LA-8036-PR Progress Report
ClC-l 4 REPORT COLLECTION C3● REPRODUCTION COPY
Applied Nuclear Data Research and Development
April l—June 30, 1979
J
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Thefourmostrecentreportsinthisseries,unclassified, areLA-7482-PR,LA-7596-PR,LA-7722-PR,and LA-7843-PR.
ThisreportwasnoteditedbytheTechnicalInformation staff.
Thisworkwasperformedundertheauspicesofthe USDepartmentofEnergy’sOfficeofMilitary Application,DivisionofReactorResearchand Technology,OfficeofBasicEnergySciences,andOffice ofFusionEnergy;andtheElectricPowerResearch Institute.
l%is r.purt wasprep. red .s an account of umtk sponsored by the United SlaLesG..mmmnt. Neither the United Stat.. north. United S,.1,s Cwmrtmmt of Ene,,y. nor .ny of Ihei, ●mployees. nor .ny of them mmractors. s. bcontr.ctors, m their ●mployees. makes my warranty. express c.. implied. or assume, any 1.”1 Imbibty or mswnsib,!ity 10, the .CCU,XY. completeness.-orusefulness of my information, .IXMr.t.s. product. or Processdisclosed. or r.uresents th.t i- ust would not in frlnze ptiv.lely owned rights.
UNITED STATES DEPARTMENT OF ENERGY CONTRACT W-740 B-ENG. 36 I
LA-8036-PR ProgressReport UC-34C Issued: September 1979
Applied Nuclear Data Research and Development
April l—June 30, 1979
C. 1. Baxman P. G. Young I
r-- I
,. .. ,-.
—— CONTENTS
I. THEORYAND EVALUATIONOF NUCLEARCROSS SECTIONS 3 A. 6Li(p,He) Cross Sections...... 1 9 B. n+ Be Evaluation...... 3 c. ArsenicCalculations...... 3 D. Erratum:Calculationof Neutron-InducedCross Sectionson Isotopesof Iridium...... 8 E. AverageNeutronicPropertiesof “Prompt”
FissionProducts...... ● *...... 8 F. GNASH Improvements...... 12 G. CSEWGActivities...... 13
II. NUCLEARCROSS SECTIONPROCESSING A. Cross SectionProcessing...... 14 B. EnergyBalanceof ENDF/B-V...... 14 c. An EpithermalDisadvantageFactorfor
EPRI-CELL● ...... 0...... 00.0. . . 17
III. FISSIONPRODUCTSAND ACTINIDES: YIELDS,YIELD THEORY, DECAYDATA, DEPLETION,AND BUILDUP
A. FissionYield Theory...... 19 B. ENDF/B-VFissionProductYieldsand Testing... 19 c. The Effectsof NeutronAbsorptionon Decay Heat...... 22 D. Decay Data Testingfor ENDF/B-V...... 28 E. AND 5.1 Decay Power Standard...... 29 F. ThreeMile IslandCalculations...... 31 Go Decay SpectralComparisons...... 35 H. CINDER-10Code...... 35
REFERENCES...... 00 ..0.00.0...... 35
iv APPLIEDNUCLEARDATA RESEARCHAND DEVELOPMENT QUARTERLYPROGRESSREPORT April 1 - June 30, 1979
Compiledby
C. I. Baxmanand P. G. Young
ABSTRACT
This progressreportdescribesthe activitiesof the Los AlamosNuclearData Group for the periodApril 1 through June 30, 1979. The topicalcontentis summarizedin the contents.
I. THEORYAND EVALUATIONOF NUCLEARCROSS SECTIONS 3 A. 6Li(p,He) Cross Section[G.M. Hale; D. C. Dodder;and S. D. Baker and E. K. Biegert (RiceUniversity)] The 6Li(p,3He)reactionis of interestat very low energiesin connection 6 with astrophysicalquestionsabout the relativeabundancesof Li and 7Li and recentlyhas been receivingattentionat higherenergiesas a possibleexotic fuel for fusionenergyapplications.Reliableintegratedcross sectionsfor this reactionhave been difficultto obtainin view of discrepanciesas largeas 50% among the measurements. Predictionsfor this crosssectionhave been availablefor more than two 7 years from our multichannelR-matrixanalysesof reactionsin the Be systemand 7 7 charge-independentanalysisof reactionsin the Be and Li systems. These re- suitshave been describedin part in previousprogressreports1-4 and at the Har- 5 well Conference. Since the experimentalcross-sectiondata includedin the anal- ysis for the 6Li(p,3He)reactionrequiredextensiverenormalizationin almost every case,we have been uncertainabout the reliabilityof the scale of our cal- culatedcross sections,which presumablywas determinedby data for other reac- 4 6 7 tions in the analysis[e.g., He(3He,3He)4Heand Li(p,p)6Liin the Be analysis]. 6 Recently,new absolutemeasurementsof Li(p,3He)4Heangulardistributions 6 at protonenergiesbetween0.14 and 3 MeV have been made by Elwynet al. at Ar- gonneNationalLaboratory. A comparisonof theirintegratedcross sectionswith our predictionsis shown in Fig. 1. It can be seen that the agreementof the calculationswith the new measurementsis excellent,both in shapeand magnitude.
The agreementof the calculatedangulardistributionswith the new data6 is gen- erallygood at energiesbelow 1.5 MeV; above that energy,interferenceeffects 6 with p- Li d-waves, whichwere neglectedin the calculation,appearto prevent good agreementwith the measuredangulardistribution,althoughthey have no effecton the integratedcross sections. This comparisonindicatesthat the other7-nucleondata in the analyses, throughunitaryand charge-conjugaterelationships,correctlydeterminedthe 6 3 7 scaleof the Li(p, He) reactioncrosssection,much as other Li data had con- 6 strainedvaluesof the Li(n,t)cross sectionin the analysis7used for the ENDF/B-V6Li evaluationat low energies. A paper8reportingvaluesof the low- energycrosssectionsand an expressionof the astrophysicals-functionhas been submittedto AstrophysicalJournal.
