 0 .34208-03 0 .56338-03 0 .75768-03 C.78808-03 0 .75208-03 0.72008-03 0 .970 38-03 0 .47398-03 0 .00008*00 0.00008*00 0 . 3 3 * 1 8 - 0 3 0.40008-03 0 .78808-03 0 .87978-03 0 .83528-03 0 .80308-03 0 .12008-02 0 .58598-03 0 .00008*00 0.00008*00 0 .33418-03 0 .40008-03 0 .75208-03 0 .83528-03 0 .90588-03 0 .10408-02 0 .14238-02 0 .77948-03 0 .00008*00 0.00008*00 0 .30858-03 0 .36938-03 0 .72008-03 0 .80308-03 0 .10408-02 0 .14158-02 0 .18178-02 O.1O76B-02 0 .00008*00 0.00008*00 0 .00008*00 0.00008*00 0 .97038-03 0 .12008-02 0 .14238-02 0 .18178-02 0 .28468-02 0 .12958-02 0 .00008*00 0.00008*00 0 .00008*00 0.00008*00 0 .47398-03 0 .58598-03 0 .77948 -03 0 .10768-02 0 .12958-02 0 .10158-02

6D 1261 10 2 1261 102 1 7D 10 1 10 2 10 3 10 4 10 5 10

6 10 7 10 8 10 9 10 10 10 80 0.34 858 • 0 0 0.15678 •00 0.51348 - 0 1 0.176VB -01 0 .72978 - 0 2

0.50008-02 0 .50008-02 0 .50008-02 0 .50008-02 0.4 9578-02 9 .156 78*00 0 .15448*00 0 .59368 -01 0 .18008-01 0 .7354S-02 0 .50008-02 0 .50008-02 0.50008-02 0 .50008-02 C.4958B-C2 0 . 5 1 3 V . - 0 1 0 .59368-01 0 .51748 -01 0 .19308-01 0.7589B-C2 0 .50008-02 0 .500JE-02 0 .50008-02 0 .50008-02 0 .49578-02 0 .1769B-01 0.1800B-01 0 .19308-01 0 .22608-01 0 .81698 -02 0.49998-02 0 .99998-02 0 .49998-02 0 .49998-02 0.4957B-02 0 .72978-02 0 .73548-02 0 .75898-02 0 .81698-02 0 .89278-02 0 .90948-02 0 .73968-02 0.50008-02 0 .50008-02 0 .49578-02 0 .50008-02 0 .50008-02 0 .50008-02 0 .49998-02 0 .90948-02 0 .10008-01 0 .79268-02 0.50008-02 0 .50008-02 0 .49588-02 0.5000B-02 0.5O00B-02 0 .50008-02 0 .49998-02 0 .73968-02 0.79268-02 0 .75728-02 0 .69108-02 0 .50008-02 0 .49588-02 0 .50008-12 0 .50008-02 0 .50008-02 0 .49998-02 0 .50008-02 0 .50008-02 0.69108-OZ 0.92488-02 0 .50578-02 0 .49588-02 0 .50008-02 0.5000E-02 0 . 5 0 0 0 8 - 0 ! 0 .49998-02 0 .50008-02 0 .50008-02 0 .50008-02 0 .50578-02 0 .5701E-02 0 .50868-02 0 .49578-02 0.49588-02 0 .49578-02 0 .49578-02 0 . 4 9 5 7 8 - - 2 0 .49588-02 0 .49588-02 0 .49588-02 0 .50868-02 0 .54328-02

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APPENDIX C Evaluators* Comments on the Construction of the Uncertainty Files

This appendix consists of reprints of the following Intra-Laboratory memoranda: 1. D. C. Larson, "Sodium Data Covariance File for Reactor Studies,"

Harch 27, 1975. 2. C. Y. Fu, "Covariance Files of EHDF/B-IV Material 1192 (Iron) for

Reactor Applications," March 31, 1975. 3. F. G. Perey, "238-U Inelastic Data Covariance File for Reactor

Studies," March 31, 1975. 4. L. W. Weston, "Error Files for 2*°Pu Neutron Capture and 2 , , 1Pu

Neutron Capture and Fission Cross Sections," July 1, 1975. 5. R. Gwin, "Error Files for the 2 3 , P u Neutron Capture and Fission

Cross Sections," July 7, 1975. 6. F. Difilippo, G. de Saussure, and R. B. Perez, "Covariance Files for

v, a'.n.f) and o(n,r) for 2 3 8 U , " July 14, 1975. 7. R. W. Peelle, "Error Files for NUBAR(E)," February 3, 1976. 8. F. G. Perey, "Covariance File for Sodium ENDF/B-IV," August 23, 1976. 9. R. W. Peelle, "Uncertainty Files for Fission Ratios 2 3 8 U / 2 3 S U and

2 3 9 P u / 2 3 S U , " February 17, 1977.

C-3

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

March 27, 1975

F. C. Maienschein E. M. Oblow R. W. Peelle F. G. Perey C. R. Ueisbin D. C. Larson

Subject: Sodium Data Covariance File for Reactor Studies

Following the guidelines set forth by Perey and Peelle, estimated data covariance files for reactor studies have been generated for the total, elastic, inelastic to first excited level, and capture cross sections. The present sodium evaluation was performed by Paik and Pitterle at WARD using data available through March 1971. Since I did not perform the evaluation, I had to rely heavily on the report1 of their evaluation for ENOF/B-III, as well as the report2 by Pitterle describing his evaluation for ENDF/B-I. However, I have performed a brief literature search for new data available ^ince March 1971, and this new information is included in the present uncertainty analysis. A brief description of the data base and techniques employed in gener­ating the covariance files follows. Total Cross Section The major resonance is at 2.85 keV, with a width of 410 eV. There is some question as to the peak cross section of this resonance; recent values range from 410 b 3 to 372 ± 22 b." For energies lower than this, the scatter of available data is within 5-10% of the evaluation. Above the 2.85 keV resonance, many data sets exist and bands were drawn such that 90% of the "good" data points were within the bands. Energy sections were then chosen and errors estimated within each section. Long-range correlations reflect mainly the different major experiments and the estimated normalization uncertainty for each experiment. Elastic Cross Section The elastic cross section uncertainty is represented as being derived from a , = a. t - a, , - a n Y , which is correct for the energy region 0.5 keV to 2 ReV, with the exception of the region 0.6 keV to 150 keV, where resonance parameters are given in the evaluation. Inelastic Cross Section The inelastic cross section uncertainty is given only for the first inelastic level at 440 keV. The major data set used is that of Perey,5

which shows much resonant structure. The long-range correlations come from the uncertainty in normalization of these data.

C-4

Maienschein, Oblow, Peelle, Percy, Wtisbin Page 2 March 27, 1975

Capture Cross Section The major (n,y) resonance is at 2.85 ke¥. There is good experimental evidence for a width r y = 0.47 i 0.045 eV from independent experiments of Yamamuro* and the analysis by Friesenhahn6 of the data of Hocken-bury.7 However, to be consistent with the oft-measured thermal capture cress section cf 0.534 t .005 b, a value r = 0.32 tV is required, and a recent analysis* of s transmission experiment (which doesn't "_asure Ty

directly), derived r y = 0.34 eV. The measurement of ."Y is a very dif­ficult one because r n / r % 900. Energy groups were chosen which include at least one of the seven capture resonances between 0.5 keV and 150 keV. The uncertainties for these resonances are estimated from BNL-325 Third Edition, and from the data of Hockenbury et al . The long-range correlations correspond to a 7% systematic uncertainty in the latter measurement.

Coviriances not specifically included in the f i l e , suc!i as 51-102, are 0.0 by definition.

References 'T. A. Pitterle ard N. C. Paik, "Studies of Applications of Cross Sec­tion Data and Critical Experiment Data to Reactor Design — Quarterly Progress Report for Period Ending April 30, 1972, WAP-D-3045T4B-2, Appendix A.

JT. A. PitterTe, "Evaluated Neutron Cross Sections of Sodium 23 for the ENDF/B File," Report APDA-217, June 1968.

3F. Rahn et al., "Neutron Resonance Spectroscopy. XIII. Na to 320 keV," Phy„. Rev. C 8, 1827 (1973). "J. Seltzer and F. W. K. Firk, "A Study of the 2.8 keV Neutron Reson­ance of Sodium and an Analysis of the Total Neutron Cross Section up to 50 keV," NSE 53 415 (1974).

5F. G. Perey, W. E. Kinney and R. L. Macklin, "High Resolution Inelastic Cross Section Measurements for Na, Si and Fe," in Proceedings of the Third Conference Neutron Cross Sections and Technology," CONF-710301, Voi. 1, August 1971, p. 191.

6N. Yamamuro et al., "A Measurement of the Radiation Width of the 2.85 keV Neutron Resonance and of the Thermal Neutron Capture Cross Section in Sodium," NSE 41_. 445 (1970).

7R. W. Hockenbury et al., "Neutron Radiative Capture in Ha, Al, Fe, and Ni from 1 to 200 keV," Phys. Rev. P 8 , 1746 (1969).

0CL:jg

C-5

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

TO: C R. Weisbm

FRO*: C. Y. Fu SIBJECT: Covariance Files of ENDF/B-IV Material 1192 (Iron) for

Reactor Applications

File 33 Section 1: Total Cross Section

10" eV - 1 keV: Derived by summing elastic-scattering and non-elastic.

1 keV - 60 keV: This energy range has resolved resonances as described by Penny and Kinney. Uncertainties are given for eight energy intervals with LB = 1. Each interval has a s-wave resonance. The uncertainty is for the resonance area and is estimated by comparing the Version-IV gf with

2 3 more recent value ' and its reported uncertainty. In addition, a long-range correlated error of 2% is assumed for the entire energy range.

60 keV - 20 M»?V: Roughly 10 energy intervals per unit lethargy are used with LB = 1. A 3% error is assumed for each interval 4 as suggested by Perey, who has recently studied the total cross secr.ion in a comprehensive manner including evaTuation, transmission testing, and integral testing.

File 33 Section 2: Elastic Scattering

:oi 3

10~ eV - 1 keV: 5% error by comparing Version-IV thermal value with a recent compilation.'

1 keV - 20 KeV: Derived by subtracting nonelastic from total.

File ?3 Section 51: inelastic to the 846-keV level

I'nc rtainf,- ^.imates are somewhat subjective but are consistent 5 with :ic^ppr.dent estimates by Smith, who has done a separate evaluation for this cross section.

File 33 Section 102: Radiative Capture -5 10 eV - 1 keV: 1% by comparing the Version-IV thermal value with

3 a recent compilation.

C-6

1 iceV - 60 keV: This energy range has resolved resorances. 17 energy intervals are used with LB = 1. Each interval -?as at least one resonance. The uncertainty is for the resonance area. The resonance parameters in Version IV •*•a based on the capture areas measured by Hockenbury et al., whose e-ror analysis seems detailed and reasonable. We therefore adopted their quoted errors for the resonance areas. A 7% long-range correlated uncertainty reflects their estiiwl •*• systematic uncertainty.

60 keV - 100 keV: The evaluated capture cr. section ii tnis energy range is substantially lower t \r f* available data. This

o

lower cross section was suggest&d by M^cdougall on the basis of reactor physics calculation and inadequate multiple scatter­ing correction. We assume 30% error.

100 fceV - 20 MeV: The evaluated cross section is the same as given g

by Schmidt. Error estimates are roughly consistent with the spread of available data.

References: 1. S. K. Penny and W. C. Kinney, "A Re-evaluation of Natural Iron Neutron

and Gamma-Ray-Production Cross Sections - ENOF/B Material r.24," Oak Ridge National Laboratory Report ORNL-4617 (1971).

2. H. S. Pandy et a l . , "High Resolution Total Neutron Cross Section in 5 I ,Fe and 5 $ Fe," Conference on Nuclear Cross Sections and Technology, Washington D.C., 3-7 March (1975).

3. S. F. Mughabghab and D. I . Garber, "Neutron Cross S c i o n s , Volume 1, Resonance Parameters," Brookhaven National Laboratoiy Report BNL-325, Third Edition, Vol. 1 (1973).

4. F. 6. Perey, private communication (1975). 5. A. B. Smith, Argonne National Laboratoi , private communication to

F. G. Perey (1973). 6. R. W. Hockenbjry et a l . , Phys. Rev. V78, 1746 (1969). 7. M. C. Moxon, Int. Conf. on the itu-*- of Nur' ^r Structure with Neutrons,

Antwerp, 19-23 July (1965). 8. J. 0. Macdougall, Atomic Energy Establishment, Winfrith, private

communication to S. K. Penny (1970). 9. J. J . Schmidt, KFK-120, Kernforschungszentrum, Karlsruhe (1962).

10. M. D. Goldberg et a l . , "Neutron O ss Sections, Vol. IIA; Z=21-40," BNL-325, Second r .dit ion, Supplemen. 2 (1966).

c-/

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

Harch 31, 1975

To: Distribution

From: F. G. Perev Subject: 238-U Inelastic Data Covariance File for Reactor Studies

This is a short documentation to accompany the 238-U inelastic data covariance file for ENDF/B-IV (HAT = 1262) given to C. R. Weisbin (March 31, 1975) for the reactor sensitivity studies.

Data files were prepared for the first four inelastic levels of 238-U from threshold to 2.0 MeV. To conform with formats of file MF=33 the covariances were set to Vero from 2 to 20 MeV.

\ To arrive at data covariance files the inelastic scattering from the 2 level at 45 keV was re-evaluated. Results were communicated to A. B. Smith; he has acknowledged receipt of the material but not commented upon it yet.

The 45-keV Level Most of the experimental data of interest are to be found in Refs. 1 to 5, and the discussions leading to the ENDF/B-IV curves are to be summarized in Refs. 6 and 7 with also input from Gene Paik. I have also made use of Ch. Lagrange's calculations.8 My personal judgement is that for some unexplained reasons the results of Barnard et al.1"1* for the 45-keV level appear to be systematically too high, but may be adequate relative measurements. Most of the data for the 45-keV level in the region of interest are due to A. B. Smith. 1" 2 There are several good overlaps with measurements performed over a decade and in the high energy region with the recent Lowell Tech data.5 The theoret­ical situation is confused if one takes at face value the calculations of A. B. Smith,' A. Prince7 and Ch. Lagrange.8 My judgement is to go along with Ch. Lagrange, whose analysis is complete (10 keV to 20 MeV), gets good agreement for. aj and a n Y and is consistent with other even-even nuclide data (Th 2 3 2, U 2 3 \ Pu 1" 0 and P u 2 " 2 ) . A. B. Smith's argu­ment6 that the ENDF/B-IV curve below 500 keV is inconsistent with theoretical expectations may not be valid since Ch. Lagrange's results8

do not agree with those of A. B. Smith. (The difference may be rooted in the use of different penetrabilities for the compound nucleus calcu­lations performed on deformed nuclides rather than in uncertainties due to width fluctuations.')

C-8

Distribution March 31, 1975

My best estimate for the excitation of the 45-keV level is as shown on the attachment. It correspond? quite closely to the ENDF/B-IV curve up to 750 keV being about 52 lower. At about 800 keV the ENDF/B-IV curve dives down below my current estimate and at 1.75 MeV is about a factor of 3 too small. This situation does not lend itself to a clean repre­sentation of uncertainties. Basically the data file represents corre­lated uncertainties from threshold to 2 MeV (LB=2) with about 90S uncer­tainties up to 100 keV, 151 from 100 keV to 1 MeV, 251 from 1 to 1.5 MeV and 501 from 1.5 to 2.0 NeV. I believe this represents a fair compromise which will be adequate for the moment. More sophistication could be used if I could substitute for ENDF/B-IV a more realistic curve in particular above 1 MeV, but this may not be important for the current study.

For the next three levels at 146, 308 and 680 keV on each of then; fjlly correlated uncertainties of 201 were assigned from threshold to 2 MeV. In view of the dominant influence of the 45 keV cross section, no :orre-lations between uncertainties for the various levels were included.

References •A. B. Smith, Nucl. Phys. 47 (1963) 633. 2A. B. Smith, private communications (1975). 3E. Barnard et al., Nucl Phys. 80 (1966) 46. "£. Barnard et al., Data for Reactors, Helsinki (1970) Vol. 2, p. 103. 5Kegel et al., Lowell Techn Inst., private communications. 'A. B. Smith, Comments on 238-U Inelastic Scattering (Sept 24, 1973 and Sept. 10, 1974).

7A. Prince, note to S. Pearlstein on 238-U inelastic scattering (Sept. 11, 1974).

'Ch. Lagrange, private communications ^973) and EANDC Topical Meeting of Tokyo.. March 27, 1974). Comrunications to Smolenice Symposium (Sept. 1974) and Predeal School (Sept.. 1974).

'P. Gunther and A. B. Smith, Conf. on Nuclear Cross Sections and Technology, Washington, D.C. (March 1975).

Distribution: G. F. Flanagan E. M. Oblow C. Y. Fu R. W. Peelle R. Gwir. G. de Saussure D. C. Larson C. R. Weisbin F. C. Maienschein L. U. Weston F. R. Mynatt

C-9

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. | - ''"ft

~5E -.a-:— - : - : --IL4 .»- -*---r"-

-JU-U.. 4-HJ-- * - ! i . " ™ T ! : "

~2 *- —*-:—:.: •ir':.':. w f t ^ — i i . — « -.-^--.- ~¥ * --T" H^{j^ i . " ™ T ! : "

~2 *- —*-:—:.: •ir':.':. w f t ^

•~~*~ i-f.'zH1 _-p^._ • * t *— TzrrH - — -i . " ™ T ! : "

~2 *- —*-:—:.: •ir':.':.

1_ K - » _ . •~~*~ i-f.'zH1

-^.U— TzrrH - — -

• • -

IS : irji '-r- —

: - ; — : • — . : -r

t::*::."

±-zL ,-^-f..

_^

xHr - irEE • • -

IS : irji '-r- — T I •""

t::*::."

±-zL ,-^-f.. "~ 1 ; ""

xHr - irEE • • -

IS : irji '-r- — T I •""

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±-zL ,-^-f.. . ! ; !

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i-mrr)

C-10

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

July 1 , 1975

To: C. R. Ueisbin

From: L. W. Weston y J r

Subject: Error Files tor 2 l , 0 Pu Neutron Capture and 2 , , 1 Pu Neutron Ccfture and Fission Cross Sections

The covariance f l ies were implemented by F. Difilippo using a Fortran program written to generate such f i l es . The method used was described by F. 6. Perey, 6. DeSaussure, and R. B. Perez, "Estimated Data Covariance Files of Evaluated Cross Sections," given at the ANS Meeting in Atlanta, Sept. 8-11, 1974.

Correlations with the "standard cross sections" such as 1 0B(n,o) and 2 3 5 U ( n , f ) were not considered. The only major correlation would be that between the 2 1 , 1 Pu(n,f ) and the 2 3 £ U ( n , f ) cross sectioi.s since in most cases aboye 200 keV neutron energy i t was the ratio of these cross sections which was measured. 2"°Pu File 33 Section 102: Radiative Capture

The uncertainty f i l e was prepared for decade type neutron energy intervals from 100 eV to 10 fteV. The only experimental data available for the average capture cross section was that of Weston and Todd1 from 100 eV to 200 keV and that of Hockenbury, Noyer, and Block2 from 6 keV to 30 keV. The evalua­tions of Prince3 and Caner and Yiftah1* were also used as data sets from 1 keV to 10 MeV in the program to jenerate covariance files since these evaluations were based on nuclear model calculations. The covariance f i l e is unrealistic from 30 keV to 200 keV because ENDF/B-4 was based on very prelim' try data of Weston and Todd1 which was later revised. Because of this, ENDF/B-4 was lower than the experimental data in this neutron energy range.

2 W P u File 33 Section 18: Fission Cross Section

The uncertainty f i l e was prepared for decade type intervals from 100 eV to 10 MeV. The experimental data considered was:

Authors Weston and Todd5

Simpson et a I . 6

Blons7

Mlgneco et a l . a

Smith, Smith, and Henkel9

Szabo-o White 1 1

Butler 1 2

Nejtron Energy Range 1UU eV to 200 keV 100 eV to 20 keV 100 eV to 3 keV 100 eV to 2 keV 200 keV to 10 MeV 20 keV to 1 MeV 40 keV to 6 MeV

300 keV to 2 MeV

C - l l

For the cases where the measurements were the ratio to 2 3 5 U fission, the average 2 3 5 U fission cross section was taken from ENOF/B-4. 2 1 , 1 Pu File 33 Section 102: Radiative Capture

The uncertainty f i l e was prepared for decade type intervals from 100 eV to 10 MeV. The only experimental differential data was that of Weston and Todd.5 The evaluations of Caner and Yi f tah 1 3 and Prince3 , which were based en nuclear model tabulations, were also used as data sets in the generation of the covariance f i les because of the dearth of experimental data.

References

1. L. W. Weston and J. H. Todd, Nucl. Sci. Eng., 63, 143 (1977).

2. R. W. Hockenbury, W. R. Mover, and R. C. Block, Nucl. Sci. Eng., 49, 153 (1972).

3. A. Prince, Paper CN-26/91, Conf. Nucl. Data for Reactors, Helsinki (1970).

4. M. Caner and S. Yiftah, "Nuclear Data Evaluation for Plutonium-240," IA-1243, Israel Atomic Energy Comsission (1972).

5. L. W. Weston and J. H. Todd, "Neutron Capture and Fission Cross Sections of 2 '* 1Pu," to be published.

6. 0. 0. Simpson, et a l . , Proc. Conf. on Neutron Cross Sections and Technology, Wasnington, Vol. I I . 910 (1966).

7. J . Blons, Nucl. Sci. Eng. 51, 130 (1973).

8. E. Migneco et a l . , Proc. Conf. Nuclear Data for Reactors, Helsinki, Vol. 1, p. 437 (1970).

9. H. L. Smith, R. K. Smith, R. L. Henkel, Phys. Rev. 125, 1329 (1SJ2).

10. I . Szabo, et a l . , Symp. on Neutron Standards, Argonne, 257 (1970).

11. P. H. White and G. P. Warner, Nucl. Sci. Eng. 21, 671 (1967).

12. D. K. Butler and R. L. Sjoblorn, Phys. Rev. 124, 1329 (1962).

13. M. Caner and S. Yiftah, Nuclear Data Evaluation for Plutonium-241, IA-1276 (1972).

C-12

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

July 7, 1975

To: C. R. Weisbin

Subject: Error Files for the 2 3 9 Pu Neutron Capture and fission42 Cross Sections

An error f i l e has been made for the neutron capture cross section, a , c

the neutron fission cross section, a., and the ratio, a /a„. The f * c f

error file was computed using a computer method written by Felix Difilippo. The input inforaaticn for fission extended from 0.1 keV to 10 MeV while for capture the data extended from 0.1 keV to 1.0 MeV. The construction of the effor file for o, and for a /a,, was straight

I c i forward in that di iect values for those quantities were available. The uncertainty f i l e for a was constructed using direct values of n nrA

c c values obtained from the ratio a fa~ and o"., taken from the evaluation of

c i i Sowerby and Patrick. From 0'ir conversation on June 19, I judge that the error file for a is of no use to you, but it is included for your disposition.

R. Gwin RG:11

aAuthor'8 Note: The error file for 2^Pu(ntf) u>as used in the creation of the multigroup covariance matrix in the LMFBH Core Physics Covuriance Matrix Library.

C-13

Sources for o only

E. R. Shunk, W. K. Brown, and R. L auve, Proc. Conf. Seutron Cross Section Technology, vol. II, p. 979 U966) Washington, D. C , COKF-660303.

G. D. James, PreJ. Conf. Nuclear Data for Reactors, vol. I, p. 267 (1970) Helsinki, IAEA.

J. Blons, Nucl. Sci. Eng. 51, 95 (1973).

M. G. Sowerfcy, B. H. Patrick, and D. S. Mather, "A Detailed Report on the Simultaneous Evaluation of the Fission Cross Section of 2 3 5 U , *'*Pu, and 2 3 , U and the 2 3 , U Capture Cross Section in the Energy Range ICO eV Lo 20 MeV," AEP.E-P.-7273, UKAEA, Harwell (1973).

Sources for a . n , and a /a

M. G. Schomberg et al., Proc. Ccnf. Nuclear Data for Reactors, vol. I, 315 (1970) Helsinki, IAEA.

R. Gwin et al., Nucl. Sci. Eng. 45, 25 (1971); also, data taken at ORELA, to be published, Nucl. Sci. Eng.

L. W. Weston and J. H. Todd, Memorandum to R. E. Chrien (December 1972).

C-M

Sources for a fa only

M. G. Soverby and V. A. Konshin, Atomic Energy Reviev 10, Ho. ht

k53 (1972), IAEA.

J. B. Crirr and J. S. Lindsey, Proc. Conf. Suclear Data for Reactors TOI. I, p. 331 (1970) Helsinki, IAEA.

P. B. Belyaer et al. Proc. Conf. Wucleer Data for Reactors, vol. I, p. 336 (1970) Helsinki, IAEA.

J. A. Parrell et al., Proc. Conf. Nuclear Data for Reactors, vol. I, p. 5*3 (1970) Helsinki, IAEA.

V. M. Kononov et al. Proc. Conf. Nuclear Data for Reactors, vol. I, p. V*5 (1970) Helsinki, IAEA* also Atomic Energy 30, 362 (1971).

C-15

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

July 14, 1975

To: G. F. Flanagan R. Gwin 0. C. Larson F. C. Maienschein F. R. tynatt E . M. O b l o w •?. H. Peelle F. G. Perey C. R. Weisbin L. W. Weston

From: F. Difilippo G. de Saussure R. B. Perez

Subject: Covariance Files for Za, a[n,ff and a(n,y) for 2 3 8 U

These covariance f i l e s were constructed by Fel ix Di f i l ippo ,

using a FORTRAN-IV program developed for th is purpose. This

program and the evaluation of the error f i l e s w i l l be described

in deta i l by Felix in a TM memo. This short note documents

some main features of the f i l e s .

The method used to generate the error f i l e s was described in

a iDemo of G. de Saussure and R. B. Perez to E. G. Silver dated

12-10-73 and in the paper "Esti-nated Data Covariance F i l e s of

Evaluated Cross Sect ions ," by F. G. Perey, G. de Saussure, and

R. B. Perez, Given at the ANS Meeting in Atlanta, Sept. 8-11,

1974.

Author's Notes: This covariance for 236U(v) was not used in this report.

This covariance file for 23&U(n,f) was used to create the multigroup covariance matrix for 238U(n,f) in the LMFBR Core Physics Covariance Matrix Library.

C-16

The aethod consists of estimating the uncertainties from the

average discrepancy between EJDF/B-IV and various data sets and

other evaluations. The various data sets are weighted according

to the usual criteria.

In the unresolved resonance region the capture and total cross

sections show nonstatistical fluctuations in addition to the

statistical fluctuations iaplied by the model, as illustrated in

Fig. 1. The effect of these fluctuations on the covariance matrix

has been largely ignored, as more development work is required

to properly treat this problem.

Similarly, in the resolved region, the covariance matrix

describes the uncertainty in the average cross section (averaged over

decimal intervals) rather than the uncertainties in the resonance

parameters.

Above the resonance region the covariance matrices for capture

and fission are defined over an energy grid with intervals of 0.1

lethargy units.

References 1 to 26 list the data and evaluation used in obtaining

the covariance matrix for fission; references 11 to 58 list those for

capture; and references 59 to 73 were used in evaluating the uncer­

tainties in v.

IBM cards, in the proper ENDF fonsst, describing the group-to-group

covariance matrices were given to C. Weisbin on 4-11-75.

We do not understand at present how to describe the error file on

V or the correlations between cross-sections in ENDF/B format, hence, we

describe those errors and correlations below:

C-17

I. v The errors on boih the thermaJ value and the coefficient of linear

energy dependence are estimated at IX. The values at all energies are

fully correlated to the value at thermal. The thermal value is fully — 2 52

correlated to the value of v for Cf. Finally the correlation between v and the fission cross section is estimated to be negligible.

II a li. f

The 2 3 8 U fission cross section is estimated to be fully correlated to

the 2 3 5 U fission cross sections; direct corrt-lations with other cross

sections are negligible.

III. a c

Below 10 keV the 2 3 e U capture cross section is assumed to be fully

correlated to the 1 0B(n,a) cross section.

From 10 to 1000 keV the correlation coefficient with standards

are assumed to be as follows:

with the 1 0B(n,a) cross section: 40%

with the Au(n,i) cross section: 202

with the 2 3 5U(n,f) cross section: 10%

Above 100 keV important correlations are assumed to be as follows:

with the 2 3 SU(n,f) cross section: 80%

with the H(n,p) cross section: 10%

C-18

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

February 3, 1976

To: C. R. Weisbin

From: R. U. Peelle

Subject: Error Files for NUBAR(E)a

The files NVR25.DAT, NVR28.DAT, NVR49.DAT, NVR40.DAT, NVR41.DAT represent efforts to give fairly good covariance information for NUBAR for the nuclides 235y, 238u, and 239--ipu.

The format assumes that the information should be carried in f i le 31, but otherwise the formats are trying tc be consistent with those used for energy-dependent cross sections in f i le 33. A section with MT=1 is included at the beginning of each f i le of card images to give all the energies referred to. I believe this is the first time we have explicitly used the option to give covariance terms linking reactions in different nuclides.

The general approach is described below. I t was assumed that uncertainty in the delayed neutron fraction could be ignored, so the evaluation actively represents prompt nubar only. In each case three types of terms were included. The first represented the uncertainty in nubar for 2 5 2 C f given by the CSEWG "2200 m/sec task force" for ENDF/B-IV on 12-13-73, and includes the uncertainties for the other thermal nubar values and the covariance terms given by the associated f i t . Note that the agreed-to uncertainties were double the ENDF/B values quoted by Lemuel at the Washington Cross Section and Technology Conference (March 1975). I arbitrarily cut off the operation of the thermal co/ariance matrix at 0.1 eV, and above this energy assumed that correlations with the 2 5 2 C f nubar occurred entirely through the dependence of all prompt nubar measurements on this standard. I t is the dependence on this standard which induces the cress terms between the different materials.

For each case I f i t the existing fast-neutron data sets as I have them. Sometimes the result was close to ENDF/B-IV and sometimes not, so in every f i le there are subsections which represent the failure of the present f i t to agree with ENDF/B-IV and which represent the covariance of values interpo­lated using the fitted line. The "non-fit" contribution is assumed to be fully correlated with a variable magnitude, and the "fit" contribution is that given by least-squares theory. This treatment of "non-fit" is a bit strange when the curves cross and recross, but in that case the covariance component is small. The "fit" contribution is almost as arbitrary because nobody knows in how many linear segments nubar(E) should be f i t , the output uncertainties depend on the number of segments chosen, and least-square theory only works when you know the fitting function.' I used one to three energy segments as the data seemed to demand.

RWP:co

lAuthor'e Note: These error files for MBAR(E) were used to create all the multigroup aovarianoe matrices for fission neutron yielc* (V) in this report.

C-19

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

August 23, 1976

To: C. R. Weisbin £. M. Oblow

From: F. G. Perey (3-6224 )-~r~S 2-Subject: Covariance File for Sodium ENDF/B-IV

I have reviewed the file SODIUM.CRW created July 27, 1976 which you are currently using for the SS-Na-Fe adjustments and found the defi­ciencies which led to the very "large uncertainties in the nonelastic and elastic cross sections at high energies. 1 have discussed with Ouane Larson and we propose the following changes: The short-range correlation numbers in file MF=3 from 0.55 MeV to 2.00 MeV should be changed to 2.5 x 10" * (i.e. 5%) then from 2 to 4 MeV 6.4 x 10' 3 (8%), 4 to 8 MeV 1.0 x 1 0 - 2 (10%), 8 to 15 MeV 2.25 x 10 - 2

(15%) and 15 to 20 MeV 2.25 x 10" 2 (15%). For the long-range correlations from 0.44 to 2 MeV, 1.0 x 10~ 2 (10%) and from 2 to 20 MeV 1.0 x 10 - 2. This will result in standard deviations of the order of 11% up to 2 MeV, then 13% up to 4 MeV, then 15% up to 8 MeV, then 13% up to 20 MeV for both the elastic and nonelastic cross sections.

FGP:jg cc: D. C. Larson

C-20

INTRA LABORATORY CORRESPONDENCE OAK RIDGE NATIONAL LABORATORY

February 17, 1977

To: C. R. Weisbin

From: R. W. Peelle

Subject: Uncertainty Files for Fission Ratios 2 38u/2 35(j and 239pu/2 35ua

These files represent '"external" analyses of the uncertainties associated with these fission ratios, the result is based on the scatter among existing experimental results, and there has been no search for systematic uncer­tainties which might have affected a substantial fraction of the measure-merts in a common manner. We have therefore assumed that all systematic uncertainties are random from one measurement to the next. This is surely not always true, as for example can be seen by considering the possibility that the 239pu half l i fe is now off by 2 percent, affecting all those "absolute'" 2 3 SPu measurements based on foil weight measurements.

The source of data was the excellent compilation prepared by W. Poenitz, ANL, in conjunction with the June 1976 NEANDC-NEACRP specialists' meeting on fast fission cross sections (ANL-76-90 with supplement). In the method used, weights were assigned to each experiment which are supposed to reflect the reciprocal relative variance of a typical point from the data set. Since uncertainties in most sets are a function of energy, an overall judgment was used. The weights chosen are exhibited in Table I. The method is also based on use of an evaluated ratio of cross sections, and is somewhat sensitive to this choice especially i f there appears to be a systematic discrepancy between the bulk of the data and the evaluated curve. For 28p/25p the proposed evaluated fission ratio for ENDF/B, Version V, was employed (Private communication, W. Poenitz, 1-77). That is , the ratio was used which best represents measurements of the fission cross section ratio. For the 2 3 9 P u / 2 3 5 U fission ratio, the Version V ratio was not available soon enough, so the "evaluated" ratio was taken from ENDF/B-IV even though much of the data used were not available at the time of the version IV evaluation.

These analyses were performed using a variant of the SUR program of Difilippo. In the original form this program computed the covariance matrix of the sample of all data which is input, assuming that the true mean of all data is correctly represented by the current evaluated result. Results are computed on an appropriate energy grid. Diagonal elements of the result are just the sample variance of elementary statistics determined by the mean square scatter of data about the evaluation, as complicated by the use of weights which are not equal. Off-diagonal covariance elements of consequence arise whenever there is systematic behavior among the experi­ments which cover any two of the energy regions represented in the grid.

Author's Hote: These fission ratio uncertainty files were used in the creation of the multigroup covarianpe matrices for 23SU(n,f) and 239Pu(n,f) in the Fission Speatrun Covariance Matrix Library.

C-21

The program SURP2 used here d i f fered in the fol lowing ways from the o r ig ina l SUR:

1. An arb i t ra ry energy g r id or group structure is input , and the input for these cases was organized to avoid the portions o f SUR which interpolate to estimate pseudo-experimental values in regions where measurements were not made by a par t icu lar author, which interpolated diagonal variance elements in energy groups where no author had measurements, and which interpolated measurements to the centers of the energy groups used. As a resu l t , only about ?0 groups were used for each cross sect ion, and some of the interpolat ion procedures of SUR were replaced by hand operations. Where a data set seemed to fol low the same shape as the evaluation wi th in an evaluation energy group, the evaluation was represented by the value a t the center of the group and each data set was represented by the value at th is energy which t yp i f i ed the re la t ion between th is set and the evalua­t ion throughout the in te rva l . Where the data set did not fol low the evaluation wi th in an energy group, considerable qua l i ta t i ve judgment entered into developing the input data set in a way consistent with the above pr inc ip les .

2. Since SUR essent ia l ly gave the covariance matrix of the sample of input data, and since the uncertainty matrix of an evaluation should be more nearly analogous to the covariance matrix of the mean of the exper i ­mental data, i t seemed important to handle in th is complex case the analog of the fami l ia r resul t that the variance among a sample of N measurements from a population is N times the variance of the mean of those N measurements. Complexities arose because of the varied pattern of measurements made by individual authors and by the unequal weights assigned.

The problem was solved by assuming that a l l experimental data sets do correspond to a given data covariance matrix except for a scale factor corresponding to the assigned weight and except for the absence of measure­ments by some authors in some o f the uncertainty evaluation energy in terva ls . Tne covariance matrix computed by SUR is interpreted as representing a data set of average weight; and, by assuming no correlations occur between d i f fe rent measurements, one can construct the j o i n t covariance matrix of the ent i re set of experimental resul ts . Least-square theory then asserts that i f the weighted average of the data sets 1s computed using the inverse of the data variance matrix as the weight matr ix , the inverse of the resul t ing least squares matrix is the desired covariance matrix of the average (evaluated) cross sections.

The indicated calculations were carr ied out. Even though some i n s t a b i l i t i e s were experienced in the required matrix inversions, the f ina l results did not seem sensi t ive to the manner in which these i ns tab i l i t i e s were handled. The resul t ing re la t ive covariance matrices of the cross-section rat ios are shown in Tables I I and I I I . One is struck by the very small re la t ive uncertainties estimated, and one must wonder whether the results are r e a l i s t i c . More work is required before th is method can be advocated fo r general use in estimating covariance matrices, but the fol lowing points already emerge.

C-22

a) The results are sensitive to the evaluation used and the relationship between mean in a certain energy region and the evaluated value used. The computing procedure has no way to sense a discrepancy, so the user Kust scar, the diagnostics provided. Where a considerable body of precise data are in close agreement, as for 2 3 8 U ( n , f ) / 2 3 5 U ( n , f ) over much of the energy range, and where the evaluation closely follows the mean of the experimental data sampled, the small output uncertainty seems reasonable. On the other hand, where some discrepancy is sensed between the data and the evaluation, a perfect procedure should require re-examination of the input data; when such a discrepancy occurs i t may not be rational to assume that the sample variance is N times the variance in the sample rnean.

b) in* fractional-percent uncertainties obtained for broad-group cross sections are so small in t h i ; case that the systematic effects ignored ir. the original assumptions must be reviewed and may become dominant.

c) The standard method to test whether input data is consistent with a least-squares f i t is to compute chi square usinq output residuals and the assumed input data variance matrix. The structure of the SURP2 method seems to assure that the resulting chi square is about equal to lbs number ov degrees o^ freedom; for simple test cases the agreement is matnematically and numerically exact. This result is to be expected since the matrices are constructed from observation of the scatter ' ong the data sets.

d) One might expect that the least-squares procedure would imply cross-section corrections just equal to the discrepancies between mean data and evaluation. While SURP2 shows this behavior on simple test cases, a different result was seen in the f i ts leading to the ir* trices shown, and the differer.ee has not been investigated .»et to see whether i t arises from numerical problems or the correlations among the data (probably the le t te r ) .

e) One must remember not to take too seriously the detaili. of the covariance matrix provided in this way. After a i l , 110 values are given (in Appendix t ) based on not many more (averaged) experimental data values, and at most about ten pairs i f experiments were uti l ized in obtaining the statistical averages. When collapsed to a more reasonable size for actual use in estimating uncertainties in computed quantities, one can respect the correlation coefficients not very small compared to unity.

In summary, an advanced method of external covariance analysis has been employed for the f i rs t time here. Full credit has been taken for the effect of replication on uncertainties in evaluate*! quantities, with the result that uncertainties are estimated to be so small that effects ignored in the analysis may dominate in the cases of the cross-section ratios studied here.

To make use of the relative covariances given for cross section ratios, one must usually combine the results given with a covariance matrix representing the 2 3 5 U ( n , f ) cross section, logical ly , the resulting covariance information for 2 3 8 U ( n , f ) and 2 3 9 P u ( n , f ) should be combined with that from direct measurements of these fission cross sections.