6LI [P, 3HEI 4HE m.+ o 5& cu_ f ~ o z -(CJo k o- $ V)m 02;- Cn 0 l% IT c)?3_ o ~ o + ELWYN ET f7L. 1979 8 0 1 I I I I 1 0.0 0.4 0.8 12 1.6 2.o 2.4 ; s PROTON ENERGY (MEV) Fig. 1. Predictionsfrom the charge-symmetric7-nucleon analysis5comparedwith recentmeasurementsof Elwyn et al.6 for the 6Li(p,3He)4Heintegrated crosssection. 2 9 B. Xl+ Be Evaluation (P. G. Young and L. Stewart) n A report’has been writtendescribingthe Los AlamosScientificLaboratory -5 (LASL)evaluationof n + ‘Be reactions, which coversthe energyrange 10 eV to 20 MeV. In the evaluationparticularemphasiswas placedon accuratelyrepresent- 10 ing new measurementsof secondaryneutron-emissionspectra and scatteringdata 11 between6 and 15 MeV. Additionally, adjustmentsto the total,(n,y),and (n,t) cross sectionsfrom previousENDF/Bevaluationswere made, and covariancedata filescontainingerrorcorrelationsfor crosssectionsand emissionspectrawere obtained. Detailedcomparisonsof experimentaland evaluateddata are presented in the report,and the new evaluationis found to representthe neutronemission 10 spectradata much more accuratelythan ENDF/B-V. The evaluateddata are avail- able in ENDF/Bformatfrom the ENDF/Alibraryat the NationalNuclearData Center at BrookhavenNationalLaboratoryand from the RadiationShieldingInformation Centerat Oak RidgeNationalLaboratory. c. ArsenicCalculations(E. D. Arthur) 74,75 Calculationsof neutron-inducedreactionson As isotopeshave been made in the energyrangebetween0.001and 20 MeV. The reactionsfor wh:Lchcross sec- tionswere calculated,theirQ values and thresholdsare given in Table I. For 12 this effort,a similarapproachto that used for our n + Y calculat:Lonswas fol- lowed. That is, independentdata [neutrontotalcrosssections,resonanceparame- ters,and (p,n)results]were used in a determinationof consistentsets of neu- tron and protonopticalmodel parameters. For example,Fig. 2 comparesour cal- 75AS culatedtotal cross sectionto experimentaldata for n + . The neutronop- ticalparametersappearin Table II. For ~ As, the (n,np)thresholdis about 3.5 MeV lower than that for the (n,2n)reaction. This leads to an incidentenergyregionin which the total protonproductioncross sectioncan be sensitiveto the parametersused to de- scribelow energyprotonemission. Therefore,we used a protonopticalparameter set similarto that from our n + Y calculationsand adjustedit slightlyto pro- 74 duce agreementwith low-energy(p,n)measurements.In Fig. 3, Ge(p,n)cross sectionscalculatedwith theseparametersand the neutronparametersof Table III 13 are comparedto experimentaldata of Johnsonet al. Along with both neutron and protonparameterdeterminations,the gamma-raystrengthfunctionwas obtained 75 throughfits to As capturedata.
3 TABLE
Q VALUESAND THRESHOLDS + As REACTIONS E~h (MeV) —MT Reaction Q @fev) 74 74A8 74As 4 As(n,n’) -0.173 0.175 74 73AS 16 As(n,2n) -7.977 8.086 74 73nlAs 16 As(n,2n) -8.475 8.59 74 7oGa 22 As(n,na) -4.378 4.437 74 73Ge 28 As(n,np) -6.854 6.948 74 102 As(n,y)75As 10.243 0. 74 75mAs 102 As(n,y) 9.939 0. 74 103 As(n,p)74Ge 3.346 0. 74 70,71Ga 107 As(n,ct+ n,an) 4.926 0.
75AS 75 75AS 4 As(n,n’) -0.198 0.201 75 74AS 16 As(n,2n) -10.243 10.38 75 17 As(n,3n)73As -18.22 18.465 75 71Ga 22 As(n,nCX) -5.316 5.39 75 74ce 28 As(n,np) -6.896 6.989 75 75mAs 54 As(n,nl) -0.304 0.308 75 76As 102 As(n,y) 7.33 0. 75 75Ge 103 As(n,p) -0.407 0.413 75 75mGe 103 As(n,p) -0.547 0.554 75 71,72Ga 107 As(n,a+ n,c%n) 1.205 0. 9.0I I I I 1 1 1 I 1 I I I I I I I 1 I I I t
7.0– v
6.0–
- n 5.0– b
4.0–
3.0– a. 2.0 [ I 1 I I 1 Y 1 I II I t I t t 1 9 11 I I 0.1 1.0 10.0 20.30. NeutronEnergy(MeV) Fig. 2. Fit to the 75As totalcross sectionusing the parametersof Table II.
TABLE II n + 75As NEUTRONOPTICALPARAMETERS
Strength(MeV) r (fro) a (fro) v= 49.96- 0.4E 1.236 0.6 W (SaxonDerivative) =7.8 - O.llE 1.26 0.69
= 6.2 1.12 0.47 ‘so 1“’’1” 1’1’’”
o.
- a b 74Ge(p,n) 0.0
o
O.oc 1 I $ f I I 1 I I I I 1 * 1 1 3.0 4.0 5.0 6.0 Proton Energy (MeV) Fig. 3. The 74Ge(p,n) crosssectioncalculatedwith the protonopticalparametersof Table III is com- pared to the resultsof Johnson.13
TABLE 111
PROTONOPTICALPAIUMETERS USED IN n + As CALCULATIONS
Strength(MeV) r (fro) a (fro)
v = 63.8 - 0.32E 1.225 0.665
w (SaxonDerivative) 3.0 + 0.6E 1.225 0.4
=6.4 1.03 0.63 ‘so
6 Theseparameterswere used in the COMNUCand GNASHstatisticalmodel codes alongwith discretelevel information,the Gilbert-Cameronleveldensitymodel, and preequilibriumcorrectionsmade using the Kalbachexcitonmodel. Good agree- ment was obtainedin comparisonsof our calculatedresultsto experimentaldata withoutneed for furtherparameteradjustments.As an example,our calculated 75 values for the As(n,2n)reactionare comparedwith experimentaldata in Fig. 4. 74 Also shownby the dashedline is the calculated As(n,2n)cross section.
r I I I I I I I I
1.2 0 0 0 0’ / / Lo /’ ~ /’ 00 1’ As (n, 2n) / 75~~ 0.6 74A~; I
t I / 0.2 – I 1’ I I I I I I 1 I I I I I 0 10 12 14 16 18 20 Neutron Energy (MeV) Fig. 4. Calculatedand ex erimental75As(n,2n)crosssections, In addition,the $4As(n,2n)crosssectioniS shownby the dashedcurve.
7 D. Erratum:Calculationof Neutron-InducedCrossSectionson Isotopesof Iridium (E. D. Arthur) 193 On page 9 of LA-7843-PR,the thresholdfor the Ir(n,3n)reactionwas in- 193 193m correctlylistedas 14.64MeV, while for the Ir(n,n’) Ir reaction,the Q value and thresholdenergywere listedas –0.803and 0.807MeV. The correctval- ues for thesequantitiesare Eth (MeV) Reaction Q (MeV) 193 1911r Ir(n,3n) -13.97 14.04 193 193m1r Ir(n,n’) -0.0803 0.0807
Neitherthe resultsof the calculationsnor the file of evaluatedcrosssec- tionsare influencedby theseerrors.