RWPrco

C-23

TABLE I . DATA SELECTED FOR STUDY OF ^VARIANCE OF FISSION RATIOS

- '^Pu/ I 3 5 u Fission Ratio

Weight Reference No. of Points

2000 Carlson, ANL-76-90 (1976) 26 20&0 Cierjacks, ANL-76-90 (1976) 15

300 Adams, JNE 14, 85 2 2000 White, JNE 21, 671 (19C7) 5 600 Uttley, AERE-1996 1 300 Moat, JNE 14, 85 :

2000 Fursov, 1975 Kiev (to be published) 15 1000 Poenitz, NSE 47, 228 14 1C: Szabo, ANL-76-9G (1976) 4

1000 Szabo, 1970-73, in ANL-76-90 5 4000 Meadows, ANL-76-90 (1976) 7 1000 Allen, PPS/A70, 573 14 300 Smirenkin, ICD 4 7

1000 Soleihac, hels., 1970 5 2000 Pfletschinger, NSE 40, 375 (1970) 14 600 Davis, ANL-76-90 (1976) 3

'000 Zhuravlev, 76 Lowell (to be published) 2 100 Dorofeev, JNE 5, 217 2

1000 Gayther, N8S Spec. Pub. 425 (1975) 13 4000 Davis, ANL-76-90 (overweighted) 1 300 Gwin, NSE 45, 25 (1976) 9 300 Letho, NSE 39, 361 (1970) 2

2 3 ° U / 2 J 5 U Fission Ratio

4000 Behrens, ANL-76-90 (1976; 19 4000 Difilippo, ANL-76-90 (1976) 19

300 Cierjacks, ANL-76-90 (1976) 11 100 Pankratov, AE 9, 399 2 100 Smith, BAP 2, 196 6

^00 Coates, NBS Spec. Pub. 425 (1975) 13 1000 White, JNE 21, 671 1 1000 Cance, ANL-76-90 (1976) 5 1000 Uttley, AHSB(S) R169 1 1000 Moat, AHSB(S) R169 1 viOO Meadows, ANL-76-90 (1976) 12 1000 Nordborg, AN' 76-90 (1976) 4 300 Fursov, 1973 Kiev 8 100 Grundl, NBS Spec. Pub. 425 (1975) 4 300 Stein, 1968 Wash 3 100 Allen, PPS/A70, 573 5 100 Lamphere, PR 104, 1654 6

4000 Poenitz, JNE 26, 483 2 100C Jarvis, LA-1571 1 1000 Kuks, 1973 Kiev 2

C-24

TABLE I I . RELATIVE COVARIANCE MATRIX OF THE FISSION RATIO 2^Pu/2iiU

The original M t r i x was produced on a 27-point energy «esh; results here were collapsed using using a unit weight function per unit energy. The region below 10 keV was not treated in this study. Only the lower "half" of the correlation matrix is printed.

Lower Relative Group Standard

Boundary Deviation (keV) (S) 100 x Correlation Matrix

9.1 0.72 100 24.8 0-53 62 100 40.9 1.32 20 50 100 67.4 0.76 14 24 52 100 111. 0.51 7 13 41 55 100 183. 0.37 9 21 16 33 44 100 498. 0.57 2 3 -1 0 -1 27 100 1353. 0.47 -2 1 3 -1 0 -2 2 100

17330.

TABLE I I I . RELATIVE COVARIANCE MATRIX OF THE FISSION RATIO ^ U / ^ H j

The original retrix was produced on a 20-point energy mesh; results here were collapsed using a unit weight function per unit energy. The region below 0.1 MeV was not really treated in the study. Only the lower half of the correlation matrix is printed.

Lower Group

Boundary (keV)

1.2 100. 183. 498.

1353. 3680.

17330.

Relative Standard Deviation

(*) (43.) 7.3 1.0 1.2 0.26 0.25

100 10 10 0 0 -1

100 98 -5 4 -8

100 x Correlation Matrix

100 -9 100 1 23

-6 -40 100 22 100

0-1

APPENDIX D Edited Tabulation of the Fission Spectra Covariance Matrix Library

In this edited tabulation of the fission spectra covariance matrix library, only the lower halves of the symmetric matrices are shown. Correlation matrix elements are multiplied by 1000 for ease in reading. Also, for convenience, diagonal elements of correlation matrices are given as zero when the corresponding relative standard deviations are zero.

D-3

ELEHEBTS OP THE COBR8LATIOB 9ATRII ( 1 0 * * 3 | POI HATE8IAL 1261 lEiCTXOI 19 KIT! IESPECT TO MATEBIAJ. 1261 BEACTIOB 18

EBBBCY BABGB fBT) % BEL 6AOOP 1 2 3 « 5 6 STD-DEV

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 8 * 0 6 3 . 1 1 1000 3 . 6 7 9 8 * 0 6 — 1 . 3 5 3 8 * 0 6 2 . 3 2 596 1000 1 . 3 6 3 1 * 0 6 — 9 . 9 7 9 8 * 0 5 2 . 7 3 18* 517 1000 9 . 9 7 9 8 * 0 5 — 1 . B32B«05 2 . S « SO 2 * 3 799 1 0 0 0 1 . 8 3 2 8 * 0 5 — 9 . 0 8 7 8 * 0 4 2 . 7 5 10 7 2 311 516 1000 1 . 0 8 7 8 * 0 * - - 1 . 0 0 0 E - 0 5 3 . 3 6 0 0 0 282 6 1 0 1000

ELEHEBTS OP TIE COBBELATIOH IUTBII (10«*3) POR MATERIAL 1261 REACT 101 952 BITK RESPECT TO 9ATEBIU. 1261 RE ACTIO! 952

ERBRCT RABGB (ET) * BEL GROUP 1

2 .000E*07— 3. 679B*06 3.679E*06— 1 . 3538*06 1.353E*06— 9 . 979E*05 9 .9798*05— 1.8328*05 1.832E*05— 9.0878*09 9 .0878*09— 1.000E-05

STD-DET 0 .5 0 .7 0 .7 0.9 0 .9 0 .9

1 1000 2 169 1000 3 137 978 1000 9 601 755 802 1000 5 752 905 971 893 1000 6 791 265 330 820 987 1000

ELEHEBTS OP THE CORBEUTIOR HATBII (10**3) FOR MATERIAL 1261 REACTIOI 102 BITH RESPECT TO MATERIAL 1261 REACTIOH 102

EBERGT aARGE (BY) X BEL GROnP 1 2 3 9 5 6 STD-DET

2 . 0 0 0 B * 0 7 — 3 . 6 7 9 8 * 0 6 6 1 . 8 1 1000 3 . 6 7 9 E * 0 6 — 1 . 353E*06 6 0 . 0 2 730 1000 1 . 3 6 3 1 * 0 6 — 9 . 9 7 9 8 * 0 5 3 9 . 7 3 593 763 1000 9 . 9 7 9 8 * 0 5 — 1 . 8 3 2 E * 0 5 2 9 . 1 9 358 917 728 1000 1 . 8 3 2 8 * 0 5 — 9 . 0 8 7 8 * 0 9 1 0 . 9 5 1*9 IV 3 292 502 1000 9 . 0 8 7 8 * 0 9 — 1 . 0 0 0 E - 0 5 8 . 9 6 97 100 150 2 9 8 6 3 3 1030

ELEBEHTS OP TB8 CORRELATION MATRIX (10**3) FOB MATERIAL 1261 RBACTIOB 18 VITH RESPECT TO MATERIAL 1262 REACT£01 18

ENERGY BARGE (EV) GROOP

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 E * 0 6 1 988 539 182 «9 10 0 3 . 6 7 9 8 * 0 6 — 1 . 3 5 3 8 * 0 6 2 521 965 • 9 3 232 6 9 0 1 . 3 5 3 8 * 0 6 — 9 . 9 7 9 8 * 0 5 3 190 5 3 * 1039 775 322 0 9 . 9 7 9 8 * 0 5 — 1 . 8 3 2 8 * 0 5 9 99 217 669 899 9 6 1 252 1 . 8 3 2 8 * 0 5 — 9 . 0 8 7 B * 0 9 5 3 25 107 178 395 210 « . 0 8 7 E * 0 « — 1 . 0 0 0 8 - 0 5 6 0 0 0 9 19 31

ELEMENTS OP TH8 COBBELATXOH 8ATBII (10**3) POB MATERIAL 1261 *EACTIO! 18 WITH BBSPECT TO HATEBil! 126* RBBCTIOB 18

8BEBGT BARGE (87)

2 .0008*07— 3.6798*06 3 .6798*06— 1.3538*06 1.3538*06— 9 . 9798*00 9 .9798*05— 1.8322*05 1.8321*06— 9 .0878*0 * «, 0 8 7 8 * 0 * — 1.0008-05

GBOOP 1

1 995 6*3 183 2 537 985 509 239 3 160 607 981 « 99 2*0 7*1

99 10 0 71 0

735 305 0 989 510 279

10 70 303 501 972 592 0 0 0 273 590 967

BLANK PAGE

D-4

B1SUBTS OP TIB CMBBUTXOI BAT I I I (10**3) POI • ITBBIAL 1261 BBACTIOI 4 5 2 IXTI RESPECT TO MATERIAL 1262 BBACTIOB 452

EIERCT BAB6E (BT) CBOOP

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 E * 0 6 3 . 6 7 9 8 * 0 6 — 1 . 3 5 3 8 * 0 6 1 . 3 5 3 8 * 0 6 — 4 . 9 7 9 8 * 0 5 4 . 9 7 9 8 * 0 5 — 1.832E*0S 1 . 8 3 2 8 * 0 5 — « . 0 8 7 E * 0 4 4 . 0 8 7 B * 0 4 — 1 . 0 0 0 8 - 0 5

1 2 3 « 5 6

356 192 181 181 181 181

225 2*1 122 115

«13 422 414 130 223 228 224 123 210 215 211

211 115 123 210 215 115 123 210 215 211 115 123 210 215 211

ELEMENTS OF THE COBBEUTIOB 8ATBIX (10**3) FOB BATERIAL 1261 BEACT10B 4 5 2 1ITH BESPECT TO HATE RIAL 126% BE ACTIO! 452

EIEBCT RAICL fET) CBOHP 1

2 . 0 0 0 E • 0 7 - - 3 . 679E«06 3 . 6 7 9 8 * 0 6 — 1, 353B*06 1 . 3 5 3 8 * 0 6 — 4 . 9 7 9 8 * 0 5 4 . 9 7 9 8 * 0 5 — 1 . 8 3 2 8 * 0 5 1 . 8 3 2 8 * 0 5 — • . 0 8 7 E * 0 » • . 0 8 7 B * 0 4 — 1 . 0 0 0 E - 0 5

1 222 1«1 151 2 5 8 2 6 4 259 2 • 0 1 2 5 * 272 • 6 6 • 76 467 3 619 392 419 718 7 3 5 720 4 366 232 2«8 • 25 • 3« 426 5 366 232 2 4 8 • 2 5 4 3 4 426 6 366 232 2«8 425 4 3 4 426

ELEBEBTS OP THE COB RELATION HATRIX (10**3) FOR HATBBIAL 1261 8EACTIOB 452 NITH BESPECT TO HATEBIAL 1265 BEACTIOB •52

EBEBCT BARGE (ET) GROtfP

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 E * 0 6 3 . 6 7 9 E * 0 6 — 1 . 3 5 ) E * 0 6 1 . 3 5 3 8 * 0 6 — 4 . 9 7 9 E * 0 5 4 . 9 7 9 8 * 0 5 — 1 .832E*05 1. 8 3 2 8 + 0 5 — 4 .087E+04 4 . 0 8 7 E + 0 4 — 1. 000E-05

1 411 260 2 7 8 • 77 • 88 • 7 8 2 279 177 189 32« 3 3 1 325 3 240 i s : 162 2 7 8 2 85 279 4 240 152 162 279 2 8 5 279 5 240 152 162 2 7 8 2 8 5 2 7 9 6 240 152 162 278 2 8 5 279

BLBREHTS OF THE CORBELATIOH HATRII (10**3) FOB MATERIAL 1261 REACTION « 5 2 NITH RESPECT TO HATERIAL 1266 BEACTIOB • 52

ENERGY RANGE (Ef)

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 E * 0 6 3 6 7 9 8 * 0 6 — 1. 353E*06 1 . 3 5 3 8 * 0 6 — « . 9 7 9 E * 0 5 4 . 9 7 9 8 * 0 5 — 1. 832B*05 1 . 8 3 2 8 * 0 5 — 4 . 0 8 7 8 * 0 4 4 . 0 8 7 8 * 0 4 — 1 . 0 0 0 B - 0 5

GROUP

1 602 381 407 6 9 8 7 1 4 700 2 195 12 3 132 226 2 3 1 227 3 150 95 101 174 1 7 8 174 4 150 95 101 174 178 174 5 150 95 101 174 1 7 8 174 fi 150 95 101 174 1 7 8 174

D-5

ELEMENTS OF TBB COBBEUTIOB HATRIX (10**3) TOR MATERIAL 1262 REACTION 18 VITB RESPECT TO MATERIAL 1262 REACTION IB

EBER6T BABGE (Ef ) X REL CBOOP 1

2 .000B*07— 3 . 6 7 9 8 * 0 6 — 1 .3538*06— • . 9 7 9 B * 0 5 — 1.832E*05— *.087B*O«—

STD-DBt 3 . 6 7 9 8 * 0 6 3 . 1 1 .353E*06 2 . S * . 9798*05 2 . 6 1 . 8 3 2 8 * 0 5 3 . 1 « . 0 8 7 B * 0 « 7 . 8 1 . 0 0 O E - 0 5 1 0 7 . 1

1 1000 2 5*2 1000 3 272 621 1000 » S3 2«1 352 1000 5 -2 32 «0 475 1000 6 0 0 0 7 8 1000

ELEBBBTS OF TBB COBBELATIOB BATRII (10**3) FOR BATBRIAL 1262 REACTION «52 BXTR BESPECT TO KATEBIAL 1262 REACTION *52

ENERGY BADGE (E»J * BEL CBOOP STD-DST

2.000B*07— 3.6798*06 0 .8 1 1 3.679E*06— 1.3538*06 1.5 2 1.3538*06— • . 9 7 9 8 * 0 5 1.6 3 • ,979B*C5— 1.8328*05 1.6 « 1.8328*05— «.0878«0« 1.6 5 • .087B»0«— 1.000B*05 1.6 (•

1000 970 1000 965 999 1000 965 999 1000 1000 965 999 1000 1000 1000 965 999 1000 1000 1000 1000

ELEBERTS OT TBE COBBEUTIOB BATRII (10**3) FOR SATEBIAL 1262 REACTIOR 51 BITB RESPECT TO 8ATEBIAL 1262 BEACTIOB 51

ERER6T BASGE (ET) * REL GBOOP 1 StfD-DET

2 . 0 0 0 E * 0 7 — 3 . 6 7 9 E * 0 6 0 . 0 1 0 3 . 6 7 9 E * 0 6 — 1 . 3 5 3 8 * 0 6 3 2 . 8 2 0 1. 353B*06— * . 9 7 9 E * 0 5 » 1 - 9 3 0 • , 9 7 9 E * 0 5 — 1 .832E*05 HO.O • 0 1 . 8 3 2 8 * 0 5 - - » . 087B*0« » 6 . 9 5 0 • , 0 8 7 E * 0 » — 1.00OE-05 0 . 0 6 0

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

0 0 0 0

ElEBESTS OF "BE COR RELIT I OR MATRIX (10**3) FOR MATERIAL 12b / REACTION 52 SITH RESPECT TO MATERIAL 1262 REACTION 52

ENERGY RANGE (EV) % REL GROOP 1 STD-OET

2»000E*07— 3 . 679E*06 0 . 0 » 0 3.679fc*Q6— 1. 353E*06 5* . • 2 0 1 . 3 5 3 8 * 0 6 — • , 9 7 9 E * 0 5 6 7 . 1 3 0 • • 9 ? 9 B * 0 5 — 1 .832E«05 6 7 . 1 « 0 1 .832B*05— • . 0 8 7 E * 0 * 6 7 . 1 5 0 ».C27E*0i»— 1 . 0 0 0 E - 0 5 0 . 0 6 0

1000 1000 1000 1000 1000 IClu 1000 1000 1003 1000

0 0 0 0

ELEMENTS OF THE CORRELATION HATRII (10**3) TOR I I & • * & » * - I *>W*. R t S V I 1 V R -*-» W

ENERGT RANGE (E7) * BEL GROOP 1 2 3 • 5 6 STD-DE? ,

2.0008*07— 3.679E»06 0 .0 1 0 J . 6 / 4 E * 0 6 — 1,J5JE*06 M . 3 2 0 1000 1.3538*06— «.979B*05 6 7 . 1 3 0 1000 1000 R.979E*05— 1.8328*05 67 .1 A 0 logo 1000 1000 1.832E*05— <I.087E*0« 0 .0 5 0 0 0 0 0 %.Q|»7B*0«— 1.000E-05 0 .0 6 0 0 0 0 6 0

53

0-6

tuatwts or T I E coatBUTxof B A T R I I f i o * * 3 ) POR MATERIAL 1262 RSACTIOI 5« «XTB iBSPECT TO KATBRIAL 1 2 6 2 B8ACTIO! S4

BBBBCY BAB6S ( I t ) * RBI 6100 9 1 2 3 •» 5 STD-0 i f

2 .0001*07— 3.6798*06 0 . 0 1 0 3 .«79E*06— 1.3538*06 S0 .1 2 0 1000 1 .3531*0*— 4.9798*05 6 7 . 1 3 0 1000 1000 4 .9798*05— 1.8328*05 0 , 0 4 0 0 0 0 1 .8321*05— 4.087B*04 0 . 0 5 0 0 0 0 0 4 .087«*0»— 1 . 0008-05 0 . 0 6 0 0 0 0 0

EIB8JERTS Of THE CO1RBUTI0I SATRII (10»*3) FOR RATERIAL 1262 REACT IOB 102 MT8 RESPECT TO a IT E RIAL 1262 RE ACTIO! 102

EIEtCr BARGE (ET) % BEL 6R00P 1 STD-DEf

2 .000B*07— 3. 6791*06 51 .8 3 .6798*06— 1. 353E*06 17 .8 1.3538*06— 4.9798*05 19.8 4 .9798*05— 1.8328*05 12.7 1.8328*05— 4.087E*04 7.6 4 .0878*04— 1.0008-05 9 .6

1 1000 2 922 1000 3 449 611 1000 4 402 547 857 1000 5 327 427 618 769 1000 6 68 150 402 404 500 1000

ELEHERTS OP THE CORBELATIGB SATRIZ (10**3) POR RATERIAL 1262 RE ACTIO* 18 HITH RESPECT TO HAT'JPTAL 1264 BEACTIO* 18

ERERGY SAHGE (EV) GBOOP 4

2 .0008*07— 3.6798*06 3.679E*06— 1.3538*06 1.3538*06— 4. 979E*05 4 .9798*05— 1.8328*05 1.8328*05— 4.0878*04 4 .0878*04— 1 . 000B-05

1 9*3 519 1*9 44 3 0 2 531 941 526 214 25 0 3 178 484 1014 656 105 0 4 48 230 766 884 176 9 5 9 67 313 448 335 18 6 0 0 0 244 203 *C

ELEREBTS OP THE CORBELATIOH HAT SIX (10**3) POR RATERIAL 1262 REACTIOR 452 HITH RESPECT TO MATERIAL 1264 REACTION 452

ENERGT BARGE (ET) GROOP 1

2.00QE*07— 3.6798*06 1 127 69 65 65 65 65 3.679E*06— 1.3538*06 2 230 124 117 117 117 117 1.353E*06— 4. 979£»05 3 355 192 181 181 181 181 4 .979E*05— 1. 832E*05 4 210 113 107 107 107 107 1.832E*05— 4.0878*04 5 210 113 107 107 107 107 «.087E*04— 1. OOOB-OI 6 210 113 107 107 107 107

D-7

ELEMENTS Of THE CORRELATION MATRIX (10**3) POR MATERIAL 1262 REACTION 4 5 2 BITH RESPECT TO MATERIAL 1265 REACTION 452

ENERGY BARGE (EV)

2 . 0 0 0 E * 0 7 ~ 3 . 6 7 9 E » 0 6 3 . 6 7 9 E » 0 6 — 1 .353E*06 1 . 3 5 3 E » 0 6 - - 4 . 9 7 9 E * 0 5 4 . 9 7 9 E » 0 5 ~ 1 .832E*05 1 .832E»05— 4 . 0 8 7 E « 0 4 4 . 0 8 7 B » 0 4 — 1 . 0 0 0 E - 0 5

GBOOP 1

235 127 120 120 120 120 2 160 86 81 81 81 81 3 138 7 4 70 70 70 70 4 138 74 70 70 7C 7 0 5 138 74 70 70 70 70 6 138 74 70 7 0 70 7 0

ELEMENTS OP THE CORBEUTICN HATBIX (10**3) POR MATERIAL 1262 REACTION 4 5 2 BITH RESPECT TO MATERIAL 1266 REACTION 452

ENERGY RANGE (ET)

2 . 0 0 0 B * 0 7 ~ 3 . 6 7 9 E * 0 6 3 . 6 7 9 E » C ~ 1 .353E»06 1 .353E*06— 4 . 9 7 9 E * 0 5 4 . 9 7 9 B » 0 5 — 1 .832E*05 1 . 8 3 2 B + 0 5 - - 4 . 0 8 7 E * 0 4 4 . 0 8 7 B » 0 4 — 1. 000E-05

GROOP 1 2 3 4 5 6

1 345 186 176 176 176 176 2 112 6 0 57 57 57 57 3 86 46 44 44 44 44 4 86 46 44 44 44 44 5 86 46 44 44 44 44 6 36 46

ELEMENTS OP THE CORRELATION MATRIX (10**3) POB MATERIAL 1264 REACTION 18 BITH RESPECT TO MATERIAL 1264 REACTION 18

ENERGY RANGE (ET) f REL GBOOP 1 2 STD-DBY

2 . 0 0 0 E O 7 - - 3 . 6 7 9 E » 0 6 3 . 1 1 1000 3 . 6 7 9 E * 0 6 — 1 .353E«06 2 . 4 2 544 1000 1 .353E*06— 4 . 9 7 9 E * 0 5 2 . 7 3 184 4 . 9 7 9 E * 0 5 ~ - 1. 832E»05 2 . 8 4 51 1 . 8 3 2 E * 0 5 - - 4 . 0 8 7 E * 0 4 2 . 8 5 9 4 . 0 8 7 B * 0 4 - - 1. 0 0 0 F - 0 5 3 . 4 6 0

511 1000 242 748 1000

74 310 509 1000 - 1 1 271 570 1000

ELEMENTS OP THE CORRELATION MATRIX (10**3) POR HATEIAL 1264 REACT TON 4 52 WITH BESPECT TO MATERIAL 1264 REACTION 452

ENEBGY RANGE (EV) t RBL GROUP 1

2 . 0 0 0 E » 0 7 ~ 3 . 6 7 9 2 * 0 6 3 . 6 7 9 E » 0 6 - - 1 .353E»06 1 . 3 5 3 E * 0 6 — 4 . 979E405 4 . 9 7 9 E » 0 5 — 1. 832E*05 1 .832E»05— 4 . 087E*04 4 . 0 8 7 E » 0 4 - - 1 .00CE-05

STD-DEf 1.3 0 .7 0 .5 0 .8 0 . 8 0 .8

1000 o«v 1000

1 2 3 - 2 7 * 4 - 6 6 5 ', - 6 6 5 (. - 6 6 5

58 1000 •458 793 1000 •458 793 1000 1000 •458 793 1000 1000 1000

ELEMENTS OP THE CORRELATION MATRIX (10**?) POR MATERIAL 1264 REACTIOR 102 NITH RESPECT TO MATERIAL 1264 REACTION 102

ENERGY RANGE (BT) % REL GROOP 1 3 STD-DE?

2 . 0 0 0 E * 0 7 - - 3 .679E*06 0 . 0 3 . 6 7 9 E * 0 6 - - 1 .353E*06 0 . 0 1 .353E*06— 4 . 979B*05 2 3 . 1 4 . 9 7 9 B * 0 5 - - 1 .832E*05 1 1 . 0 1 . 8 3 2 E » 0 5 - - 4 .087E«04 1 3 . 9 4 . 0 f i 7 E » 0 » - - 1 . 0 0 0 E - 0 5 6 . 6

1 1000 2 IOOO moo 3 0 0 1000 4 0 0 TO 1000 5 0 0 164 572 1000 6 0 0 768 161 141 1000

D-8

BLEBBBTS OF TBE COB RELATION BATBII (10**3) fOB BATEBIAL 126« BE ACTIO* 18 BITS RESPECT TO BATEBIAL 1264 REACT I Oi 102

EREBCT BiBCB (BT)

2 .0008*07— 3.6798*06 1 3 .6798*06— 1 . 3538*06 2 1.3538*06— 4.9798*05 3 4 .979B*05— 1. 8328*05 * 1.8328*05— «.087B*0« 5 4 .0878*04— 1. 0008-05 6

GROOP 1

1 1000 54* 18* 51 9 0 54* 1000 511 242 7« - 1 184 511 1000 748 310 1

51 2*2 7*8 1000 599 271 9 74 310 509 1000 570 0 - 1 1 271 570 1000

ELEBEBTS OP T O CORRELATION BATBII (10**3) FOB HATBBIAL 1264 BEACTIOB «S2 BITS BESPECT TO BATEBIAL 1 2 6 5 REACTION • 52

BBBB6T BAB6B (BT)

2 .0008*07— 3.6798*06 3 .6798*06— 1.3538*06 1.3538*06— 4.9798*05 4 .9798*05— 1.8328*05 1.8328*05— 4.0878*04 4 .0878*04— 1.0008-05

GBOOP

1 2 3 86 155 239 « 86 155 239 5 86 155 239 6 86 155 239

147 265 409 242 242 242 100 180 278 164 164 164

141 141 141 141 1*1 141 141 141 141 141 141 141

B1BBBBTS OP TBE CORRELATION BATBXI (10**3) FOR HATEBIAL 1264 BEACTIOB 4 5 2 BITS RESPECT TO BATEBIAL 1266 REACTIOB 452

BBBB6T BARGE (ET)

2 . 0 0 0 E * 0 7 — 3 . 6 7 9 8 * 0 6 3 . 6 7 9 B * 0 6 — 1 . 3 5 3 8 * 0 6 1 . 3 5 3 8 * 0 6 — 4 . 9 7 9 8 * 0 5 * . 9 7 9 E * 0 5 — 1 . 8 3 2 e * 0 5 1 . 8 3 2 8 * 0 5 — 4 . 0 6 7 E * 0 4 4 . 0 8 7 B * 0 4 — 1 . 0 0 0 E - 0 5

GROOP 1

1 215 389 600 355 355 355 2 70 126 194 115 115 115 3 54 97 149 88 88 88 4 54 97 149 88 88 88 5 54 97 149 88 88 88

97 149 88 88 88

ELEB8NTS OP TBE CORRELATION BATRIX (10**3) FOR 8ATERIAL 1265 BEACTIOB 452 HITH RESPECT TO BATERIAL 1 2 6 5 REACTION 452

EBEBGX BARGE (ET) X BEL GROOP 1

2.0O0B*07— 3.679E*06 3 .679E*06— 1.3538*06 1 .3538*06— 4 .9798*05 «.979B*05— 1.8328*05 1 .8328*05 - - 4.087E*04 4.087*.*04— 1.000B-05

STD-DEV 0 .7 1.0 1.2 1.2 U 2 1.2

1 1000 2 954 1000 3 930 997 1000 4 930 997 1000 1000 5 93C 997 1000 1000 1000 6 930 997 1000 1000 1000 1000

ELEBENTS OP THE CORRELATION flATRIX (10**3) FOR HATEBIAL 1265 REACTION 102 VITH RESPECT TO BATERIAL 1265 REACTION 102

EBEBCT RANGE (ET) % BEL GROOP 1 ST0-D8T

2 .0008*07— 3.6798*06 17.9 1 3 . 6 7 9 8 * 0 6 — 1.3538*06 11.9 2 1 .3538*06— * . 9 7 9 8 * 0 5 7 . 9 3 4 . 9 7 9 8 * 0 5 — 1.8328*05 23 .3 4 1 .8328*05— 4 . 0 8 7 8 * 0 * J5.4 5 «. 0 8 7 8 * 0 * — 1.0008-05 10.9 6

1000 1000 1000 -995 - 9 9 * 1000 -927 -927 915 1000 -218 -218 215 538 1000 -268 -266 284 499 713 1000

D-9

ELBHEBTS OB THZ CORRELATION HATR^I (10**3) POR RATBBIAL 1265 REACTION 452 HITH RESPECT TO HATERIAL 1266 REACTIOR 452

EBERGT RABGE (Ef) GROUP

2.0O0B»07~ 3-6798*06 1 398 270 232 2 3 2 2 3 2 232 3.6798*06— 1.353E*06 2 129 88 75 75 75 75 1.3538*06— 4.9798*05 3 99 6 7 58 58 58 58 4 .9798*05— 1.832E«05 i i 99 67 58 5 8 5 8 58 1.8328*05— 4.0878*04 5 99 6 7 58 58 5 8 58 4.0878*04— 1.000E-05 6 99 67 58 58 58 58

BLEREBTS OP TBB CORRELATION HATRIX (10**3) POR HATBRIAL 1266 REACTIOR 18 HITH RESPECT TO SATERIAL 1266 REACTIOi 18

BBBBGY RARCE (Bf) f BEL GROOP 1 STD-DET

3 .679E*06 3 . 5 1 .353E*06

2 . 0 0 0 E O 7 -3 . 6 7 9 8 * 0 6 - - 1 .353E*06 3 . 0 1 . 3 5 3 8 * 0 6 — 4 . 9 7 9 E * 0 5 5 . 7 4 . 9 7 9 E * 0 5 — 1.832E*C5 7 . 9 1 . 8 3 2 8 * 0 5 — * . 0 8 7 E * 0 4 3 . 7 4 . 0 8 7 8 * 0 4 — 1 . 0 0 0 B - 0 5 3 . 3

1 2 3 4 5 6

1000 871 1000 544 804 1000 713 886 935 1000 145 6 -80

16 1 -34 71 1000

-18 612 1000

ELEBENTS OP THE COS8ELATI0H RATRIX (10**3) POR MATERIAL 1266 REACTIOR 452 HxTH RESPECT TO BATERIAL 1266 REACTIOI 452

ERERGT RABGE ( E f ) X RBL GROOP 1 2 3 4 5 6 STD-D8?

2 . 0 0 0 8 * 0 7 — 3 . 6 7 9 8 * 0 6 0 . 5 1 1000 3 . 6 7 9 E * 0 6 — 1 . 353E*06 1 . 5 2 674 1000 1 . 3 5 3 8 * 0 6 - - 4 . 9 7 9 8 * 0 5 1 .9 3 620 997 1000 4 . 9 7 9 8 * 0 5 - - 1 . 8 3 2 8 * 0 5 1 . 9 4 620 997 1000 10G0 1 . 8 3 2 8 * 0 5 - - 4 . 0 8 7 8 * 0 4 1 .9 5 620 9 * 7 1000 1000 1000 4 . 0 8 7 8 * 0 4 - - 1 . 0 0 0 8 - 0 5 1 . 9 6 620 997 1000 1000 1000 1000

ELEREITS OP THE CORRELATIOB HATRIX (10**3) POR HATBRIAL 1266 REACTIOR 102 HITH RRSPECT TO HATERIAL 1266 RBACTIOH 102

EREBGT RAHGE (E?) t REL GkOOP 1

2 . 0 0 0 E * 0 7 - -3 .679B*06— 1 .353E*06- -4 . 9 7 9 8 * 0 5 - -1 .8328*05— 4 . 0 8 7 8 * 0 4 —

STO-DE? 3.6798*06 60.6 1.3538*06 48 .2 4.9798*05 15.3 1.8328*05 18.2 4.0878*04 24.4 1.000B-05 11.5

1 1000 2 1000 1OC0 3 685 704 1000 4 -406 -382 384 1000 5 103 103 58 42 1000 6 227 226 143 -20 931 1000

E-l

APPENDIX E Edited Tabulation of the LMFBR Core Physics Covariance Matrix Library

In this edited tabulation of the LMFBR Core Physics Covariance Matrix Library, only the lower halves of the symmetric matrices are shown. Cor­relation matrix elements are multiplied by 1000 for ease in reading. Also, for convenience, diagonal elements of correlation matrices are given as zero when the corresponding relative standard deviations are zero.

E-3

ELEBENTS or THE CORRELATION HATBII MO«*3) FOB "ATEBIAL 1261 REACTION 18 WITH BESPECT TO "ATERIAL 1261 REACTIOR 18

EHEBGT RANGE (ET) t BEL GBOOP 1 2 3 a 5 6 7 8 9 10 STD-DET

1 . 7 3 3 E * 0 7 - - 1 . 3 5 3 E » 0 6 2 . 2 1 1000 1 . 3 5 3 E » 0 6 - - 4 . 9 7 9 E * 0 5 2 - 9 2 • 2 * 1000 » . 9 7 9 6 » 0 5 - - 1 . R 3 2 E + 0 5 2 - 8 3 200 716 1000 1 . 8 3 2 E » 0 5 - - 1 . 1 1 1 E » 0 5 3 . 3 a 8« • 2 3 4 9 8 1000 1 . 1 1 1 E » 0 5 - - 6 . 7 3 8 E * 0 « I 2 . * 5 17 94 446 62S 100r> 6 . 7 3 8 S » 0 4 - - 4 . 0 8 7 E * 0 « 3 . 0 6 0 0 404 • 12 9 6 5 1 0 0 0 4 . 0 8 7 B » 0 4 - - 2 . 4 7 9 E » 0 U 3 . 0 7 0 0 399 4 0 6 9 0 8 9 3 6 1000 2 . 4 7 9 E » 0 4 - - 9 . 1 1 9 E * 0 3 3 - S 8 0 0 294 300 6 9 5 7 2 0 919 1 0 0 0 9 . 1 1 9 E » 0 3 — 1 . 2 3 « E » 0 3 5 - 3 9 0 0 0 0 6 6 1 758 886 9 0 5 1000 1 . 2 3 4 E » 0 3 - - 1 . 0 0 0 E - 0 5 3 . 2 10 0 0 0 0 5 4 0 6 2 0 813 8 9 8 7 6 2 1000

EL8HEHTS OP THE CORRELATION RATRIX (10**3) POB -ATERIAL 1261 REACTION 4 5 2 illTH RESPECT TO HATERIAL 1261 REACTION # 5 2

ENERGY RANGE (EV) * RSI GROUP STD-DEV

1 . 7 3 3 E » 0 7 - - 1.J53E*Oo 0 . 6 1 .153E»06— 4 . 9 7 9 E * 0 5 0 . 7 4 . 9 7 9 E + 0 5 - 1 . 8 3 2 E * 0 5 0 . 4 1 .832E*05— 1 .111E»05 0 . 4 1. 111E*05— 6. 738E»04 0 . 4 6 . 7 3 3 E » 0 4 — 4 . 0 8 7 E * 0 4 0 . 4 4 . 0 « 7 E * 0 4 — 2 . 4 7 9 E * 0 4 0 . 4 2 . 4 7 9 E » 0 4 — 9 . 119E*03 0 . 4 9 . 1 1 9 E + 0 3 - - 1 .234E»03 0 . 4 1 . 2 3 4 5 * 0 3 - - 1 . 0 0 0 E - 0 5 0 . 4

1 1000 2 969 1000 3 805 821 1000 4 5 37 560 920 1000 5 352 364 823 974 1000 6 352 364 823 7 352 364 823 8 3 52 364 823 9 352 364 823

10 352 364 823

8 10

974 1000 1000 974 1000 1000 1000 974 1000 1000 1000 1000 974 1000 1O00 1000 1000 1000 974 1000 1000 1000 1000 1000 1000

BLEHEPTS OP THE CORRELATION HATRIX (10«»3) POB "ATEBIAL 1261 REACTION 102 WITH RESPECT TO flATERIAL 1261 REACTIOll 102

INERGY RANGE (EVI

1 .733B*07 — 1. 35 3E»06— 4 . 9 7 9 E * 0 5 - -1 .832E*05— 1.111E»05— 6 . 7 3 8 E + 0 4 - -4 . 0 8 7 E » 0 4 - -2 . 4 7 9 P » 0 4 - -9 . 119E»0 3— 1 .234E»03—

* BEL GROOP 1 STD-DEV

3 10

1 .353E»06 5 9 . 0 4 . 9 7 9 E » 0 5 3 9 . 3 1 . 8 3 2 E * 0 5 2 2 . 7 J 1. 111E»05 1 5 . 0 4 6 . 7 3 8 E » 0 4 9 . 4 5 4 . 0 8 7 2 * 0 4 1 0 . 0 6 2 . 4 7 9 E * 0 4 H.7 7 9 . 1 1 9 E » 0 3 9 . 6 8 1 .234E»03 7 . 6 9 1 . 0 0 0 E - 0 5 7 . 4 10

1 1000 2 6 76 1000

382 664 1000 305 566 1000 198 353 127 220 146 253 132 229

200 131

85 97 88

112 1 14

169 291 171 296

576 1000 333 963 1000 383 900 911 1000 347 550 520 826 1000 441 701 662 761 696 1000 448 7 1 2 6 7 3 773 7 0 0 914 1000

ELEMENTS OP THE C0*3?.LATX0» MTRIX (10**3) POB HATEBIAL 1261 BEACTIOH 4 5 2 HITri RESPECT TO MATERIAL 1262 BEACTION 452

ENERGT BANGE (ET)

1 .733B*07— 1. 353E»06— 4 . 9 7 9 E » 0 5 — 1. 332E»05— J. 11IE»05— 6 . 7 3 8 E * 0 4 — 4 . 0 8 7 E » 0 4 - -2 . 479E»0«— 5 . i i 9 e » u i — 1 . 2 3 4 E + 0 3 - -

1 .353E»06 4 . 9 7 9 E * 0 5 1 .832E»05 1 . 1 1 1 E » 0 5 6 .73f lE»04 4 . 0 8 7 E * 0 4 2 . « 7 9 E » 0 4 9 . 119E»03 t .23*E*G3 1 . 0 0 0 E - 0 5

GBOHP 1 2 3 4 5 6 7 8 9 10

1 154 149 244 249 244 244 244 244 244 244 2 133 129 210 215 211 211 211 211 211

133 133 133 133 133 1 33

129 129 129 129 129 129

210 210 210 210 210 210

215 215 215 215 215 215

211 211 211 211 211 211 ?11

211 211 211 211 211 211 711

10 i .13 129 210 215 211 211 211 211 211 2

211 211 211 211 211 211 211

211 211 211 211 211 211 711

211 211 211 211 211 211 211

E-4

BUIBRTS OP THE COBBELtTIOl BATIIX (10*«3) POI BATE IIM. 1261 IEKCTIOI 452 WITH lESPECT TO BATEHIAl 126* IBACTIO* «52

o BIBRCT IAICE (CT) GIOOP 1 10

1 . 7 J 3 B * 0 7 ~ 1.353E*06 1 268 259 • 23 •3» • 2 5 • 2 5 • 25 • 2 5 •25 •25 1.3538*06— • . 9 7 9 8 * 0 5 2 ««0 •25 69« 711 697 697 697 697 697 697 • , 9 7 9 B * 0 5 — 1.8328*05 3 269 260 •2« •35 026 • 2 6 •26 • 2 6 • 26 •26 1 .8328*05 - - 1.1118*05 • 269 260 • 2 * •35 • 26 • 26 •26 • 2 6 •26 •26 1.1118*05— 6.738E*0« 5 269 260 •2« •35 • 26 • 2 6 •26 • 2 6 •26 •26 6 .738E*0«™ « .087E*0* 6 269 260 «2« •35 426 • 2 6 •26 • 2 6 •26 •26 • , 0 8 7 B * 0 « — 2.»79B»0» 7 269 260 «2« •35 • 26 • 26 •26 • 2 6 •26 •26 2 .«79E*0«— 9.119E*03 8 269 260 •2« •35 • 26 • 26 •26 • 2 6 •26 •26 1.119E*03— 1.23«E*03 9 269 260 • 2* •35 • 26 • 2 6 •26 • 2 6 126 •26 1 . 2 3 « * 0 3 — 1.000E-05 10 269 260 •2« •35 • 26 • 26 •26 • 2 6 •26 •26

ELEHEITS OP THE COSREUTIOI HATBIX (10**3) POB BUTEtlJll 1261 IBACT109 «52 WITH lESPECT TO HATEIIAL 1265 IE ACTIO! • 5 2

EIEBGT BARGE (ET) CIOOP 1 10

1 . 7 3 3 B * 0 7 ~ 1.3538*06 1 218 210 3*3 352 3«5 3«5 3*5 3 * r 3«S 1«5 1 .353B*06- - • . 9 7 9 8 * 0 5 2 176 170 278 285 279 279 27'i 279 279 279 «.979E*05— 1.8328*05 3 176 170 278 285 279 279 279 T.79 279 279 1.8328*05— 1.111E*05 « 176 170 278 285 279 279 279 279 279 279 1.1118*05— 6.738E*0« 5 176 170 278 285 279 779 279 279 279 279 6. 738E*0«— • . 0878*0* 6 176 170 278 285 279 •»9 279 279 279 279 • • 0 8 7 B * 0 » ~ 2.«79E*0« 7 176 170 278 2J5 ?"»*» ".J 279 279 279 279 2 . • 7 9 8 * 0 * - - 9 .1198*03 8 176 170 278 285 279 279 279 279 279 279 9 . 1 1 9 B * 0 3 ~ 1.23«E*03 9 176 170 278 285 279 279 279 279 279 279 1 . 2 3 * 8 * 0 3 - - 1.000E-05 10 176 170 278 285 279 279 279 279 2 79 279

BLSHEHTS OP THE COIBELATIOI BATtlX (10**J) .'01 *J RATERI1L 1261 BERCTIOH • 5 2 I I T H 8B5PBCT TO • .TEBIAl 1266 I B ACTIO! • 5 2