E. AverageNeutronicPropertiesof “prompt”Fissionproducts (E. D. Arthurand D. G. Foster,Jr.) The neutronicpropertiesof mixturesof fissionproductsbefore the first beta decay takesplacewould be very useful to know with moderateaccuracyfor a numberof applications.We are preparingcross sectionsthat shouldrepresenta reasonableaveragefor fissionproductsfrom fast-neutron-inducedfissionof 235U and 239Pu. Sincemost of the roughly1000 nuclidesinvolvedare far from the line of beta stability,clearlywe must rely almostentirelyon averagepropertiesde- duced from nuclearmodels,exceptfor simplepropertiesof the groundand first few excitedstates. We have chosena weightedaverageover a few selectednuclidesas a crude approximationto the sum over all nuclides. Thesenuclidesare chosenfrom the maximumand the half-valuepointsof the yield curvesfor both low- and high-mass 235 fragments,usingdistinctsets for Uand ‘9 Pu fission. The resulting19 nu- clidesare listedin Table IV, For each of theseas a target,we are calculating cross sectionsfor the (n,y),(n,n’),(n,2n),and (n,3n)reactions,together with theirneutronspectraand angulardistributions,for incident-neutronenergies -3 from 10 to 20 MeV. Approximatelyhalf of the 44 nuclidesinvolvedin thesereactionswith the specifiedtargetslie outsidethe range for which mass excesseshave been meas- ured,but thereare at leasta few excitedstatesreasonablywell determinedfor most of the requirednuclei. We are using adjustedmasses givenin the 1977 Nu- clearWallet Cards (includingsome “takenfrom nuclearsystematic”),supplemented 8 by extrapolationsusing the Garvey-Kelsonrelations. We have used simple Sh.ell- * model arguments to identifythe levelsin level schemesthat are otherwiselarge- ly completeand to supplya few missingground-statespinsor parities.
In additionto discretelevels,leveldensity information,neutronoptical parameters,and gamma-raystrengthfunctionsare employedin the model calcula- tionsdescribedhere. To representthe continuumexcitationenergyregionwhere no discretelevel informationexists, we are using the Gilbert-Cameronlevel- densityexpressionswith the Cook parameters,as obtainedfrom a systematicstudy of resonancespacingsnear the neutronbindingenergy. To determineneutronoptical-modelparameters,we rely on totalcrosssec- tionsalongwith resonancedata (s- and p-wavestrengths)for stableisotopesof the elementsshown in Table IV. The variationof the resonancedata as a func- tion of the quantity(N-Z)/Afor a particularZ permitsour determiningthe iso- spin dependenceof both the real and imaginaryportionsof the neutronoptical potential. As an example,the calculatedtotalcross sectionusing the parame- ters of TableV for n + Xe is comparedto experimentaldata in Fig. 5. In Fig. 6, calculateds-wavestrengthsfor isotopesof xenonhavingA = 128-138are com- pared to experimentalresults. To describegamma-rayemissionboth in the calculationof capturecross sec- tionsand in competitionwith (n,2n)and (n,3n)reactions,we have chosenthe Brink-Axelgiantdipoleresonance(GDR)form for gamma-raytransmissioncoeffi- cients. Instead,of normalizingthese transmissioncoefficientsto the ratio 2T
* We are gratefulto D. G. Madlandfor theseestimates.
9 TABLE IV
NUCLIDESUSED FOR FISSIONPRODUCTCALCULATIONS
235U 239PU Lower Peak 87,88Se Low 92,93Kr Center 94,95sr 99,100Z= High 102,103Zr 107,108M0
HigherPeak Low 131sn 130sn Center 138,139Xe 137,138Xe High 146Ba 145Ba
TABLEV
NEUTRONOPTICALPARAMETERSUSED FOR n + Xe CALCULATIONS Strength(MeV) r (fro) a (fro)
v= 55.4 - 50~ - 0.35E 1.25 0.65 W (SaxonDeriv.)= 12.8 - 50~ + 0.4E 1.25 0.56 W (maximum)= 17.1 - 50q vso =7.5 1.25 0.65
n = (tf-z)/A
10 W 1 1 J 1 1 I I I 1 I I 1 1 u I 1I
8.0 – Xe uTo+a,
3.0
2.0
[ ~~ 10.0 20. NeutronEnergy (MeV) Fig. 5. Comparisonof calculat~dand experimentalvalues for n + Xe.
1 1 I 1 I T 1 I 128 130 132 134 136 138 A Fig. 6. Calculatedand experimentaldependenceof the s-wave strength,S on (N-z)/Afor isotopesof xenon. o’
11 We are using COMNUCand GNASH for the actualcalculationsof cross sections and spectra. Neithercode can cover the entireenergyrangeof interestwith acceptableaccuracy. COMNUCincludeswidth-fluctuationcorrectionsthat are importantat low excitationenergiesand calculatesangulardistributionswithin the Hauser-Feshbachapproximation,but it does not treatpreequilibriumprocesses nor calculateneutronspectra. Thus, it is most usefulfor low incidentenergies. GNASHcalculatesspectrabut not angulardistributions,lackswidth-fluctuation correctionsbut includespreequilibriumeffects,so that it is most usefulat higherenergies,especiallyabove the (n,2n)and (n,3n)thresholds.We intend to use a simpleopticalmodel to supplythe angulardistributionfrom elastic scatteringthat is absentfrom the GNASH calculations.We have modifiedGNASH to write disk filesof the constituentsof the neutronspectra,so that these can be summedfor the filesexpectedin ENDF/B. At the end of the quarter,all inputdata had been collected,and all COMNUC calculationshad been carriedout and stored. Modificationsto GNASHare almost complete. We expectthe GNASHcalculationsand collectionof the resultsinto a singleaverageENDF/Bfile to requireanotherquarter’swork.
F. GNASH Improvements{E. D. Arthur) The GNASHpreequilibrium-statisticalmodel code has been modifiedso that the amountof centralprocessortime (CPU)used is abouthalf that of previous versions. The changeinvolvedeliminationof two computationalloops in which the totaland partialwidths,I’totand ri, were calculatedseparately. Now the partialwidthsare normalizedconcurrentlyby the totalwidth for each compound nucleusspin and paritystate,resultingin only one pass throughthe loop. The totalrunningtimes (1/0and CPU) betweenthe presentand olderGNASHversions are comparedin TableVI. In addition,severalother changeshave been made. The abilityto produce populationinformationso that complexspectracan be obtainedhas been rein- statedalongwith the abilityto providefor the existenceof targetnucleiin excitedstates. The representationof the gamma-raystrengthfunctionhas been improvedto includea two-Lorentzline descriptionof the giant dipoleresonance (GDR),a step in the GDR tail,and the possibilityof a pygmy resonanceoccurring at energieslower than the GDR.