EBEIGX RiRGE (BT) C I OOP 1 2 3 • 5 6 7 8 9 10

1.733B*07— 1.3S3E«06 1 165 159 260 266 261 261 261 261 261 261 1.353E*06— • •979E*05 2 110 105 173 178 1 7 * 17» 17» 17« m 17* » .979E*05— 1.812E*05 3 110 106 173 178 17« 17« 17» 17« 17« 17» 1 .8328*05- - 1.111E*05 « 110 106 173 178 1 7 * 17* 17« 17« m 17* 1.1118*05— 6.738E*0« 5 110 106 173 178 17« 17« 17« 1 7 * 17« 17« 6.738E*0« — «.087B*0« 6 110 106 173 178 17« 17» 17* 17« 17* 17* • •087E*0«— 2.«79B*0« 7 110 106 173 178 17« 17« 17* 17« 17« 17» 2 .»79E*0»— 9.1198*03 8 110 106 173 178 17« 17» 17« 17« 17« 17» 9 .119E*03— 1.23«E*03 9 110 106 173 178 17» 178 17« 17« m 17» 1.23*B»03— 1.000E-05 10 110 106 173 178 1 7 * 17« 17« 17« 17* 17»

ElEHEHTS OP THE COIIELATIOI BATIIX (10* *3 ) POB RATERIAL 1262 IEACTIOH 18 WITH RESPECT TO BATEIHI . 12»2 IBJCTIOH 18

EIERGT RAI IGE (E»> f BEL GfOTI ? 1 2 3 « 5 6 7 8 9 10 Sfb-DCT

1.73?B*07— 1.J53E*06 2 . 2 1.3S3E*06— • .979E*05 10 .9 • , 9 7 9 E * 0 5 — 1. 83?E*05 0 .0 1.8328*05— 1.111E*05 0 . 0 1.1118*05— 6.738E«0« 0 . 0 6 .736E*0«— « . 0878*0* 0 . 0 « .087E*0«— 2.«79E»0« 0 . 0 2 . « 7 9 E * W — 9.119E*03 0 . 0 9 . 1 1 9 8 * 0 3 — 1.23*8*03 0 . 0 1.23»E*03— 1.000S-05 0 . 0

1000 203 1000

8 9

10

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0

@

E-5

ELEHEBTS OF THE COBBELATIOR HATBIX ( 1 0 « 3 ) FOB RATEBIAL 1262 BEACTIOB « 5 2 WITH BESPECT TO RATEBIAL 1262 I E K T I O I • 5 2

EBEBGT BABSE (ET) f BEL GBOUP STD-orr

10

1 . 7 3 3 E * 0 7 ~ 1.353E*06 1.» 1 . 3 5 3 E * 0 6 ~ «.979E*05 1.6 • . 9 7 9 B * 0 5 - - 1.832E*05 1.6 1 . 8 3 2 E * 0 5 ~ 1 . 111E»05— 6 .738E*0«— • • 037E»0»— 2. 4 7 9 E O * - -9 . 1 1 9 E * 0 3 - -

1.111E*05 6.738E*0« «.087E*0« 2.«79E*0« 9.119E*03 1.23«E*03

1.6 1.6 1.6 1.6 1.6 1.6

1 1000 2 999 1000 3 999 1000 1000 • 999 1000 1000 1000 5 999 1000 1000 1000 1000 6 999 1000 1000 1000 1000 1000 7 999 1000 1000 1000 1000 1000 1000 8 99° 1000 1000 1000 1000 1000 1000 1000 9 999 '000 1000 1000 1000 1000 1000 1000 1000

1.23«E«03— 1.000E-05 1.6 10 999 1000 1000 1000 1000 1000 1000 1000 1000 1000

BLEBBUTS Op THE COBBELATIOB HATBII (10«*3) p o t HATEBIAL 1262 BEACTIOB 5 1 BITS BESPECT TO BATEBIAL 1262 BEACTIOB 51

^J

EBBBCT BABGE (Ef) * BEL CBOOP 1 10 STO-DEf

1 .733E*07 - - 1.353E*06 3 3 . 5 1 1000 1 .353E*06 - - «.979E*05 « 1 . 2 2 1000 1000 • . 9 7 9 E * 0 5 - - 1.832E*05 • O.O 3 1000 1000 1000 1 .8328*05— 1.111E*05 « 0 . 0 « 1000 1000 1000 1000 1 .1113*05— 6.738E«0* 75 .6 5 1000 1000 1006 1000 1000 6 .738E*0«— • . 0 8 7 8 * 0 * 9 0 . 0 6 1000 1000 1000 1000 1000 1000 « .087E»0«— 2 . *79E*0« 0 . 0 7 0 0 0 0 0 0 0 2- • 7 9 E * 0 « — 9.119E*03 0 . 0 8 0 0 0 0 0 0 0 0 9 .119E*03— 1.23«E*03 0 . 0 9 0 0 0 0 0 0 0 0 0 1 . 2 3 « * 0 3 — 1.000B-05 0 . 0 10 0 0 0 o 0 0 0 0 0

BLEHEBTS OP THE COBBELATIOR HAT3H (10*«3) FOB HATEBIAL 1262 BEACTIOB 5 2 IITH BESPECT TO HATEBIAL 1262 BEACTIOB 52

EBEBGT BABGE (ET) % BEL GBODP 1 9 I d

1 . 7 3 3 E * 0 7 ~ 1 . 3 5 3 S * 0 6 ~ » . 9 7 9 E * 0 S - -1 . 8 3 2 E » 0 5 ~ i . * : U * 0 5 ~ 6 . 7 3 8 E * 0 « « • . 0 8 7 B * 0 « - -2 . •79E*C«— 9 . 119E*03—

STD-DEf 1.353E*06 5 5 . 8 • -979E*05 6 7 . 1 1.832E*05 6 7 . 1 1 - ^ 1 S » i 3 6 7 . 1 6.738E*0« 0 . 0 * .087E*0« 0 . 0 2.»79E»0« 0 . 0 9.119E*03 0 . 0 1.23«E*03 0 . 0

1.23«E»03— 1.000E-05 0 . 0

1 1000 2 1000 1000 : *.ooo IOOO IOOO * 1000 1000 1000 1000 5 0 0 0 0 6 0 0 0 0 7 0 0 0 0 8 0 0 0 0 9 0 0 0 0

10 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0

0 0 0

ELEBEBTS OP THE COBBEIATIOB HATBII (10«*3) fOB RATEBIAL 1262 BEACTIOB 5 3 BITH BESPECT TO B4TEBIAL 1262 BEACTIOB 53

O

BBEBGT BARGE (BT) X BEL GBOJP 1 9 10 STD-D8T

1 .733E*07 - - 1.353E*06 • 6 . 3 1 1000 1. J53E*06— • •979E*05 6 7 . 1 I 1000 1000 • . 9 7 9 8 * 0 5 - - 1.832B*05 6 7 . 1 1 1000 1000 1000 1 .8328*05— 1.111B*05 0 . 0 ' 1 0 0 0 0 1 . 1118*05 - - 6 .7388*0* 0 . 0 ' > 0 0 0 0 0 6 .738E*0B— * .087E*0« 0 . 0 < i 0 0 0 0 0 0 • . 0 8 7 E * 0 » - - 2 .*7SE*0« 0 . 0 r o 0 0 0 0 0 0 2 . • 7 9 B * 0 « ~ 9.119B*03 0 . 0 ( i 0 0 0 0 0 0 0 0 9 . 1198*03 - - 1. 2 3 * E O J 0 .0 < ) 0 0 0 0 0 0 0 0 0 1 . 2 3 « * 0 3 - - 1.000E-05 0 . 0 K ) 0 0 0 0 0 0 0 0 0 0

E-6

EUSEBTS OP TBE COBBELATIOB BBTBIX ( 1 0 * * 3 ) POE 8BTEBIU. 1 2 6 2 BEBCTIOB 5 9 WITl RESPECT TO IATEBIH. 1262 BE4CTIOB 54

EBSBCT BBRCE (ET» * BEL 6BOBP 1 10 STO-DEf

1 .733B*07- - 1.353E»06 5 1 . 8 1 1000 1 .353E*06- - 4 .9798*05 6 7 . 1 ; 2 1800 1000 4 . 9 7 4 8 * 0 5 — 1.832E*05 0 .0 i 0 0 0 1 .8328*05— 1.111E*0S 0 .0 I 1 0 0 0 0 1 . 1118*05— 6.7388*04 0 .0 ' 0 0 0 0 A « . 7 3 8 * * 0 4 — • .0878*04 0 .0 1 > 0 0 0 0 0 0 4 . 0 8 7 E * 0 4 ~ 2.4798*04 0 .0 J 0 0 0 0 0 0 0 2 . 9 7 9 8 * 0 4 — 9.1198*03 0 .0 1 1 0 0 0 0 0 0 0 0 9 .119E*03— 1.234E*03 0 .0 1 1 0 0 0 0 0 0 0 0 0 1 .2348*03— 1.OO0E-0S 0 .0 K ) 0 0 0 0 0 0 0 0 0

ELEBEJTS OP THE COBBELATIOB BBTBIX ( 1 0 * * 3 ) POB RBTEBIkL 1 2 6 2 BEACTIOB 102 «ITR BESPECT TO HKTBBIU. 1262 BEBCTIOB 1 0 2

EBEBCT BASSE (EV) % BEL CBOOP 1 10 STD-DEV

1 .7338*07— 1.3538*06 18.8 1 1000 1 .3538*06— 4.979E*05 18 .7 2 585 1000 4 . 9 7 9 8 * 0 5 — 1.8328*05 12.4 3 518 83« 1000 1 . 8 3 2 8 * 0 5 " 1.111E*05 10.3 4 454 615 320 1000 i . 1 1 1 ! * 0 5 — 6 .7388*0* 8 .7 5 291 973 • 6 9 569 1000 6 .7388*04— 4.0878*04 C.8 6 178 31*) 395 355 710 1000 4 .0878*04— 7.4798*04 10 .1 7 115 276 2*4 279 510 742 1000 2 .4798*04— 9.1198*03 12.3 8 158 414 382 308 9 97 426 668 1000 4 .1198*03— 1.2348*03 4 .6 9 119 966 390 202 397 334 358 580 1000 1.2348*03— 1.000E-05 7 .3 10 0 51 31 15 127 216 201 189 500 1000

Ei,EHERTS OP THE COBBBLBTIOB flATBII (10«*3) POB KftTBBIftL 1 2 6 2 BE ACTIO! 4 5 2 BITB BBSP8CT TO BATESIM. 1264 BEHCTIOB 4 5 2

EIEB6T BJLB6E |ET) GBOOP 10

1.73 38*07— 1.3538*06 1 129 107 107 107 107 107 107 107 107 107 1 .3538*06— 4.9798*05 * 203 175 175 175 175 175 175 175 175 175 4 .9798*05— 1.8328*05 3 124 107 107 107 107 107 107 107 107 K 7 1 .8328*05— 1.1118*05 4 124 107 107 107 107 107 107 107 107 107 1 .1118*05— 6.7388*04 5 124 107 107 107 107 107 107 107 107 107 6 .7388*04— 4.087B*04 6 124 107 107 107 107 107 107 107 107 107 4 . 0 8 7 8 * 0 4 — 2.4798*04 7 123 107 107 107 107 107 107 107 107 107 2 .4798*04— 9. 1198*03 8 124 107 107 107 107 107 107 107 107 107 4 .1198*03— 1.2348*03 9 124 107 107 107 107 107 107 107 107 107 1.2348*03— 1.000E-05 10 124 107 107 Id? 107 107 107 107 107 107

I lk lEBTS OP TAB COBBELATIOB 8ATBII ( 1 0 * * 3 ) POB BATBBIAL 1 2 6 2 BSACTIOB 4 5 2 BITB BESPECT TO BATBUAL 1265 BEBCTIOB 4 5 2

EBEBCT BBB6B (ET) CBOOP 10

1 .7338*07— 1 .3538*06— 4 . 9 7 9 8 * 0 5 — 1.8328*05— 1. 1 1 1 E * 0 S ~ 6 .738B*04— 4 .087E*04— 2 . 9 7 9 E * 0 4 ~ 9 . 1 1 9 8 * 0 3 — 1 .2348*03—

1.353E*06 4 .9798*05 1.8328*05 1 .11 IE*05 6 .7388*04 4.087E*04 2 .4798*04 9 .1198*03 1.234E*03 1.000E-05

1 100 86 86 86 86 86 86 86 86 86 2 81 70 70 70 70 70 70 70 70 70 3 81 70 70 70 70 70 70 70 70 70 4 81 70 70 70 70 70 70 70 70 70 5 81 70 70 70 70 70 70 70 70 70 C 81 70 70 JO 70 70 70 70 70 70 7 81 70 70 70 70 70 70 70 70 70 8 81 70 70 70 70 70 70 70 70 70 9 81 70 70 70 70 70 70 70 70 70 0 91 70 70 70 70 70 70 70 70 70

E-7

BLEHEBTS OP Tf»E CORRELATION BATBII (10»»3) POB

HATEKAL 1262 REACTION 9 5 2 BITH RESPECT TO BATEBIAL 1 2 6 6 HEACTIOB 9 5 2

EBEBGT BiBGE (ET) CBOOP 1 2 3 * 5 6 7 8 9 10

76 65 65 65 65 65 65 65 65 65 51 99 99 99 99 99 99 9« 99 9« 51 «« 9« • « 99 99 99 9« 99 99 51 9« 99 99 99 * • 99 9« 99 99 j l « • 99 «9 99 99 99 9« 99 99 51 « • 99 99 99 99 «9 9« • « 99 51 «4 9» 99 99 99 99 9« • • 99 51 99 99 99 99 «9 99 9« 99 99 51 M 9« «9 99 99 99 « • 99 M 51 99 99 «« 99 99 99 « • 99 99

BLEPBBTS OP THE COBBELATIOB HATBII '10**3) POB BATERIAL 1269 BEACTIOB 18 BITH RESPECT TO BATEBI1L 1269 BEBCTIOB 18

BBEBGT BABGE (ET) % BEL GBOIP 1 2 3 * 5 6 7 8 9 10

1.733E*07— 1.353E«06 1 1 . 353E*06— 9.979B*05 2 9 . 9 7 9 E * 0 5 ~ 1.832E*0S 3 1 . 8 3 2 E * 0 5 ~ 1.111E*05 9 : . 1 1 1 E * 0 5 ~ 6 .7388*09 5 6 .738E*09— 9.087B«0« 6 9 .087E*09— 2.979E*09 7 2 .979E*0»— 9.119E*03 8 9 .1198*03— 1.2398*03 9 1.239E«03— 1.000E-05 10

STD-OET 1 . 7 3 3 E * 0 7 ~ 1.353E*06 6 . 0 1 1000 1 . 3 5 3 E * 0 6 ~ 9.979E*0S 5 .7 2 792 1000 9 .979E*05— 1.832E*05 10 .9 3 313 502 1000 1.832E*05— 1. 1118*05 19 .3 • 193 265 589 1000 1 .111E*05- - 6.738E*09 12 .9 5 209 257 675 879 1000 6 .7388*09— 9.0878*09 6 . 3 6 382 9 1 329 179 373 1000 9.087E«09— 2 . 9 7 9 8 * 0 * 3 . 2 7 569 79t • 22 229 271 529 1000 2 .979E*09— 9.119E*03 3 .8 8 929 957 238 139 192 297 699 1000 9 . 1 1 9 E * 0 3 ~ 1.239E*03 5 . 1 9 32* 395 180 102 108 187 393 996 1000 1 .239E*03- - 1.000E-05 3 . 9 10 279 292 152 86 91 158 320 206 720 1000

ElEHEBTS Or THE COBBELATIOH BATBII «10**3) POB RATERIAL 1 2 6 * BEACTIOB 1 0 2 WITH RESPECT TO HATEBIAL 1269 BEBCTIOB 102

EBEBGT BABGE (ET) « BEL GROUP 1 2 3 9 5 6 7 8 9 10 STO-OET

1 . 7 3 3 E * 0 7 ~ 1.353E*06 0 .0 1 1000 1 .353E*06-- • . 9 7 9 8 * 0 5 1 9 . 1 2 0 1000 9.979E»05— 1.832E*05 11 .5 3 0 99 1000 1.8328*05— 1.1118*05 2 3 . 2 9 0 352 536 1000 1. 11 IE* 05— 6.738E«09 13.3 5 0 -199 586 359 1000 6.7 38E*0«— 9.087E*0« 12 .2 6 0 -360 113 -391 579 1000 « .087E*0« - - 2.«79E*0« 7 . 9 7 0 223 155 1»9 38 39 1000 2 . *79E*09— 9.119E*03 8 .5 8 0 38 98 19 77 109 563 1000 9.119S*03— 1.23«E*03 12.0 9 0 189 85 189 - 8 7 - 1 8 2 919 • 1« 1000 1 .23»E*03~ 1.000E-05 9 . 5 10 0 87 55 82 - 1 7 - 5 3 152 95 681 1000

ILEBEBTS OP THE COBBELATIOB BATBII (10«*3) POB HATE RIAL 1269 BEACTIOB 9 5 2 BITH RESPECT TO HATEBIAL 1 2 f * BEACTIOB « 5 2

ENERGY RABGE (ET) t BEL GROUP 1 2 3 9 5 6 7 8 9 10 STD-DET

1 .7338*07- - 1.353E+06 0 .8 1 1000 1 .35 IE*06 - - » .979E*Ci 0 . 5 2 -95 1000 « .9798*05— 1.832E*05 0 .8 3 -523 891 1000 1.832E»05— 1.111E*05 0 .8 9 -523 891 1000 1000 1.1112*05— 6.738E*09 0 .8 5 - 5 2 3 891 1000 1000 1000 6 .738E*09— 9.087E*09 0 .8 6 -523 891 1000 1000 1000 1000 9 . 0 8 7 8 * 0 9 - - 2.979E*09 0 .8 7 -523 891 1000 1000 1000 1000 1000 2 .«79E*09— 9.119E«03 0 .8 8 -523 891 1000 1000 1000 1000 1000 1000 9. '19E*03— 1.239E*03 0 .8 9 -523 891 1000 1000 1000 1000 1000 1000 1000 1.23sS*03-- 1.000E-05 0 .8 10 - 5 2 3 881 1000 1000 1000 1000 1000 1000 1000 1000

E-8

BUHEBTS OP TIE COBBEUTIOB HtTBIX (10**3) POt •kTEBIkL 126% BEkCTIOB 18 »ITH 1BSPECT TO BkTEBIAL 126* BEkCTIOB

BaetCT RkBGE JET) CtOOP 1

102

10

O 1 .733E*07- - 1.353Z«06 1 0 0 0 0 0 0 0 0 0 0 1 .3538*06— * .979E*0S ; I 0 1000 502 265 i 5 7 • 5 1 7 U •57 3*5 292 * . 9 7 9 t * 0 5 — 1.8328*05 1 0 502 1000 589 675 329 •22 238 180 152 1.832E*0S— 1.111E*05 I 1 0 26S 589 1000 87« 179 22* 13* 102 86 1.111E*05— 6.738E»0* 5 0 257 675 87« 1000 373 2?1 1*2 108 91 6 . 7 3 8 E * 0 * — «.087E*0» i » 0 •51 329 179 373 1000 52* 2*7 187 158 * . 0 8 7 E * 0 * — 2 .«*9E*0« r o 7 M •22 22 « 271 5 2 * MOO 699 393 320 2 . * 7 9 B * 0 * ~ 9.119E*03 ( i ) • 57 238 13« 1«2 2«7 699 1000 • 9 6 206 9.119E* 03— 1.23«E*03 * » 0 3*5 180 102 108 187 393 •96 1000 720 1 . 2 3 * 8 * 0 3 — 1.000E-05 1( ) 0 292 152 86 91 158 329 206 720 1000

BLEBEBTS OP TIE COBBELkTIOB 1UTBIX J10»*3) POI MTtBXkL 126* HEkCTIOB «52 BIT* IESPECT TO HftTSBIkL 1265 BBkCTIOR • 5 2

EBEBCT BkBGB (ET) CtOOP 1 2 3 « 5 6 7 8 9 10

1 .733 t *07— 1.3S3B*06 1 17* 286 175 175 175 175 175 175 175 175 1.353B*06— «.979E«05 2 141 231 1*1 1«1 1*1 1*1 1*1 1*1 1*1 1*1 * . 9 7 9 B * 0 5 — 1.8328*05 3 1*1 231 1«1 181 1*1 1*1 1*1 1*1 1*1 1*1 1.832E*05— 1.111B*C5 « 1*1 231 1*1 1«1 1*1 1*1 1*1 1*1 1*1 1«1 1 . 1118*05— 6.73BE*0* 5 1*1 2^1 1*1 1*1 1*1 1*1 H I 1*1 1*1 1*1 6 . 7 3 8 E * 0 « " « .087E*0* 6 1 M 231 1*1 1*1 1*1 1*1 1*1 1*1 1*1 1*1 * . 0 8 7 E * 0 * ~ 2 . 4 7 9 8 * 0 * 7 1«: 231 1*1 1«1 1*1 1«1 1*1 1*1 1*1 1*1 2 . * 7 9 E * 0 « — 9.119B*03 8 1«1 231 1*1 1«1 1*1 1*1 1*1 1*1 1*1 1*1 9,119B»03— 1.23*E*03 9 i * i 231 1*1 1*1 1*1 1*1 1«1 1*1 1*1 1*1 1 .23*8 *03— 1.000E-05 10 i * i 231 1*1 1*1 1*1 1*1 1*1 1*1 1*1 1*1