12 G. CSEWGActivities (G.M. Hale, L. Stewart,and P. G. Young) 10 1. DosixnetrySpecialPurposeFiles. Files for the 6Li and B totalheli- 27 um productioncross sectionsand the Al(n,p)and (n,a)cross sectionswere pre- pared and sent to the NationalNuclearData Centerfor incorporationinto the VersionV SpecialDosimetryFile. Error files (File33 data) are includedfor each of the cross sectionslistedabove. 2. StandardReferenceand Other ImportantNuclearData. A statusreporton this subjectis being preparedby the CSEWGNormalizationand StandardsSubcommit- 10 tee. Paperson H(n,n) scattering,14 the 6Li(n,a)and B(n,a)reactions,and promptfissionneutronspectrahave been preparedat MSL for inclusionin this report. Contributionsfrom other laboratorieshave been criticallyreviewedas requested.
TABLEVI
GNASH RUNNINGTIME COMPARISONS(CDC7600)
Total 7600 Time (1/0+ CPU) Problem Old Version ——New Version 184W E MeV 20.1 s Y n = 12 9.93 s AE = 1.0 MeV
184W E = 20 MeV 27.7 Y n 47 AE = 1.0 MeV
184W E = 14 MeV 23 9 n 36.2 AE = 0.5 MeV
13 II. NUCLEARCROSS SECTIONPROCESSING A. Cross SectionProduction (R. B. Kidman,R. M. Boicourt,and R. E. MacFarlane) The ENDF/B-Vgeneralpurposefileshave been released(139nuclides),and they are now being processedusingNJOY. So far, 75 nuclideshave been processed into pointwiseform (PENDF),61 nuclideshave been convertedto multigroupcon- stants (30neutrongroupsand 12 photongroupsat 300 K and infinitedilution), and 28 nuclidesare availablefor continuous-energyMonte-Carlocalculations. Duringthe next quarter,additionalmaterialsand groupstructureswill be for- matted into librariesto be used for testingENDF/B-V.
B. EnergyBalanceof ENDF/B-V (R. E. MacFarlane) The latestversionof the EvaluatedNuclearData Files (ENDF/B-V)15contains photonproductiondata for 24 fissionableand 36 nonfissionablematerials. It thereforeprovidesa nearly comprehensivesourceof data for coupledneutron- photon transportcalculationsof heat depositionand radiationexposure. Before thesedata may be used with confidence,theymust be tested. In the standard ENDF testingprocedure,the filesare used to computethe photonproductionfor a set of benchmarks. Unfortunately,the stateof the art is such that 10 to 20% 16 agreementis consideredvery good. Furthermore,many materialsare not tested 17,18 by the existingexperimentalbenchmarks. As introducedin previousreports, the traditionaltestscan be supplementedwith an energybalanceanalysisthat finallyresultsin a ratingof the usefulnessof each ENDF/B-Vmaterialfor ex- actingheat/dosecalculations. The kineticenergyreleasedin a material(KERMA)due to a neutronreaction is just the energyavailable(E+Q)less the energycarriedaway by secondaryneu- 19 tronsand photons. !lhissecondaryenergyis transportedelsewherein the cou- pled calculationand depositedin subsequentreactions. Clearly,in a system largewith respectto neutronand photonmean-freepaths,the heatingdependsonly on flux,cross section,and Q-value;it is independentof the detailsof neutron and photonspectraand yields. This KERMA factoris a sensitivetest of the energybalanceof an evaluation. As an example,if the evaluationgives too much energyto secondaryphotons,the KERMA can be negative. In a largesystem,this negativenumberwould exactly cancelthe excessheatingdue to the hot photons,but in a smallsystem,the photonsmight escape, The calculationwould predicta net coolingeffect.
14 Meanwhile,the photonswould causean overestimateof the heatingor radiation dose elsewhere. Equallyseriousproblemsarise if the energy-balanceKERMA fac- tor is too large. In many cases,reasonableboundsmay be placedupon the KERMA factorsby kinematics. The averagerecoilenergycan be computedaccuratelyfor two-body scattering(elasticor inelastic)and radiativecapture. For a reactionlike (n,a),boundscan be establishedby takingthe limitwhere all availableenergy comesout with the alphaor the limitwhere the alpha is emittedwith zero energy. Similarargumentscan be used for otherreactions. The HEATRmoduleof the NJOY 20 cross-sectionprocessingsystem has been coded to comparethe energy-balance KERMA factorswith theirkinematiclimitsand to produceinformativediagnostics wheneverthe limitsare violated. For the naturalelementevaluations,the kinematicchecksare less useful since the isotopiccrosssectionsand Q-valuesneededto computethe available energyare not includedin the ENDF/Bformat. However,usefulindicationsare stillobtainedfor energyregionsdominatedby elasticor inelasticscattering. These energy-balancecheckshave been carriedout for most of the nonfis- sionablematerialsfrom ENDF/B-Vwith photonproductiondata. The resultsare summarizedqualitativelyin TableVII for threedifferentenergyranges: THER (below1 keV), FAST (1 keV-2MeV), FUSN (2-20MeV). The usefulnessof the data in each range is classifiedas G (good),F (fair,possiblyadequatefor minor ma- terialsor mid-sizeregions),or P (poor,adequateonly for traceelementsor large systems). An inspectionof the tableshows that the light isotopesare in good shape; that stainlesssteelsshouldbe treatedwith caution, especiallyat high ener- gies; and that copperand the heavymetalsmay give poor answerswhen used in smallpieces (e.g.,coils for magneticfusionmachines). Effortsare underwayin the ENDF communityto resolvethe more important discrepancies(e.g.,the tungstenisotopesare being reevaluatedat LOS Alamos and iron KERMA factorsare being calculatedfor the FusionMaterialsIrradiation Test Facilityat Hanford). Thfs study suggeststhat evaluatorsshould (1) do isotopicevaluationswhen possible,(2) use model codeswhereverpractical,(3) avoidplacingexperimentaldata directlyinto the fileswithoutanalysis,(4) use yieldsratherthan productioncross sectionswhere possible,(5) use dis- cretephotonsratherthan continuousdistributionswhere possible,and (6) check the energybalanceat each stagein the evaluation. TABLEVII