EUBEBTS OP THE COBIELATIOB IUTBIX (10*«3) POB HkTEBIkL 126* BEkCTIOB «52 BITH BBSPBCT TO RkTBBIkL 1266 BEkCTIO* •52 V >

EBEBGT BkBCE (ET) CtOOP 1 2 J • 5 6 7 8 9 10

1 .733E*07- - 1.3538*06 1 132 216 132 132 132 132 132 132 132 132 1.353E*0>— * .979E*05 • ^

A 88 1«* 88 88 88 88 88 88 88 88 « .979B*Ci— 1.832E«05 3 88 1«* 88 88 88 88 88 88 88 88 1 . 8 3 2 E * 0 3 ~ 1.111E*05 • 88 1 * * 88 88 88 88 88 88 88 88 U111E*05— 6.738E*0« K 88 1 * * 88 88 88 88 88 88 88 88 6 . 7 3 8 E * 0 « ~ « .087E*0* 6 88 1 * * 88 88 88 88 88 88 88 88 • . 0 8 7 8 * 0 * — 2 .«79E*0* 7 88 1«« 88 88 88 88 98 88 88 88 2 . « 7 9 B * 0 « ~ 9.119E*03 8 88 1«« 88 88 88 88 88 88 81 88 9.119B*«>3— 1.23*E*03 9 88 1*« 88 88 88 88 88 88 88 88 1 .23*E*03— 1.000E-05 10 88 1«« as 88 88 88 88 88 88 88

ELEBEBTS OP THE COBBEikTIOB RftTBIX (10**3) POB RkTERIkL 1265 BEACTIOB «52 BITH BESPECT TO HUTEBIJU 1265 BEACTIOH «52

EBEBCT BkBCE (ET) % BEL CtOOP 1 STD-DET

10

1 1000 2 99* 1000

1.733E*07— 1.3538*06 1.0 1.3538*06— * . 9 7 9 8 * 0 5 1.2 * . 9 7 9 E * 0 5 — 1.832E»05 1.2 1.3328*05— 1.111B*0S 1.2 1.111B*0S— 6.738E«0* 1.2 6 .738E*0«— «.087E»0« 1.2 • , 0 8 7 E * 0 « — 2 . * 7 9 E * 0 * 1.2 2 . * 7 9 I * 0 * — 9.1198*03 1.2 9 .1198*03— 1.23*8*03 1.2 1 .23*8 *03— 1.000E-05 1.2 10 99* 1000 1000 1000 1000 1000 1000 1000 1000 1000

99* 1000 i."00 99* 1000 1000 1000 99* 1000 1000 1000 1000 99* 1000 1000 1000 1000 1000 99* 1000 1000 1000 1000 1000 1000 99* 1000 1000 1000 1000 1000 1000 1000

©

E-9

EUIEBTS OP TIC COBBELATIOB BATIII ( 1 0 » * 3 ; POl HAT'BIAL 1 2 6 5 BEACTIOB 1 0 2 1ITH BE3PBCT TO B1TEBIU. 12S5 BE ACTIOS 102

eaeicT BABCE ccf) « t c i GBODP 1 2 3 * 5 6 7 8 10 STD-DBf

1 .731E*07- - 1.3538*06 12.0 1 1000 1.353B*06™ • , 9 7 9 E * 0 5 12.9 2 -999 1000 • . 9 7 9 E * 0 5 - - 1.832C*0S 22 .0 3 -853 850 1000 1.832C»05— 1. 111E*0S 3 * . 1 • -217 216 666 10 JO 1.1111*05— 6.738E*0« 3 5 . 9 5 -239 238 691 198 1000 6 .738B*0«— «.087E»0« 37 .2 6 -192 192 6 3 * 997 9 9 1 1000 «.087E»0«— 2 .«79E*0* 1«.0 7 -287 253 fcJ2 855 865 859 1000 2 .#79C*0*— 9.119E*03 10.0 8 -159 162 183 35 61 32 519 1000 9 .119E*03— 1.23«C«03 10.7 9 - 3 6 2 370 573 396 • «3 372 677 629 1000 1 .23«C«0J~ 1.000E-05 2 .5 10 - 3 0 3 310 666 7 8 * 807 780 890 379 808 1000

ELEHEBTS or THE COBBCLATIOI NUTBIX |io««3) POI HATEBIAL 1 2 6 5 BEACTIOB « 5 2 BIT* BEFPECT TO RATEBIAL 1 2 6 6 BEACTIOB « 5 2

eBEBGT B1I6E (11) CtOOP 10

1.73 3E*07- - 1.353E*06 1 107 87 87 87 87 87 87 87 87 • 7 1 . I53E»06— %.979E*0S 2 71 58 58 58 56 58 58 58 58 58 • ,979E»05— 1.832E*0S 3 71 58 58 58 58 58 58 58 58 58 1.832B*0S-- 1 . 1 1 1 ^ 0 5 * 71 58 58 58 58 58 58 58 58 58 1. 111E»05— 6 .738E*0* 5 71 58 58 58 58 58 S8 58 58 58 S .738E*0« - - «.087E*0« 6 71 58 58 58 58 58 58 58 58 58 ».087E»0»— 2.«79E»0« 7 71 58 58 58 58 58 58 58 58 58 2 . »79E*0»- - 9.119E*03 8 71 58 58 58 58 58 58 58 58 58 9. 1196*03— 1.23«E*03 9 71 58 58 58 58 58 58 58 58 58 1 . 2 3 « * 0 3 — 1.000E-05 10 71 58 58 58 58 58 58 58 58 58

ELEHEBTS OP THE COBBELATIOB HATBIX (10**3) POB 8ATEBIAI 1 2 6 6 BEACTIOB 18 BITH BCSPECT TO 4ATEBIAL 1 2 6 6 BE ACTIO! 18

EBEBGY BABGE (ET) t BEI CROUP 1 10

1 . 7 3 J E » 0 7 — 1 .35 3E*06— » . 9 7 9 E * 0 5 - -1 .832E»0S— 1 .111E*05— 6 . 7 3 8 E * 0 « - -9 . 0 8 7 E * 0 » — 2 . » 7 9 E * 0 » " 9 . 1 1 9 E * 0 3 - -1 . 2 3 9 E * 0 3 —

STO-DCf 1 . 3 5 3 E 0 6 3 .1 1 • . 979E*05 6 . 1 2 1.832E*05 7 . 5 3 1.1118*05 5 .2 9 6.738C*0« 3 . 0 5 «.087E*0« 3 .0 6 2.«79E*0« 3 .6 7 9.1191*03 5 .« 8 1.23«E»03 7 .0 9 1.000E-05 10.5 10

1000 768 1000 810 906

0 - 6 0 in -55 29 - ' 2 8

2 -'»• 0 - i l 0 0 0 0

1000 81 1000

163 M S 1000 130 - 1 3 * 5 3 * 1000 - 9 66 * 90 - 3 5 7 39 631 393 - 2 2 1

• 59 36 - 1 5 - 9 - 1 2 2 - 8 2 33

1000 659 1000

•0 - 3 9 2 1000 -79 - 1 9 6 7*3 1000

•LEBEBTS OP TIC COBBCLATIOB HATBII ( 1 0 « * 3 ) POI RATCBIAL 1 2 6 6 ICACTIOB « 5 2 BITH BCSPKCT TO BATEBIAL 1266 BEACTIOB • 5 2

CBCICT BABCB fBT) « BCl CIOOP STD-OCT

1.733C*07— 1.353C*06 1.3

10

1 1000 993 1000 993 1000 1000 993 1000 1000 100C 993 1000 1000 1J00 1000 993 1000 1000 1000 1000 1000 993 1000 1000 1000 1000 1000 1000 993 1000 1000 1000 1000 1000 1000 1000 993 1000 1000 1000 1000 1000 1000 1000 1000

1 . 2 3 * 1 * 0 3 - - 1.000B-05 1.9 10 991 1000 1000 1000 1000 1000 1000 1000 1000 1000

1.353B*06— • . 9 7 9 1 * 0 5 1.9 2 * . 9798*05— 1.8J2B*05 1.9 3 1.832C«0S— 1.1118*05 1.9 • 1 . 11 IB* OS— 6 .738C*0* 1.9 5 6 .738C*0«— «. 0 8 7 8 * 0 * 1.9 6 9 . 0 8 7 B * 0 * - - 2.«79C*0« 1.9 7 2 . * 7 9 E * 0 * — 9.1191*03 1.9 8 9. 119C*03— 1.23*E*03 1.9 9

E-10

ELS8EBTS o r TIB COBIELATIOB RATIIX |10**3) PO« BATEBIAl 1266 BSACTIOI 102 WITH BE5PSCT TO BATEBIAL 1266 IE ACTIO! 102 o

E8EB6T MICE (BT1 % EEL SBOOP STD-3CT

1 .7338*07— 1.J53E«06 « * . 7 1.3S3E*06— « .979BOS 1 * 5 « . 9 7 9 8 * 0 5 — U832E*05 16.7 1.832E*05— 1.*11E*05 3 0 . 2 U111E*0S— 6 .?38E*0* 18 .5 6 . 7 3 8 E * 0 * — «.087E*0« 22 .0 « . 0 8 7 E * 0 * ~ 2 . * 7 9 E * 0 * 9 . 7 2 . 4 7 9 8 * 0 * — 9.119E*03 18.9 9 .119E*03— 1.23*E*03 10 .2 1 . 2 3 * E * 0 J ~ 1.000E-05 7 .0

10

1 1000 2 •00 1000 3 - 3 3 6 70S 1000 « 59 29 206 1000 c 162 - 1 0 75 938 1000 6 179 55 123 917 976 1000 7 293 90 • 6 796 927 9 5 * 1000 8 119 37 156 9 *5 968 990 901 1000 4 186 57 119 912 976 1000 959 987 1000

10 25* 78 76 850 955 9 *1 99* 9 * * 985 1000

SUBSETS or TIC COIBILATIOB BATEII (10«*3) FOE •ATEBIAL 127* BEACTIOB 1 EITI BB5PBCT TO OATEN AL 127* BEACTIOB

EBEBCT IABCE (ETJ % BEL CEOBP 1 2 3 * 5 6 7 STD-9ET

10

1.733E*07— 1.3S3E*06 0 .8 1 1000 1.353E*06— * . 9 7 9 E * 0 5 0 .9 2 39* 1000 * . 9 7 9 8 * 0 5 — 1.832B*0S 0.9 3 353 75* 1000 1 .8328*05— 1.1118*05 0 .9 « 353 75* 1000 1000 1 .1118*05— 6 .738C*0* 0 .9 5 370 789 812 812 1000 6 .738B»0*— «. 0 8 7 8 * 0 * 0 .9 6 353 752 719 719 989 1000 * . 0 8 7 8 * 0 * — 2 . * 7 9 E * 0 * 0 .9 7 353 752 719 719 989 1000 1000 2 . * 7 9 5 - 0 * ~ 9.119B*03 0 .9 8 353 752 719 719 989 1000 1000 1000 9 .119E*03— 1.23*E*03 0 .9 9 353 752 719 719 989 1000 1000 1000 1000 1 . 2 3 * 8 * 0 3 — 1.000B-05 0 .9 10 373 79* 760 760 858 833 833 833 833 1000

ELBREBTS ?P TBE COBBEMTIOI RATIII (10**3) FOB (IATEIIAL 127* BEACTIOB 51 BITE BB5PECT TO BATEBIAL 127* BEACTIOI 51

V >

EIEBCT RAICE (ET) t BEL GIOOP 1 9 10

1.733E*07— 1. 35 3* • 06— * . 9 7 9 E * 0 5 — 1.a3JE*05— 1 . 111E*05— 6 . 7 3 8 5 * 0 * - -«.O87fc*0*— 2 . * 7 9 E * 0 * — 9.119S*03— 1.23*E*03—

1.353B*06 * . 979E*05 1.832E*05 1.111E*05 6 .738 0 * * . 0 8 7 s 0 * 2 . « 7 9 E * 0 * 9. 119E*03 1. 23*E»03 1.OOOE-05 0 .0

STD-DEf 6 .3 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0

1 1000 2 0 3 « 5 6 7 8 9

10

0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0

0 0 0

ElEflEBTS Or TBE COBIELATIOB BATH I (10**3) POI RATEIIAL 127* BEACTIOB 91 UTH IESPBCT TO HATCH AL 127* BEACTIOI 91

EIEBCT BAKE (ET) % BE1 GIODP 1 9 10 STD-DEf

1.733E*07— 1 . 3 5 l r * 0 6 — * . 9 7 9 E * 0 5 — 1.832E*05— 1.111E*0S— 6 . 7 3 8 8 * 0 * — * . 0 8 7 E * 0 * — 2 . * 7 9 E * 0 * — 9 .119E*03— 1 .23 * f»03—

1 1000 2 0

1.3S3B*06 * 8 . 0 * .979E*05 0 .0 1.8328*05 0 .0 3 0 1. 111E*05 0 .0 • 0 6 .738E*0* 0.0 5 0 9 . 0 8 7 E O * 0 .0 6 0 2.«79E*0« 0 .0 7 0 9.119E*03 0 .0 8 0 1 .23*Et03 0 .0 9 0 1.000E-05 0.0 10 0

0 0 0 0 0 0 J 0

0 0 0 0 0

0 0 0 0

0 0 0

0 0 0

©

E - l l

ELen?rrs or THE COBIELATIOI .I«TBII no*«3i rot 9ATERIAL 127« BEACTIOB 102 BITH r.BSPECT rO HtTERIU. 127« I F ACTIO! 102

E9EB6T BABGE (rT) * kEL GB00P 1 2 3 • 5 STO-DEf

1 .733E*07— 1.353E»Q6 0 . 0 1 0 1. 3 5 3 S » 0 6 — 9 . 9 7 9 E » 0 5 0 - 0 2 0 0 • • 9 7 9 E » 0 5 ~ 1 .832E»05 0 . 0 3 0 0 0 1 . 8 3 2 E O S - - 1 .111E«05 0 . 0 9 0 0 0 0 1 .111E»0S— 6 . 7 3 8 E 0 9 0 . 0 5 0 0 0 0 0 6 . 7 3 8 E » 0 9 — « . 0 8 7 E « 0 « 0 . 0 6 0 0 0 0 0 « . 0 8 7 E * 0 « — 2.«79E»0«! 0 . 0 7 0 0 0 0 0 2 . 9 7 9 E » 0 « - - 9 . 1 1 9 E » 0 3 0 . 0 8 0 0 0 0 0 9 . 1 1 9 E 0 3 - - 1-239E*03 0 . 0 9 0 0 0 0 0 1 . 2 3 9 E » 0 3 - - 1 . 1 0 0 E - 0 5 5 . 6 10 0 0 0 0 0

10

0 0 0 0 0

0 0 0 0

0 0 1000

EUREBTS OF TIE CORBELATI01 1I1TRIX ( 1 0 * * 3 ) FOB BATERIAL 1279 IEACTIOS 107 SITS 9SSPECT TO RATES!At 127« BEACTIOS 107

<J

EBEBGT RABCE (ET) I BEL CBOOP 1 2 3 • 5 6 7 8 9 STD-DET

1 .733B»07~ 1.353E*06 13.0 1 1000 1.353E»06-- 9 .979EOS 0 . 0 2 0 0 9 . 9 7 9 I » 0 S — 1.832E*05 0 . 0 3 0 0 0 1.S321*OS-- 1.1118*05 0 . 0 9 0 0 0 0 1 . 1 1 1 E 0 5 - - 6.738E«0* 0 . 0 5 c 0 0 0 0 6.738E«0«— 9.087E*09 0 . 0 6 0 0 0 0 0 0 9 . 0 9 7 E O 9 - - 2.979E»09 0 . 0 7 0 0 0 0 0 0 0 2.979E»09— 9.119E«03 0 . 0 8 0 0 0 0 0 0 0 0 9 .119E*03— 1.23«E*03 0 . 0 9 0 0 0 0 0 0 0 0 0 1 .239E»03~ 1.000E-05 0 . 0 10 0 0 0 0 0 0 0 0 0

10

ELEREBTS OP THE COSftELATIOB RATRIX ( 1 0 * * 3 } POB HATEBrAL 1276 IEACTIOB 1 SITU BESPCCT TO HATEBIAL 1275 BEACTIOB 1

ESEBCT HSGE (ET) « BEL GIOOP 1 STO-DEf

1.733E»07— 1.3S3E»06 1.1 1 1000 1 .353 t>0*— «.979E»05 1.7 2 902 1000 9 . 9 7 9 E 0 5 - - 1.832E»05 3 .1 3 72 932 1000 1.832E#05— 1 .1M?*05 3 . 1 • 72 92* 991 1000 1 . 111E»0S~ 6-730E*O9 3.0 5 73 936 996 991 1000 S.738E»C9-- 9.087E»09 3 . 0 6 73 936 99S 987 1000 1000 9 . 0 8 7 E * 0 9 - - 2.«79E»0* 3 .0 7 73 936 995 987 1000 1000 1000 2 .979B*09 - - 9.119E»03 3 .0 8 73 936 99S 987 1000 1000 1000 1000 9. 119E»03— 1.23«E»03 3 .0 9 73 936 995 987 1900 1000 1000 1000 1000

10

1 . 2 3 « E * 0 3 " 1.00OE-0S 2 . 9 10 22 28S 303 300 309 309 309 309 30« 1000

EUREBTS OP THE CORBELATIOS HATRIX ( 1 0 * * 3 ) POB HATERIAL 1 2 - 5 BEACTIOS 2 BITR RESPECT TO HATESIAL 1275 BEACTtOI

EBEBCT RABCE (ET) f BEL CBOOP 1 10

V-' '

STD-DET 1 . 7 3 3 B » 0 7 — 1.353E»06 2 . 3 1 . 3 5 3 E * 0 6 ~ 9 . 9 7 9 E O S 1 .8

1 1000 2 321 1000

* . 9 7 9 B » 0 5 ~ 1 . 8 3 2 E * 0 5 ~ 1 . 1 i « » O S -6 . 7 3 8 E * 0 * - -9 . 0 8 7 E O 9 - -2 . 9 7 9 E * 0 9 ~ 9 . 119E#03—

1.832E»0S 1. 111E*05 6 . 7 3 8 E « 0 « 9 . 0 8 7 E * 0 9 2 . 9 7 9 t » 0 « 9 . 1 1 9 E * 0 3 1 .23*E*03

3 . 1 3 .1 3 .1 3 .1 3 . 1 3 . 1 3 .1

3 * 5 6 7 8 9

60 60 61 61 61 61 61

882 1000 87* 991 1000 835 996 492 1000 986 99S 987 1000 1000 886 995 987 1000 1*00 1000 886 886

1 . 2 3 9 E » 0 3 ~ 1 . 0 0 0 E - 0 5 2 . 9 10 19 272

995 99S

987 1000 1< )J 1000 1000 987 1000 10JO 1000 1300 1000

305 303 306 307 307 307 307 1000

E-12

ELSBEHTS OP THE COIIEUTIOI 8ATBIX (10**J> POI •UTEB2AL 1275 IIACTIO! « BITS IBSPtCT TO HATEBIAL 1275 I B ACTIO*

EBEBCT BABCE (ET| % BEL 6B0BP 1 8

o 10

STD-DE* 1 .733E*07— 1.3538*06 6 . 0 1 1000 1 . 3 5 3 C 0 6 — 4.979E+05 0 .0 2 0 0 • . * 7 9 E * 0 5 - - 1.8328*05 0 .0 3 0 0 0 1 .332E*05 - - 1.1118*05 0 . 0 • 0 0 0 0 1.111E*05— 6.738E*0« 0 . 0 5 0 0 0 0 0 6 .738E»0« - - «.087E*0« 0 . 0 6 0 0 0 0 0 0 «.0ft7E*0«— 2.«79B*0« 0 .0 7 0 0 0 0 0 0 0 2. « 7 9 E * 0 * — 9.1198*03 0 . 0 8 0 0 0 0 0 0 0 0 9 . 1 1 9 E * 0 3 - - 1.23*E»03 0 .0 9 0 0 0 0 0 0 0 0 0 1 . 2 3 « « 0 3 — 1.000E-05 0 . 0 i n 0 0 0 0 0 0 0 0 0