QUALITATIVERATINGOF ENERGYBALANCEFOR MATERIALSFROM ENDF/B-V (G=Good,F=Fair,P=Poor)BY ENERGYRANGE (THER= H-1 G G G K a a P H-2 G G G Ca G G G Li-6 G G G Ti G F F Li-7 G G G v G G F Be-9 G G G Cr a a P B-10 G G G Mn-55 P P P c G G G Fe a F P N-14 G G G co-59 G P P N-15 G G F Ni G P F 0-16 G G G Cu a a a Nb-93 P P F F-19 G G F Mo a a a Na-23 G G F Ba-138 :b F F Mg G F F Ta-181 P P AI-27 G G F W-182 G P P Si G G F W-183 G P P P-31 G G F w-184 G P P s-32 G G F W-186 G P P cl a G a Pb a G F aTestsmaskedby elementeffect bPossiblymaskedby internalconversion c. An EpithermalDisadvantageFactorfor EPRI-CELL (R. E. MacFarlane) The thermalreactorfuel cyclecode EPRI-CELLuses the B1 approximationin a homogenizedcell to computethe neutronabsorptionbetween1.855eV and 10 MeV. This calculationrequirescell-averagedcrosssectonsratherthan the zone- averagedcrosssectionsnormallyproducedby NJOY. SinceCELL alreadyuses cell- averageddensities,it is convenientto definea “disadvantagefactor”for a cross sectionin zone i using flux and volumeweighting, V4 x j ig D= j ig 9 (1) V.4 x J jg j where the Vi and @ are volumesand group fluxesfor zones (zonesare regions i.g of constantcross sections,such as fuel f or moderator m). The EPRI-CELL code assumesthat $- = ~=, so the disadvantagefactorsare unity. A more realist~ces~imatefor @f and $ can be obtainedby using the stand- m ard two-regionequivalencetheoryand assumingthat all resonancesare narrow with respectto moderatorscattering.We obtain ($m % (1-f3)* + Wf , (2) where (3) Using the intermediate-resonanceapproximationfor fuel scatteringgives (4) In these equations,.Xeis the equivalentescapecross section,AZ is the ef- P fectivefuel potentialscattering,Zm is the moderatorcross section, and Za is the fuel absorptioncross section. Coingover to multigroupnotation,the two- regiondisadvantagefactorsbecome “D = 1 fg 1 + dx s (5) ag and Vm + Vf 1+ v dZag m D= 9 (6) mg 1 + d~ ag where (7) The qualitativeeffectis clear from Eq. (5);the effectivefuel cross section is reducedfor groupswith high absorption.Note that D goes to 1 for the homogeneouscase (6=1). Codinghas been added to the GAMIOOsubroutineof EPRI-CELLto apply these 21 factorsand testedon the BAPL-U02-1benchmark. The resultsare comparedwith experiment,continuousenergyMonte-Carlo,and the originalCELL methodin Table VIII. The new factorremovesa largepart of the discrepancy;the remainderis probablydue to intermediate-resonanceeffectson spatialself-shieldingand resonanceinterference. TABLEVIII EFFECTOF EPRI-THERMALDISADVANTAGEFACTORON EPRI-CELLRESULTSFOR THE BAPL-U02-1BENCHMARK(d = 0.335) Integral CELL CELL Monte- Exper- Parameter W/Disad. W/o Disad. Carloa iment 0.625-5530eV 2.069 2.246 2.019 U-238 groupabs. cross section k 1.1223 1.1020 1.1353 w . k 0.9877 0.9701 1. eff ’28 1.383 1.39fi.ol aInfinitelatticecalculation. 18 111. FISSIONPRODUCTSAND ACTINIDES: YIELDS,YIELD THEORY,DECAY DATA,DEPLE- TION,AND BUILDUP A. FissionYield Theory [R. E. Pepping(Universityof Wisconsin);D. G. Mad- land;C. W. Maynard (Universityof Wisconsin);T. R. England;and P. G. Young] The investigationof the fissionprocessthroughthe statisticalmodel has been completed,and a detailedreportof the findingsis forthcoming.In it a model is developedto understandfission-productyieldsbased upon a thermal equilibriumassumptionand employinga recentnuclearmass formulaand nuclear densityof statesformalism. An indicationof the sourceof mass asymmetryin fissionis given. Semi-quantitativeagreementis obtainedwith measuredmass- 233 235 238 chainyieldsfor ‘(nth,f), 239Pu(nth,f),235U(n14,f),. f), Oco ‘(nth,f), U(n14, and ‘JLcf(sf). The validityof modelscurrentlyused in the generationof data librariesis investigated.A generalprocedurefor the estimationof fission- productyields for an arbitralyfissioningsystemis presented. B. ENDF/B-VFissionProductYieldsand Testing [T. R. England;I).G. Madland; B. F. Rider (GeneralElectric);R. E. Schenter(HanfordEngineeringDevelop- ment Laboratory);and J. R. Liaw (ArgonneNationalLaboratory)~ The reporton END’F/B-Vyield testingis stillbeing prepared;the sup- portingwork is complete. The literaturehas been reexaminedby one of us (BFR)and verifiedfor N18 000 yieldsand quotederrors. All of the UK experimentalyielclshave been checkedfor differenceswith ENDF/B-V,and errorshave been corrected. Question- able yields and severalduplicationsdue to the same experimentaldata appearing in more than one publicationhave been removed. Recentexperimentaldata pro- ,. vialedby B. Maeck andB. Wehringhave been incorporated.The next mod of ENDF will incorporatethe effectsof thesechanges. 