I U i r ; i S OP THE COIIEUTIOI H I T ! I I ( 1 0 * * 3 ) POB nATKBIAL 1275 BEACTIOB 102 IITH IBSPECT TO HATEBIAL 1275 BE1CTIOI 102

EBEBCT MICE (ET) t IEL GBOOP 1 10 STD-PET

1.73 38*07— 1.3538*06173.9 ")00 1 . J 5 3 B * 0 6 " «.979E»05321.2 163 1000 • , 9 7 9 E * 0 5 - - 1.832E*05 8 1 . 2 r 780 1000 1.S32E*05— 1.111E*0S « 0 . 0 0 172 :ooo 1.111E*C5— 6.738E*0« 17.9 0 0 67 389 1000 6 . 7 3 8 E * 0 « ~ « .087E*0* 2 0 . 0 0 0 0 0 921 • . 0 « 7 E * 0 « - - 2.*79E+0« 20 .0 0 0 0 0 921 2 . » 7 9 E * 0 » - - 9.119B*03 2 0 . 0 e 0 0 0 0 921 9. 119E*03 - - 1.23*E*03 2 0 . 0 9 0 0 0 0 921 1.2 3 « E * 0 3 ~ 1.000E-05 9 . 0 1u 0 0 0 0 371

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 403 403 «03 «03 1000

ELEHEBTS OP THE COIBBLATIOB HATCH ( 1 0 * * 3 ) POB MATERIAL 1275 BEACTIOB 103 WITH IBSPtCT TO HA7BBIAL 1275 BEACTIOI 103 KJ

EBEIGT BAI6E (ET) t BEL SBOOP 1 to STD-DET

1.73 3E*07— 1.3531*06 19.3 1 1000 1 . 3 5 3 8 * 0 6 - - 4.979B*05 22 .3 2 32 1000 « . 9 7 9 E * 0 5 - - 1,8328*05 23 .9 ) 0 607 1000 1.S32B*05— 1.111E»05 28 .3 • 1 0 0 138 1000 1. 111E*05— 6 .73*E*0« 20.4 5 0 0 147 832 1000 6 . 7 3 8 8 * 0 4 — 4.0878*04 2 0 . 0 t > 0 0 138 707 981 4 . 0 8 7 8 * 0 9 " 2.4798*04 2 0 . 0 t 0 0 138 707 981 2. «79B*04— 9.1198*03 20 .0 ( 1 0 0 138 707 981 9.119E*C3— 1.2348*03 2 0 . 0 < » 0 0 138 707 981 1 .2348*03— 1.000E-05 5.4 1( ) 0 0 91 465 6 *5

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

658 658 658 658 1000

PISBBBTS OP TIB CDIIELATIOI HATBII ( 1 0 * * 3 ) POB HATEBIAL 1275 BEACT101 107 WIV? IBSPBCT TO BATBBIAL 127$ BBACTIOB 107

BBBBCT BABC8 (ET) I BEL 6BO0P 1 STD-DBV

10

1 .7331*07— 1.3538*06 2 0 . 2 1 1 1000 1 .3538*06— 4.9791*05 3 8 . 5 i I 515 1000 4 . 9 7 9 8 * 0 5 — 1.8328*05259.6 1 76 40 1000 1 .8328*05— 1.1111*05400.5 I > 49 26 179 1000 1 . 1111*05— 6 . 7 3 8 1 * 0 * 0 .0 « 5 0 0 0 0 0 6 . 7 3 8 8 * 0 4 — • . 0 8 / 8 * 0 1 0 .0 I i 0 0 0 0 0 0 4 . 0 8 7 8 * 0 4 — 2.4791*04 0 .0 1 0 0 0 0 0 0 0 2 . 4 7 9 1 * 0 4 — 9.1191*03 0 . 0 1 1 0 0 0 0 0 0 0 0 9 . 1 1 9 1 * 0 3 — 1.2341*03 0 .0 « t 0 0 0 0 0 0 0 0 0 1 .2348*03— 1.0001-05 0 .0 1( ) 0 0 0 0 0 0 0 0 0

Q

E-13

ELE8EBTS OF THE COBBELATIOB BAT*II (10«*3) POB HATEBIAL 1275 BEACTIOB 1 * I W IESPECT TO U T E R I AL 1275 BEACTIOS 2

EHEBGT BABGE fET) GBWIP 1 2 3 « 5 6 7 8 9 10

1.733E*07— 1.353E*C6 1 fcM 260 «7 • 7 * 7 • 7 *7 • 7 • 7 1» 1.353E*06— *-979E»05 2 • 86 973 871 86 * 876 876 876 876 876 267 • . 9 7 9 B 0 5 — 1.832E*05 3 93 938 999 9'iO 995 993 993 993 993 302 1-832E>05~ 1.111E»05 « 92 930 990 «99 9 90 986 986 986 986 300 1.111E»05-- 6.738E*?« 5 93 9*2 995 990 999 998 998 998 998 30« 6 .738E*0«— q.087E*0« 6 93 943 993 986 998 999 999 999 999 30« • • 0 8 7 E * 0 « ~ 2.»79E»0« 7 93 9*J 993 986 998 999 999 999 999 30* 2 . « 7 9 E * 0 * - - 9.119E*03 8 93 943 993 986 998 999 999 999 999 30 « 9 -119E«03- - 1.23«E»03 9 93 9*3 993 986 998 999 999 999 999 30« 1 . 2 3 « * 0 3 - - I.OOOE-OS 10 29 289 30« 302 306 306 306 306 306 998

ELE8EBTS OP THE COBBELATIOB BATBIX ( 1 0 * * 3 ) TOI BATEBIAL 1276 BEACTIOB 1 BITB BESPECT TO BATEBIAL 1275 BEACTIOB 103

EBEBCT BABGE (ET) GBoqp 10

1.733B»07— 1.3538*06 1 0 0 0 0 0 0 J 0 0 0 1.353E»06— • .979E*05 2 0 0 0 0 0 0 0 0 0 0 «.979E»05— 1.832E*0S 3 0 0 0 0 0 0 0 0 0 0 1 . 8 3 2 E 0 5 — 1.111E»05 « 0 0 0 0 0 0 0 0 0 0 1 . 111E»05~ 6.738E»0» 5 0 0 0 0 0 0 0 0 0 0 6 . 7 3 8 E O * - - «.087E»0* 6 0 0 0 0 0 0 0 0 0 0 • , 0 8 7 E * 0 « — 2.«79E«0* 7 0 0 c 0 0 0 0 0 0 0 2 - « 7 9 E » 0 » ~ 9.119E*03 8 0 0 0 0 0 0 0 0 0 0 9. 119E»03— 1.23«E*03 9 0 0 0 0 0 0 0 0 0 0 1 . 2 3 M » 0 3 ~ 1.000E-05 10 0 0 0 0 0 0 0 0 0 2

ElEflERTS OP THE COBBELATIOB HATBIX (10«*3) POB HATEBIAL 1275 BEACTIOB 1 HITH BESPECT TO HATEBIAL 1275 BEACTIOB 107

EBEBGT BABGE (ET) GBOOP 10

1 . 7 3 3 E 0 7 - - 1.353E»06 1 « 3 2 2 2 2 2 2 2 2 1-353E*06— «.979E»05 2 2 2 1 1 1 1 1 1 1 1 a.979E»05— 1.832E*05 3 0 0 0 0 0 0 0 0 9 0 1.S32E»05— 1.111E»05 « 0 0 0 0 0 0 0 0 0 0 1 . 111E»05~ 6.738E»0« 5 0 0 0 0 0 0 0 0 0 0 6.738E»0»— • •087»;0» 6 0 0 0 0 0 0 0 0 0 0 » .0»72*0»— 2 . *79E»0* 7 0 0 0 0 0 0 0 0 n 0 2.»79E»0«— 9. 119E*03 8 0 (• 0 0 0 0 0 0 0 0 9-119E*03— 1.23«E*03 9 0 0 0 0 0 0 0 0 0 0 1 . 2 3 « » 0 3 — 1.000E-05 10 0 0 0 0 0 0 0 0 0 0

ELEREBTS OP THE COBBELATIOB HATBIX (10**3) POB HATEBIAL 1275 BEACTIOB 2 «1TH BESPECT TO SATEtlAL 1275 BEACTIOB

EREBGT BABGE fEV) GBOfJP 1 10

1.73 3E»07— 1 .353E»06— » . 9 7 9 E » 0 5 — 1 .832E»05— 1 . 1 1 1 E » 0 5 ~ 6 .738E»0B— » . 0 B 7 E * 0 * - -2 . » 7 9 E » 0 « — 9 . 1 1 9 E * 0 3 — 1 t 2 3 « e » 0 1 - -

1 .353E*06 » . 9 7 9 E * 0 5 1 .832E*05 1 .111E»05 6 . 7 3 8 E » 0 « « .087E»0« 2 . » 7 9 E * 0 * 9 . 119E ,3 1.23«E*03 1.000E-OS

8 9

10

19 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 J 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

E-14

ELBHEHTS OP THE COBBEUTIOI H4T1IX (10«»i) POI BATERIAL 1275 IEACTIOB 2 •ITH IESP8CT TO BATEUAL 1275 1EACTIOB 10 3 O

EBEIGT IABCE (ET) C10OP 1 10

1 .7338*07— 1.353E*06 1 - 226 - 1 % 0 0 0 0 0 0 0 0 1 .3538*06— 9.9798*05 2 -7 -195 - 8 0 0 0 0 0 0 0 9.979S»05— 1.8321*05 3 0 -112 - 1 1 0 0 0 0 0 0 0 1 .9328*05 - - 1.1118*05 * 0 0 0 0 0 0 0 0 0 0 1 .1118*05— 6 . 7 3 * 8 * 0 * 5 c 0 0 0 0 0 0 0 I t 0 6 .73dE*09— 9 .0878*0 * t 0 0 0 0 0 0 0 0 0 0 9 .0878*09— 2.«798*0« 7 0 0 G 0 0 0 0 0 0 0 2 . * 7 9 t * 0 9 — 9.1198*03 8 0 0 0 0 0 0 0 0 0 0 9 .119E*03— 1.23*8*03 9 0 0 9 0 0 0 0 0 0 0 1 .23*5*03— 1.000E-05 10 0 0 0 0 0 0 0 0 0 0

ELEBEBTS OP TIE C01BEIATI01 BIT* I I | 10*«3 | POt HATBBIAl 1275 BS1CTI0B 2 «ITB BBS PICT TO BIT H I At 1275 BEACTIOB 107

• I I K I BAHGE (IT) CIOOP in

1 . 7 3 3 E 0 7 — 1.3531*06 1 -729 - 3 0 0 0 3 0 0 0 0 1 .3538*06— • • 9 7 9 1 * 0 5 2 - 375 -13 0 0 0 0 0 0 0 0 9 .9791*05— 1.8321*05 3 -55 0 0 0 0 0 0 0 0 0 1 . 8 3 2 E 0 5 — 1.1111*05 * - 3 6 0 0 0 0 0 0 0 0 0 1.1118*05— 6.738C*0« 5 0 0 0 0 0 0 0 0 0 0 6 . 7 3 8 B * 0 * ~ « . 0878*0* *> 0 0 0 0 0 0 0 0 0 0 9 .0878*09— 2 .«79B*0* 7 0 c 0 0 0 0 0 0 0 0 2 . 9 7 9 8 * 0 * - - 9 .1191*03 8 0 0 c 0 0 0 0 0 0 0 9 .1198*03— 1.239E*03 9 0 0 0 0 0 0 0 0 0 0 1 .23*E*03— 1.000E-05 10 0 0 0 0 0 0 0 0 0 0

EL'REBTS OP THE COltlUTIOB BftTRIX (10*«3) POB HATEHAL 1276 BE ACTIO* 1 IITH tESPECT TO BATElIAt 1276 IE ACTIOS 1 KJ

EBEICT lAiCE (ET) f BEL GIOOP 1 10 ST0-0E1

1.733E*07— 1.353E*06 1.0 1.3532*06— ».979E*05 1.» « .979E*05— 1.8321*05 2 . 9 1.832E*05— 1.1111*05 1.9 1.1118*05— 6 . 7 3 8 E * 0 * 1.9 6 .738E*0«— 9 . 0 8 7 8 * 0 * 1.9 9 .0971*09— 2.979E*09 1.9 2 .9791*09— 9.1198*03 1.4 9 .1198*03— 1.2398*03 1.9 1 .2348*03— 1.0008-05 1.9

1 1000 2 710 1000 3 396 337 1000 9 681 521 311 1000 5 681 521 311 1000 1000 6 681 521 3 . 1 1000 1000 1000 7 681 521 311 1000 1000 1000 1000 8 681 521 311 1000 1000 1000 1000 1000 9 681 521 311 1000 1000 1000 1000 1000 1000

10 681 521 311 1000 1000 1000 1000 1000 1000 1000

ELSH8BTS OP THE COBBELATIOB HATBIZ (10««3) POI HATEII1L 1276 BEACTIO! 2 WITH 1BSP8CT TO BATBIIAL 1276 BEACTIOB

1IEBCT BABC8 (ET) % 881 6B00P 1 10 STD-DSV

1.7338*07— 1.3538*06 1 .1 1.3538*06— 9 .9798*05 1.9 9 .9798*05— 1.8328*05 2 . 9 1.8328*05— 1.1118*05 1.1118*05— 6 .7388*09 6 .7388*09— 9 .0878*09 9 .0878*09— 2 . - 7 9 8 * 0 9 2.9- '9B*09— 9.1198*03 9 .1198*03— 1.2398*03

1.9 1.9 1.9 1.9 1.9 1.9

1 1000 2 709 1000 3 395 337 1000 9 680 521 311 1000 5 680 521 311 1000 1000 6 680 521 311 1000 1000 1000 7 680 521 311 1000 1000 1000 1000 8 680 521 311 .000 1000 1000 1000 1000 9 680 521 311 1000 1000 1000 1000 1000 1000

1 .23*8*03— 1.0008-05 1.9 10 680 521 311 1000 1000 1000 1000 1000 1000 1000

Q

E-15

ELEREBTS O P T H : C O B B E L A T I O B HATBIX M O * * 3 I POB BATE H A L 1 2 7 6 REACT 1 0 SI • B I T H B E S P E C T TO H A T B B I A L 1 2 7 6 B E A C T I 0 1

BBEBGY BABGE (ET)

1.~i .JE»07 l . : 5 3 E * 0 6 - - * . 9 7 9 E * 0 5 * . 9 7 9 E * 0 5 - - 1 . 8 3 2 E * 0 5 1 . 3 3 2 E * 0 5 - - 1 . 1 1 1 E * 0 5 1. 111E*05— 6 . 7 3 8 E * 0 * 6 . 7 3 8 E » 0 * -* . 0 8 7 E * 0 * -2 . * 7 9 E * 0 * -<*. 1 1 9 E * 0 3 — 1 . 2 3 « E * 0 3 1 . 2 3 « E * 0 3 - - 1 . 0 0 0 E - 0 5

% BEL CBOOP STD-DEf

1 . 3 5 3 8 * 0 6 1 2 . * 0 . 0

« . 0 8 7 E * 0 * 2 . * 7 9 E * 0 * i . 119B*03

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

1 2 3 « 5 6 7 8 9

10

1000 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

c 0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0

10

0 0

ELEHEBTS OP THE COBBELATIOB NATBIX ( 1 0 * * 3 ) POB RATEBIAL 1276 BEACTIOB «0 3 BITH BESPECT TO HATEBIAL 1276 BEACTIOB 103

EBEBGT RkBGE (ET) X BEL CBOOP 1 2 3 * 5 STD-OET

1 . 7 3 3 5 * 0 7 - - 1 . 353E*06 1 2 . * 1 1000 1 .353E*06— « . 9 7 9 E * 0 5 0 . 0 2 0 0 » . 9 7 9 E * 0 5 — 1 . 8 3 2 E * 0 5 0 . 0 3 0 0 0 1 - 8 3 2 E * 0 5 ~ 1 . 1 1 1 E * 0 5 0 . 0 • 0 0 0 0 1 . 1 1 1 E * 0 5 — 6 . 7 3 8 E * 0 * 0 . 0 5 0 0 0 0 0 6 . 7 3 6 E * 0 » - - « . 0 8 7 E * 0 « 0 . 0 6 0 0 0 0 0 * . 0 8 7 E * 0 * - - 2 . * 7 9 E * 0 * 0 . 0 7 0 0 0 0 0 2 . * 7 9 E * 0 * ~ 9 . 119E*03 0.0 H 0 0 0 0 0 9 . 1 1 9 E * 0 3 — 1-23*E*03 0 . 0 9 0 0 0 0 0 1 . 2 3 » E * 0 3 - - 1 . 0 0 0 E - 0 5 0 . 0 10 0 0 0 0 0

10

0 0 0 0 0

0 0 0 0

0 0 0

0 0

ELEREBTS OP THE COR I ELATION HATRII ( i0**3) POB MATERIAL 1276 B'ACTIOB 107 BITH BESPBCT TO HATEBIAL 1276 BEACTIOB • 07

EBEBGT BABGE (ET) % BEL GBOfJP 1 2 3 * 5 STD-DET

1 . 7 3 3 E * 0 7 — 1 .353E*06 9 . 2 1 1000 1 . 3 5 3 E * 0 6 — » . 9 7 9 E * 0 5 0 . 0 2 0 0 « . 9 7 9 E * 0 5 - - 1 . 8 3 2 E * 0 5 0.0 3 0 0 0 1 . 8 3 2 E * 0 5 - - 1 . 1 1 1 E * 0 5 0 . 0 U 0 0 0 0 1. 1 1 1 E * 0 5 - - 6 . 7 3 8 E * 0 * 0 . 0 5 0 0 0 0 0 6 . 7 3 8 E * 0 * - - « . 0 8 7 E * 0 « 0 . 0 6 0 0 0 0 0 » . 0 8 7 E * 0 » — 2 - * 7 9 E * 0 * 0 . 0 7 0 0 0 0 0 2 . » 7 9 E * 0 » — 9-119E*03 0 . 0 8 0 0 0 0 0 9 . 1 1 9 E * 0 3 ~ 1 . 2 3 « E * 0 3 0 . 0 9 0 0 0 0 0 1 . ? 3 » E * 0 3 - - 1 .000E-OS 0 . 0 10 0 0 0 0 0

10

0 0 0 0 0

0 0 0

ELEREBTS OP THE COB8ELATIOB SATBIX f10**3) POI BATEIIAL 1 2 7 6 BEACTIOB 1 BITS BESPECT TO RATEBIAL 1 2 7 6 BBACTIOB

EBERG7 BABGE (ET) GBOOP 1 2 3 • 5 6 7 8 9 10

1 .7338*07— 1.3538*06 1 997 709 39* 680 680 680 680 680 680 680 1. 353E*06— * . 9 7 9 E * 0 5 2 710 1000 337 521 521 521 521 521 521 521 ». 9798*05— 1.832E»05 3 396 337 1000 311 311 J11 311 311 311 311 ' .B32E*05— 1.111E*05 « 681 521 311 1000 1000 1000 1000 1000 1000 1000 1. 111E>05— 6.738E*0« 5 601 521 311 1000 1000 1000 1000 1000 1000 1000 6 . 7 3 8 8 * 0 * - - * . 0 8 7 E * 0 * 6 681 521 311 1000 1000 1000 1000 1000 1000 1000 » .087E*0*— 2 . « 7 9 E * 0 * 7 681 521 311 1000 1000 1000 1000 1000 1000 1000 2 . » 7 9 E * 0 * - - 9 .119E*03 8 681 521 311 1000 1000 1000 1000 1000 1000 1000 9 . 1 1 9 E * 0 3 ~ 1 . 23*E*03 9 681 521 311 1000 1000 1000 1000 1000 1000 1000 1 . 2 3 * 8 * 0 3 - - 1.000E-05 10 681 521 311 1000 1000 1000 1000 1000 1000 1000

E-16

EU8ERTS OP THE CORREUTIOH BiTBII (1C**3) POl RATBBIAL 1276 REACTION 1 fTTH RESPECT TO B I T E l l U . 1 2 7 6 REACTION 10*

BHE9GY RABGB (IT) GROUP 1 10

1.733E*C7— 1.3538*06 1 .3532*06™ • - 9 7 9 8 * 0 5 • • 9 7 9 8 * 0 5 — i .8328*05 1.8328 05— 1.1118*05 1 . 1118*05— 4.738B»0« 6 . *38B*0«— •.'J87E»0« -,U87B»C»— 2.4798*04 2.«79B*0«— 9.11»E*03 9 .1198*03— 1 . 2 3 « * C 3 1.23«B*03— 1.0001-05 10

8 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

3 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0

ELBHEITS OP THE CORRELATION BATRIX <10**3) POfi NATE RIAL 1276 XEACTXOH 1 HTTB7 IESPECT TO HATStlAL 1 2 7 6 IBACTIO! 107

EHERCT RARCB (ED GBOOP 10

1.7338*07— 1.3538*06™ • •9798*05— 1.8328*05— 1.1118*05— 6.738B*0«— • .087B*0«— 2 . « 7 9 B * 0 « ~ 9 .1198*03— 1 . 2 3 « * 0 3 —

1.353B*06 «.979B*05 1.832E*0S 1.1118*05 6 . 738E*0« • . 0 8 7 8 * 0 4 2.«79E*0« 9 . 119E*03 1 .23*8*03 1.000E-0S

1 11 8 • 8 8 8 8 8 8 8 2 0 0 0 0 0 0 o 0 0 0 3 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 « 0 0 0 0 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 c 0 0

10 0 0 0 0 0 0 0 0 0 0

ELEHBHTS OP TBE COBRELATION HATRII (10**3) POl HATBRIAL 1276 REACTION 2 WITH RESPECT TO MATERIAL 1 2 7 6 REACTION

<J BRBRGT RANGE (CV) GR03P 1 10

1.7338*07— 1.3538*06— • • 9 7 9 k * 0 5 - -1.8328*05— 1. 1118*35— 6 .738^*0«— • • 0 8 7 B * 0 » - -2 .«79E*0» - -9 .1198*03— 1.23*8*03—

1.3538*06 • •9798*05 1.8.>VE*05 1.1118*05 6.7388*04 « .0878*0 * 2 .«79E*0* 9.119E*03 1.23«E*03 1.000E-05

1 2 3 « 5 e 7 3 9

10

-35 0 0 0 0 0 0 0 0 0

0 0 0 0 0

t

6 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 a 0 0 0 0 0 0

0 0 0 A 0 0 0 0 0 0

21BHEBTS OP THE CORRELATION HATRIX (10*«3) POB HATERIAL 1276 REACTION 2 WITH RESPECT TO HATEBIAL 1 2 7 6 REACTION 107

ERERGT BARGE (EV) GROUP 1 10

1.7331*07— 1.353E*06 1.3538*06— *.979B»05 • • 9 7 9 8 * 0 5 — 1.8328*05 1.8328*05— 1.1118*05 1.1118*05— 6.738E*0« 6.738B*0«— «.087E*0« «.087E*0«— 2.«79B*04 2 .»7»8*0«— 9.1198*03 9 .1198*03— 1.2348*03 1 . 2 3 « * 0 3 — 1.000E-05

8 9

10

-55 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 c 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

Q

ElEREITS Of THE COIIELATI RAT EMM. 1 2 7 6 REACTION

EIER6T BARGE fET)

1 .73 3E»07— 1 .353E*06 1 . 3 5 3 B » 0 6 — « , 9 7 9 E » 0 5 • , 9 7 9 E * 0 5 — 1 .83?E»0S 1 . 8 3 2 E » 0 5 ~ 1 . 1 1 1 E O S 1 - 1 1 1 E » 0 5 — 6 . 7 3 8 E * 0 » 6 . 7 3 8 E * 0 » - - « . 0 8 7 E » 0 * • , 0 8 7 B » 0 « ~ 2 . * 7 9 E « 0 * 2 . « 7 9 I * 0 « ~ 9„119E*03 9 . 1 1 9 E » 0 3 — 1 .23»E*03 1 . 2 3 « E » 0 3 ~ 1 . 0 0 0 E - 0 5

E-17

I n iTRII ( 1 0 * * 3 ) TO* • IITH RESPECT TO RATERIAL

GROOP 1 ~ 3 •

1 -2 0 0 0 2 0 0 c 0 3 0 0 0 0 a 0 0 0 0 5 0 0 0 A

6 0 0 0 0 7 0 0 0 0 8 0 0 0 0 9 0 0 0 0

10 0 0 0 0

1276 IEACTIOI 103

5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 r 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

<J

F-l

APPENDIX F Edited Tabulation of the LMFBR Shielding Co variance Matrix Library

In this edited tabulation of the LMFBR Shielding Covarlance Matrix Library, only the lower halves of the symmetric matrices are show. Correlation matrix elements are multiplied by 10C0 for ease in reading. Also, for con .nlence, diagonal elements of correlation matrices are given as zero Mhen the corresponding relative standard deviations are zero.

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r - i o * 1 p i r t f i i n ^ i i r 9 9 9 « n r M < -*» o o o o o o o o o o o o o o o u • • * • • * • • • • * • » • • 0E M M M M ^ M O O M M M M M M M M M m o o o o o o in o o © o m <n oo • «> o © m oe o © e* n» o © o ao »• nt M 9 9 ws <•>• ooo w © <o) W ©»n m •• ©

w » n * w r > i n 9 ' ^ r « j > « « ' " » » m w

BLRRRRTS OF TBI COBRBUTXOB BftTRIf (10"*3) FOR rUTBRIll. 115* RRkCTXOR 3 BXTfl RESFBCT TO IUTBBHL 1156 BBACTXOR 3

BBBRQT BABGB ( I T ) t RBL OROOP 1 2 3 a 5 6 7 8 9 10 11 12 13 ia is STD-OI i

1 . a 9 2 B * 0 7 ~ a . • 0 0 1 * 0 6 • 2 . 6 1 1000 » . * 0 0 B * 0 6 - - 2 . 6 0 0 1 * 0 6 • 1 .2 2 922 1000 2 . 6 0 0 8 * 0 6 - - 1 . 3 5 0 1 * 0 6 2 1 . 8 3 819 908 1000 1 . 3 5 0 8 * 0 6 - - 7 . 0 6 0 1 * 0 5 1 6 . 9 a 0 0 322 1000 7 . 0 8 0 B * 0 5 ~ 5.aoei*os 1 7 . 0 5 0 0 320 877 1000 5 . 8 0 0 8 * 0 5 - - •.loot*os 2 0 . 1 6 0 0 266 653 725 1000 * . 1 0 0 8 * 0 5 - - 3 . 0 9 5 1 * 0 5 5 0 . 0 7 0 0 0 0 0 7 1000 3 . 0 9 5 B » 0 5 - - 2 . 6 2 0 B « 0 5 5 0 . 0 8 0 0 0 0 0 7 1000 1000 2 . 6 2 0 B * 0 5 — 6 . 2 0 0 8 * 0 * 2 0 . 2 9 0 0 0 0 0 6 77« 77a 1000 6 . 2 0 0 8 * 0 * - - 1 . 0 0 0 8 * 0 * 1 3 . 8 10 0 0 0 0 0 0 0 0 160 1000 3 . 0 0 0 8 * 0 % - - 1 . 5 0 0 B * 0 « 1 * 5 11 0 0 0 0 0 0 0 0 115 aa2 1000 1 . 5 0 0 B * 0 * - - 1 . 5 8 5 1 * 0 3 12 . 1 12 0 0 0 0 0 0 0 0 137 293 297 1000 1 . 5 8 5 8 * 0 3 - - 2 . 1 1 5 a * 0 2 7 . * 13 0 0 0 0 0 0 0 0 136 290 276 998 1000 2 . 1 8 5 8 * 0 2 - - 1 . 0 6 8 1 * 0 1 1 . 0 1 * 0 0 0 0 0 0 0 0 0 0 0 0 5a 1000 1 . 0 6 8 8 * 0 1 — 5 . 0 « 3 1 * 0 0 1 .0 15 0 0 0 0 0 0 0 0 0 0 0 0 5 * 1000 1000

8 IB HERTS OF THB CORRUPT I OB HATRTI (10**3) FOR IUTRRIM. 1156 RIRCTXOR 102 KITH RBSP8CT TO lUTBRIJU 1156 REACTION 102

IB1RCT RMOI (IT)

1.*92B*07--a .aooB*06- -2 .600B*06- -1.35OB*06--7 , 0 8 0 8 * 0 5 - -5 . 8 0 0 8 * 0 5 - -a . 1 0 0 8 * 0 5 - -3 , 0 9 5 8 * 0 5 - -2 . 6 2 0 8 * 0 5 - -6 . 2 0 0 8 * 0 * - -3 .0008»0a - -i .500R*oa- -1 .5858*03- -2 . ia5B*02--1 .068E«01--

a . a o o s * 2 .600B* 1.350B* 7.080B* 5 . 8 001* *.1OOE* 3 .095E* 2 .620B* b 2001* 3 .0008* 1.500B* 1 .5858* 2.1H5B* ' . .0688* 5.01*38*

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06 50. 06 50. 06 36. 05 3 5. 05 50. 05 35. 05 50. 05 53. OB 20. oa 13. oa i*. 03 12. 02 7. 01 *. 00 1.

BL GROOF DBf

1 2 3 a 5 6 7 a 9 10 11 12 13 14 15

1000 1000 1000 -S17 517 1000

0 50* 1000 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

10 11 12 13 1* 15

809 1000 552 683 1000 0 0 731 1000 0 0 731 1000 1000 0 0 566 778 77a 1000 0 0 0 0 0 IbO 1000 o o o o o 11* a39 1000 0 0 0 0 0 137 293 296 1000 0 0 0 0 0 136 290 275 998 1000 0 0 0 0 0 0 0 0 0 52 1000 0 0 0 0 0 0 0 0 0 52 1000 1000

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I ILBRBRTS OP TRB CORRELATION RATRII ( 10 *"J ) FOR BATBBIAl 1192 RRACTIOR 1 RITR RBSPBCT TD RATBRIAL 1192 R8ACTIOH

BRBRGT RANGR { « » ) « R B I GROUP 1 2 1 4 5 6 7 8 9 S T D - D B 7

1 . 4 9 2 8 * 0 ? - - 4 . 4 0 0 8 * 0 6 1 . % 1 1 0 0 0 4 . 4 0 0 8 * 0 6 - - 2 . 6 0 0 8 * 0 6 2 . % 2 %1 1 0 0 0 2 . 6 0 0 8 * 0 6 - - 1 = 3 5 0 8 * 0 6 1 . 6 3 0 %5 1 0 0 0 1 . 3 5 0 8 * 0 6 - - 7 . 0 S O B * 0 5 . . 5 % 0 0 1 7 5 1 0 0 0 7 . 0 8 0 8 * 0 5 - - 5 . 8 0 0 8 * 0 5 2 . 6 5 0 0 0 5 0 2 1 0 0 0 5 . 8 0 0 8 * 0 5 - - 4 . 1 0 0 1 * 0 5 2 . 2 6 0 0 0 0 1 7 0 1 0 0 0 4 . 1 0 0 8 * 0 5 - - 3 . 0 9 5 8 * 0 5 3 . 0 7 0 0 0 0 0 4 5 6 1 0 0 0 3.0»M*05— 2 . 6 2 0 8 * 0 5 2 . 8 R 0 0 0 0 0 36 7 9 1 0 0 0 2 . 6 2 0 8 * 0 5 - - 6 . 2 0 0 8 * 0 4 1 . 2 9 0 0 0 0 0 0 0 46 1 0 0 0 6 . 2 0 0 8 * 0 4 - - 3 . 0 0 0 8 * 0 % 3 . 5 10 0 0 0 0 0 0 0 0 7 3 . 0 0 0 8 * 0 % - - 1 . 5 0 0 8 * 0 % % . 2 11 0 0 0 0 0 0 0 0 0 1 . 5 0 0 8 * 0 4 - - 1 . 5 8 5 8 * 0 3 6 . 3 12 0 0 0 0 0 0 0 0 0 1 . 5 8 5 8 * 0 3 - - 2 . 1 % 5 B * 0 2 2 . 2 13 0 0 0 0 0 0 0 0 0 2 . 1 * 5 8 * 0 2 - - 1 . 0 6 8 8 * 0 1 0 . 0 1« 0 0 0 0 0 0 0 0 0 1 . 0 6 8 8 * 0 1 - - 5 . 0 4 3 8 * 0 0 0 . 0 15 0 0 0 0 0 0 0 0 0

10 11 12 14 15

1000 666 1000 180 186 1000 110 91 509 1000 0 0 0 0 0 0 0 0

RL8RSRTS OP THB CORRELATION HATH I * ( 1 0 * * 3 ) POR NAT8RIAL 1192 REACTION 2 WITH RBSPBCT TO HATBRIAl 1192 REACTION

BRBRGT RANGE ( B f ) « R B I GROUP 1 2 1 4 5 6 7 8 9 S T D - O B f

1 . 4 9 2 R * 0 7 - - 4 . 4 0 0 8 * 0 6 1 2 . 2 1 1 0 0 0 4 . 4 0 0 8 * 0 6 - - 2 . 6 0 0 8 * 0 6 9 . 3 2 2 1 1 0 0 0 2 . 6 0 0 8 * 0 6 - - 1 . 3 5 0 R * 0 6 3 . 5 3 13 6 1 9 1 0 0 0 1 . 3 5 0 8 * 0 6 - - 7 . 0 8 0 8 * 0 5 1 . 8 4 0 0 187 1 0 0 0 7 . 0 8 0 8 * 0 5 - - 5 . 8 0 0 8 * 0 5 2 . 6 5 0 0 0 4 7 3 1 0 0 0 S . 8 0 0 6 * 0 5 - - U . I 0 0 9 * 0 5 2 . 2 6 0 n 0 0 170 1 0 0 0 % . 1 0 0 R * 0 5 - - 3 . 0 9 5 8 * 0 * 3 . 0 7 0 0 0 0 n 4 56 1 0 0 0 3 . 0 9 5 R * 0 5 - - 2 . 6 2 0 8 * 0 5 2 . 8 ft 0 0 0 0 0 36 7 9 1 0 0 0 2 . 6 2 0 8 * 0 5 - - 6 . 2 0 0 8 * 0 4 1 . 2 <* 0 0 0 0 0 0 0 46 1 0 0 0 6 . 2 0 0 8 * 0 4 - - 3 . 0 0 0 8 * 0 4 1 . 5 10 0 0 0 0 0 0 0 0 7 1 . 0 f | 0 « ! * 0 4 - - 1 . 5 0 0 8 * 0 4 4 . 2 11 0 0 0 0 0 0 0 0 0 1 . 5 0 0 8 * 0 % - - 1 . 5 8 5 8 * 0 3 6 . 3 12 0 0 0 0 0 0 0 0 0 1 . 5 8 * 8 * 0 3 - - 2 . 1 4 5 8 * 0 2 4 . 6 13 0 0 0 0 0 0 0 0 0 2 . 1 % 5 8 * 0 2 - - 1 . 0 6 8 8 * 0 1 5 . 0 14 0 0 n 0 n 0 0 0 0 1 . 0 6 8 8 * 0 1 - - 5 . 0 4 1 8 * 0 0 5 . 0 15 0 0 0 0 0 0 0 0 0

10 11 12 11 14 15

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0 0 0 872 1000 0 0 0 R72 1000 1000

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BLBHBMTS OF TUB CORBBUTIOR BATRIX (10**3) P08 MATERIAL 1 1 9 2 REACTION 3 MITH RBSPECT TO RATBRIAL 1 1 9 2 RBACTIOB

BMBRGY RARGB (BT)

1 .892B*07 -4 . 8 0 0 8 * 0 6 -2 . 6 0 0 8 * 0 6 -1 . 3 5 0 8 * 0 6 -7 . 0 8 0 8 * 0 5 -5 . 8 0 0 8 * 0 5 -8 . 1 0 0 8 * 0 5 -3 . 0 9 5 8 * 0 5 -2 . 6 2 0 8 * 0 5 -6 . 2 0 0 8 * 0 8 -3 . 0 0 0 8 * 0 4 -1 . 5 0 0 8 * 0 4 -1 . 5 8 5 8 * 0 3 -2 . 1 8 5 8 * 0 2 -1 . 0 6 8 8 * 0 1 -

- 4 . 4 008 * - 2.6008* - 1 . 3 5 0 8 * - 7 . 0 8 0 8 * - S.800B* - 4 . 1 0 0 8 * - 3.0958* - 2 . 6 2 0 1 * - 6 . 2 0 0 B * - 3 . 0 0 0 8 * - 1.S00E* - 1.S8SB* - 2 . 1 8 5 8 * - 1 . 0 6 8 8 * - 5 . 0 4 3 8 *

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CLI8BNTS OP THE CORRELATION MATRIX ( 1 0 * * 3 ) POR NATBRIAL 1 1 9 2 REACT 1 0 8 1 0 2 HITH RBSPBCT TO HATER I A l 1192 REACTION 102

B8BRGT RA8GB (BV) 1 I d GROUP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 STD-DEV

1 . 4 9 2 8 * 0 7 — 8 . 8 0 0 8 * 0 6 2 0 . 0 1 1000 4 . 4 0 0 8 * 0 6 — 2 . 6 0 0 8 * 0 6 2 0 . 0 2 1000 1000 2 . 6 0 0 8 * 0 6 — 1.3 508*06 2 0 . 0 3 1000 1000 1000 1 . 3 5 0 8 * 0 6 — 7 . 0 8 0 8 * 0 5 15. 1 » 420 420 420 1000 7 . 0 8 0 8 * 0 5 — 5 . 8 0 0 8 * 0 5 2 0 . 0 5 0 0 0 908 1000 5 . 8 0 0 8 * 0 5 — 4 . 1 0 0 8 * 0 5 1 5 . 6 6 0 0 0 854 94 1 1000 8 . 1 0 0 8 * 0 5 — 3 .0 958*05 2 0 . 0 7 0 0 0 0 0 338 1000 3 . 0 9 5 8 * 0 5 — 2 . 6 2 0 8 * 0 5 2 0 . 0 8 0 0 0 0 0 3 38 1000 1000 2 . 6 2 0 8 * 0 5 — 6 . 2 0 0 8 * 0 8 1 3 . 0 9 0 0 0 0 0 2 34 692 6 92 1000 6 . 2 0 0 8 * 0 4 — 3 . 0 0 0 8 * 0 4 9 . 9 1 0 0 0 !) 0 0 0 0 0 22 1000 3 . 0 0 0 8 * 0 4 — 1 . 5 0 0 8 * 0 4 1 0 . 3 1 1 0 0 0 0 0 0 0 0 0 474 1000 1 . 5 0 0 8 * 0 4 — 1 . 5 8 5 8 * 0 3 1 2 . 8 1 2 0 0 0 0 0 0 0 0 0 393 388 1000 1 . 5 8 5 8 * 0 3 — 2 . 1 4 5 8 * 0 2 2 2 . 8 1 3 0 0 0 0 0 0 0 0 0 192 1B8 157 1000 2 . 1 8 5 8 * 0 2 — 1 . 0 6 8 8 * 0 1 1 .0 1 * 0 0 0 0 0 0 0 0 0 0 0 0 5 1000 1 . 0 6 8 8 * 0 1 — 5 . 0 4 3 8 * 0 0 1 .0 1 S 0 0 0 0 0 0 0 0 0 0 0 0 5 1000

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BLBNBRTS OP THB CORRELATION MATRIX ( 1 0 * * 1 ) POR IUTBRIAL 1274 REACTION 107 WITH RESPECT TO HATERIAL 1274 RBACTXOR 107

BNBRGT RANGE <ET) « BEL GROUP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 STD-DB?

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BLBRFNTS OP TRB CORRELATION HATRIX (10»*3) POR 8ATBRIAL 1275 REACTION 1 WITH RESPECT TO HAfERIAL 1275 REACriON 1

ENERGY R A It Gt. (BV) X R BL GROUP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 IS STO-OB?

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BLEHENTS OP THB CORRELATION HATRIX ( 1 0 * * 1 ) FOR MATERIAL 1275 RBACTION 4 WITH RESPECT T3 RATBRIAL 1275 REACTION 107

BHSRGT RANGE ( 8 ? ) GROOP 1 2 3 4 5 6 7 8 9 10 11 12 13 1U 15

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BNERGT RANGE (EV) « RBL GROUP 1 2 3 4 5 6 7 8 9 1 0 1 1 12 13 14 STD-DEV

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BIBHBMTS OP THE CORRBLATIOH BATHIX (10""3) POR MATERIAL 1276 RBACTIOM 1 HXTH RESPECT TO HATERIAL 1276 REACTION 4

BRPRGY RANGE (BY) GROUP 1 2 1 4 5 6 7 n 9 10 11 12 13 14 15

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