234U 238PU In addition,independentand cumulativeyieldswill be added for 241~ 243Am 238 242 240PU 234U 236U 14 ~ej fis ‘ 9 9 Np, and Cm fast fissionand for s 9 sion. We estimatethesewill be addedwithin‘1one year. The new ENDF/B-Vyieldshave been incorporatedinto the CINDER-10library 235 and comparedwith the LASL decay-heatexperimentfor U and 23’Pu. The new yieldsdo not significantlyeffectthe integraldecay-heatcomparisons. The cal- 239 culationaldifferencewith Pu apparentlyresideswith decay energies,not yields. Comparisonswith experimentare providedin TablesIX and X. 19 1 TABLEIX COMPARISONYARNELLAND BENDTDECAYHEAT EX2ERTMENT(LA-NUREG-6713) FOR 235UUSING ENDF/B-IVAND V YIELDSWITH IV DECAYDATA Calculation UeinR Exp iitiDF/B-vRatio Ratio Ratio Cooling Exp UncertaintyENDF/B-IV Yields V/IV Exp/Cal ExpfCal -m (1UIn%) Data (-IVData) Cal -IV -v 10 8.10 4.1 7.780 7.783 1.000 1.041 1.041 15 7.38 3.0 7.239 7.248 1.000 1.019 1.018 20 6.933 2.6 6.842 6.854 0.998 1.013 1.012 30 6.335 2.3 6.276 6.290 0.998 1.009 1.007 40” 5.920 2.1 5.873 5.888 0.997 1.008 1.005 50 5.614 2.0 5.562 5.577 0.997 1.009 1.007 60 5.358 2.0 5.309 5.324 0.997 1.009 1.006 70 5.141 1.9 5.097 5.113 0.997 1.009 1.005 80 4.958 1.8 4.915 4.932 0.997 1.009 1.005 90 4.806 1.8 4.758 4.774 0.997 1.010 1.007 100 4.667 1.8 4.619 4.636 0.996 1.010 1.007 150 4.170 1.7 4.112 4.128 0.996 1.014 1.010 200 3.841 1.6 3.780 3.796 0.996 1.016 1.012 250 3.608 1.6 3.541 3.556 0.996 1.019 1.015 300 3.419 1.6 3.355 3.370 0.996 1,019 1.015 350 3.265 1.6 3.205 3.218 0.996 10019 1.015 400 3.135 1.6 3.078 3.091 0.996 1.019 1.014 450 3.022 1.6 2.969 2.981 0,996 1.018 1.014 500 2.920 1.6 2.873 2.884 0.996 1.016 1.012 600 2.746 1.5 2.709 2.719 0.996 1.014 1.010 700 2.598 1.5 2.572 2.581 0.997 1.010 1.007 800 2.474 1.5 2.455 2.462 0.997 1.008 1.005 900 2.363 1.5 2.351 2.358 0.997 1.005 1.002 1000 2.264 1.5 2.258 2.264 0.997 1.003 1.000 1500 1.886 1.5 1.901 1.905 0.998 0.992 0.990 2000 1.627 1.5 1.650 1.652 00999 0.986 0.985 5000 0.9111 1.5 0(9362 0.9338 1.003 0.973 0.976 8000 0.6480 1.6 0.6553 0.6521 1.005 0.989 0.994 10000 0.5401 1.7 0.5440 0.5408 1.006 0.993 0.999 15000 0.3803 1.8 0.3778 0.3751 1.007 1.007 1.014 20000 0.2918 2,0 0.2874 0.2853 1.007 1.015 1.023 30000 0.1947 %.3 0.1923 0.1910 1.007 1.012 1.019 100000 0.0454 2.2 0.0455 0.0450 10011 0.971 1.009 20 TABLEX COMPARISON~~~NELLAND BENDTDECAY HEAT EXPERIMENT[NUREG/CR-0349(LA- 7452-Ms)]FOR ~~ypuFISSIONUSING ENDF/B-IVAND V YIELDSWITH IV DECAY DATA Calculation Using Imp fiDF/B-vRatio Ratio Ratio Cooling Exp UncertaintyENDF/B-IV Yields V\IV ExpfCal Exp/Czl Time(s) KcV/F (10in %) Data J-IVData) Cal -Iv -v 20 6.482 5.0 5.850 5.881 1.005 1.108 1.102 6.014 3.0 5.416 5.441 1.005 1.110 1.105 :: 5.640 3.0 5.098 5.118 1.004 1.106 1.102 50 5.366 3.0 4.848 4.865 1.004 1.107 1.103 60 5.116 3.0 4.641 4.656 1.003 1.102 1.099 70 4.923 3.0 4.466 4.479 1.003 1.102 1.099 80 4.756 3.0 4.314 4.326 1.003 1.102 1.099 90 4.605 3.0 4.181 4.192 1.003 1.101 1.099 100 4.488 3.0 4.064 4.074 1.002 1.104 1.102 150 4.027 3.0 3.627 3.636 1.002 1.110 1.108 200 3.739 3.0 3.339 3.346 1.002 1.120 1.117 300 3.361 3.0 2.966 2.971 1.002 1.133 1.131 400 3.096 3.0 2.720 2.724 1.001 1.138 1.137 500 2,885 3.0 2.535 2.538 1.001 1.138 1.137 600 2.710 3.0 2.385 2.389 1.002 1.136 1.134 700 2.556 3.0 2.259 2.262 1.001 1.131 1.130 800 2.432 3.0 2.149 2.153 1.002 1.132 1.130 900 2.311 3.0 2.051 2.056 1.002 1.127 1.124 1000 2.206 3.0 1.964 1.969 1.003 1.123 1.120 1500 1.802 3.0 1.625 1.634 1.006 1.109 1.103 2000 1.527 3.0 1.389 1.400 1.008 1.099 1.091 5000 0.7973 .3.1 0.7445 0.7536 1.012 1.071 1.058 8000 0.5457 3.1 005100 0.5189 1.017 1.070 1.052 100)0 0.4566 4.0 0.4220 0.4287 1.016 1.082 1.065 15000 0.3226 4.0 0.2952 0.2988 1.012 1.093 1.080 2@200 0.2485 4.0 0.2282 0.2303 1.009 1.089 1.079 30000 0.1721 3.9 0.1586 0.1591 1.003 1.085 1.082 40000 0.1302 3.8 0.1206 0.1209 1.002 1.080 1.077 50000 0.1044 3.4 0.0958 0.0962 1.004 1.090 1.085 81899a0.0596 3.4 0.0549 0.0566 1.031 1.086 1.053 99740a0.0467 3.4 0.0435 0.0434 0.998 1.074 1.076 aThecalculatedvaluesat 81899and99740s wereactuallyfor80297 and100000s, respectively, . 21 c. The Effectsof NeutronAbsorptionon DecayHeat (R. J. LaBauve,T. R. Eng- land,and W. B. Wilson) Neutronabsorptionby fissionproductsbecomesimportantat high-flux levelsand long coolingtimes. The flux level can reducethe densityof direct- ly yieldedproductsat short irradiationtimes,significantfor nuclideshaving large crosssectionsand largeyields,and neutronabsorptionin stableand long- livednuclidestends to buildupthe concentrationof more unstablenuclides. Generalequationsare developedin AppendixD of Ref. 22 for both positiveand negativeeffectsof absorption using two-nuclidechains.Pairs of couplednu- clides,ratherthanmultipleabsorption,have been found to be a sufficient representationof the effectof absorptionon totalheating. The equationsin Ref. 22 are used with two incidentneutron-energygroups (thermaland epither- mal) but can be used with any group structure. For the purposeof exposition,simplificationscan be made to the general- ized equationsin Ref. 22 that are appropriatefor a reactionsuch as 133 134CS Cs(n,y) . For the case of constantfluxesand fissionrate for an irra- diationtime T, the absorptioncorrectionis givenby the equation -A2t AF(t,T,$)= N2(T,~)A2Ee 3 (8) where the correctionAF is the decay energyto be added to the calculationwith- out absorption;t is the coolingtime; X2 is the decay constantof the second 134 nuclidein the two-nuclidechain ( Cs in the above example)?E is the average gamma-,beta-,or total-energyper decay for nuclide2; and N2(T,$)is the addi- tionalatom densityof nuclide2 resultingfrom radiativecapturein nuclide1. (9) L where (3= A+ x @=A+A. &3P Radiativecapturein nuclide2 must also generallybe included,as indicated using 132;the generalequationsmust also accountfor neutronabsorptionon the decay energyrate from nuclide1 and reductionin densityof nuclide2 due to buildupfrom its mass chainyield. 22 . In the equationfor N2(T,@),Y1 is the fissionyield for the precursornu- 133 elidein the chain ( Cs in the example),T is the irradiationtime at constant power representedby a thermalflux $th and an epithermalflux $ and S is the epi’ fissionrate. Let the thermaland epithermalcross sectionsin the two nuclides involvedin the (n,y)reactionbe representedby o~h and 01 for the firstnu- epi elideand 02 and 02 for the secondnuclide. Also let th epi (lo) Then, ‘1 = (a:h+ RO1~pi) x 10-24$th , (11) (12) ‘2 = (U:h+ Ra:pi)x 10-24+th , (31= Al + Al , (13) $2 = A2 + ~ (14) 2“ This correction,AF, for a particulartwo-nuclidechaincan then be added to the ANS 5.1 expression 23 ~ . F(t,T)= (15) z < e-Ait(l-e-AiT) , i=l for calculatingdecayheat afteran irradiationtime T and for a coolingtime t, using the fittedpulse parametersa and A.. i 1 To demonstratethe accuracyof the approximationusingonly two-nuclide 235 chains,we have made calculationsfor U irradiatedfor 20 000 hrs with thermal 13 14 neutronfluxesof 10 and 10 n/cm2-3used with effective2200 m/s cross sec- tionsand comparedresultswith those from CINDER-10calculations.Fissionpro- ducts importantfor absorptioneffectsare shown in TableXI, and those two- nuclidechainsused in the approximatecalculationsare indicatedin the table (19 in toto). Note that the chainschosenincludeboth positiveand negative effects. Comparisonresultsare shown in Figs. 7-9 for totalbeta, total gamma, 13 14 and totalbeta -t-gamma,respectively,for fluxesof 10 and 10 . Note that 23 TABLEXI FISSIONPRODUCTSIMPORTANTIN DETERMINATIONOF a. NEUTRONABSORPTIONEFFECTSON DECAY POWER Nuclide Precursor(s) Nuclide Precursor(s) a148pm 147 147pm a90Y a89Y,agOSr Nd, a 1OOTC a99Tc 148pm 147 a a Nd, a147Pm 104M 103M 147pm 147Nd 147pm a a Y 105M 105RU 148pm s 148bm 1161n 1151* a150pm 147Nd 147pm 9 1301 1291 130m1 148pm a a s Y 148%. 134c~ 133C5 149pm a a a 135xe 1351 151~m 150sm a a 136c~ 135 153~m 152Sm a Xe, a135Cs a a 140La a140 a154Eu a153Eu a Ba, a13’La a142pr 141pr a156Eu a155Eu a a144pr a144 143pr Ce, a 147Nd 146Nd aNuclidesincludedin two-nuclidechainsin CALENDAcode as of June 1979. 135Xe givesthe major negativeeffeCt and 134c5 the ~jor positiveeffeCt. Pm DEV ALL GRPS (B13XS) i! H)( E F *M I ~llioD.l!ioi ,i8;oe#18&$.rn~oi8<8~06.,,io8t4.~o+ 88,10,1,: 2“;ok’’’10~ok’loi’’’10~04’10i’’’~04’“;&’~&’’’;or D’ C4)OL1NGTIME(S) cOOIJNGTIME:(S) Flux = 1.E + 13 WI’ DEV ALL GRPS.(BEX!AS) MEV/FISSALL GRPS.(BETM3) M L& ., B *logloi’ioi’io’lo’loslo’”if’ loii COOLINGTIME(S) GOOLtNGTIME(S) Flux = 1.E + 14 Fig. 7. Comparisonof approximatemethodwith CINDER-10results(bet:as). 25 P(7I’DBV ALL GRPS (G~) MEV/FISSALL GRPS.(GAW) XH xx % I 1 COOLINGTIME(S) COOLINGTIME(S) .FIUX= 1.E+ 13 WI’ DEV ALL GRPS.(GAMMAS) KEV/FISSALL GRPS.(GAMMAS) z I e CXX)LINGTIME(S) Flux = 1.E + 14 Fig. 8. Comparisonof approximatemethodwith CINDER-10results(gammas). 26 WI’ DIN ALL GRPS. (TKITAL) ME@ES ALL GRPS. (TOTAL) M ~ ! m ,,,,,’T -lAfl 10’ 10’ 10’ j )’ COOLINGTIME(S) COOLINGTIME(S) Flux = 1.E + 13 PC1’DEV ALL GRPS. (TOTAL) MEV\FISSALL GRPS.(TOTAL) 3 lmm ,8 h ,.llI1(A lo~AITZ’ITW%O’ Mr’%%o’ 10’: 104IO”‘d ‘ioe‘;0’Io’10’10’Io’‘IO’\ COOLINGTIk_fE(S) COOLINGTIME(S) > Flux = 1.E + 14 Fig. 9. Comparisonof approximatemethodwith ~INDER-10results(total= beta + gamma). 27 theseare expressedboth as per cent deviationfrom the caseswithoutabsorption 19 and as MeV/fis(x104),i.e., Individualpointsin the figuresare for E ‘1 ● i=l CINDER-10calculationsat speciffccoolingtimes;the continuouscurves (actually 200 points)representthe approximatecalculations.Some of the 19 chainsare not very significantto totalh-eatingbut are neededin a similarapplicationto few-groupspectra.23 As can be observed from these figures, quite accurate absorption effects can be calculatedusing two-nuclide chains. M@eover, the equat D. Decay Data Testingfor ENDF/B-V (T. R. England,W. B. Wilson,and N. L. Whittemore) Tests of the preliminaryspectraldata for ENDF/B-Vfissionproductnuclides were completedand suppliedto CSEWG. The filescurrentlyhave decaydata for 317 nuclideswith 261 havingspectraldata. (Thecompletefission-productfile will contain877 nuclides,but only the 261 will have detailedspectraldata -- 28 this is an increaseof 81 nuclideshavingspectraover ENDF/B-IV.) The initial testingis for consistencyof Q valueswith decay energiesand averagebeta and gammaenergieswith the detailedspectra. There are ’134nuclidescontainingsome consistencyerrorsof >5%. In addition,comparisonswere made with ENDF/B-IV. Sixtynuclidesdifferby >20% in totalrecoverableenergyor Q value; largerdif- ferencesin more nuclidesare found in averagebeta and gamma energies. Half- livesagreewith ENDF/B-IVwithin 10%, exceptfor 40 nuclides. All differencesare being investigatedat the IdahoNationalEngineering Laboratory,HanfordEngineeringDevelopmentLaboratory,and Los Ali~mosScientific Laboratory. E. ANS 5.1 Decay Power Standard (T. R. England,R. J. LaBauve,W. B. Wilson, and N. L. Whittemore) The ANS 5.1 decay power standardcommitteemet in Atlantaon June 4, 1979. The new standardhas now completedall reviewprocessesand shouldbe published for generaldistributionas an ANSI Standardby Augustor September. There are known deficienciesin the standard. In particular,the treatment of absorptioneffectsrequiresa more precisemethodologyin the absenceof de- tailedsummationcalculations.A method developedat LASL (T-2)was presented and acceptedas a workabletechniquefor futureversionsof the standard(See Sec. III-B). In addition,the T-2 calculationof actinideheatingshow that 239 239 more nuclidesmust be includedthan simplythe U and Np actin.idesnow in the standard. Figures10 and 11 show fractionsof each actinidecontributionvs. decay 232n 233 time for a 235U-238U fueledLWR systemand a - U system,each irradiated for 34 000 MWd/t. Figures12 and 13 show the total fissionproductand actinide contributionsfor each system. Figure14 comparesa conceptualupper-boundac- tinidecorrectionto the ANS 5.1 fission-productdecay-heatstandardwith the upperbound correctionfor absorptioneffects,G———., containedin the standard. t. 235U 238 ‘ax The actinidecorrectionis limited U fuel case studies, which varied from 0.1 to 34 Gwd/t. 233U 241 Finally,measurementsof heatingat LASL and Pu at ORNL will prob- ably be used, alongwith summationcalculations,in a futureextensionof the standard. 29 tkolingTimes,B Fig. 10. Fig. 11. Nuclidecontributorsto actinidede- Nuclidecontributorsto ar.tfnidede- cay power,PWR 2.561%235U/238Ufuel, cay power,PWR 2.95%233U/232Thfuel, 34-Gh/MT~ 1082 days. 34 GWD/MT,835 days. 10’ “~ 10’ 10° i 10 ~.w. % ❑ ‘*\ + 1 — ANS5.1 Standarfl ANS5.lStandnrd● i With dmrption(cxu) ❑ F“”— with t90rpti0n(cMu) M 104 -–-+---~~&-CCDER ZPRI-CINDER SPRI-CINDER ❑ m 10 Fldon ~UCtS mu 10- n tiionHuctd 10 l?. lo”~I 10° 10’ 104 10” 10” low 10° 10’ 104 10’ 10’ @ 1OU Cmunmem lkdlngl’lmsm Fig. 12. Fig. 13. Fissionproductand act$~~dedecay Fissionproductand actinidedecay power,PWR 2.561%235U/ U fuel,34 power,PWR 2.95%233U/232Thfuel,34 GWD/MT,1082 days. GWD/MT,835 days. 30 L6 $ !: u Actinide Correction ~ \ -.1.51 n Cm Correction ;0 “ t! o 1.4 z 1 3 1.3 i! a 12 1 1 10 3 Ceding Timas Fig. 14. Conceptualupper-boundactinidedec y power correctionfactorfor 235U/23sU- fueledLWRS. F. ThreeMile IslandCalculations (W. B. Wilson,T. R. England,R..J. LaBauve, and N. L. Whittemore) Calculationsof decayheatingsourceterms (fissionproductsand actinides), beta- and gamma-decayspectra,and gas contentfollowingthe TMI-2 incidentwere requestedby ElectricPower ResearchInstitute,NuclearRegulatoryCommission, (NRC),and more recently,by the President’sTMI Commission. A largeamountof data was suppliedbased on an assumedfull power operationfor 88 days prior to the incidenton March 28, 1979. More recently,we generateda variablepower historyfrom the MetropolitanEdisonmonthlyoperatingreportsto NRC. All cal- culationswere repeatedusing the new historyprovidedin TableXII and Fig. 15. The heating (alpha,beta, and gamma)from actinidesand fissionproductsusing the historyis given in Table XIII and Fig. 16. Figure17 shows the component heatingfrom actinidesand fissionproducts. Heatingvaluesapply for the totalcore,assumingall productsare present. Some fractionof the heatingis due to the escapinggasesand volatileproducts; therefore,theseresultsrepresentan upper limitof the totalcore value. Work on thisprojectis continuing. 31 TABLEXII CINDERHISTOGRAMCORE POWERHISTORY THREEMILE ISLAND,UNIT 2 Start End lit Elapsed Ave. Power Period Time/date Time/date (h) Time (h) Mw(th) 1 0300/4-21-78 1700/4-23-78 62.0 62.0 611.6 2 1700/4-23-78 2030/9-17-78 3531.5 3593.5 0.0 3 2030/9-17-78 2400/9-30-78 315.5 3909.0 524.52 4 0000/10-1-78 1400/10-5-78 110.0 4019.0 1109.0 5 1400/10-5-78 2400/10-12-78 178.0 4197.0 0.0 0000/10-13-78 0500/10-28-78 365.0 4562.0 1488.94 ! 0500/10-28-78 1400/11-1-78 105.0 4667.0 0.0 8 1400/11-1-78 2400/11-3-78 58.0 4725.0 2397.8 9 0000/11-4-78 0230/11-5-78 26.5 4751.5 0.0 10 0230/11-5-78 0530/11-7-78 51.0 4802.5 2034.1 11 0530/11-7-78 1800/12-3-78 636.5 5439.0 0.0 12 1800/12-3-78 0200/12-16-78 296.0 5735.0 2104.09 13 0200/12-16-780700/12-22-78 149.0 5884.0 0.0 14 0700/12-22-782400/12-31-78 233.0 6117.0 2467.3 15 0000/1-1-79 0800/1-14-79 320.0 6437.0 2281.8 16 0800/1-14-79 1440/1-31-79 414.67 6851.67 0.0 17 1440/1-31-79 2400/1-31-79 9.33 6861.0 33.4 18 0000/2-1-79 2400/2-28-79 672.0 7533.0 2462.14 19 0000/3-1-79 1545/3-6-79 135.75 7668.75 2743.5 20 ‘1545/3-6-79 0815/3-7-79 16.5 7685.25 0.O 21 0815/3-7-79 2400/3-7-79 15.75 7701.0 1697.6 22 0000/3-8-79 0400/3-28-79 484.0 8185.0 2699.704 32 yyy;y Wm l+ua Inlnwww Xl+mmm..0 yyy -00 Inwa. . . mmm -1 I=hhIll r+ow mw. a . . . I-44W yyyuy y~u Sruu-llnln NW A Inlnw-ltn u-1 Inlnl+ ...0 . . . mmmmc+ mlq e-i gj~$] 77”7 hin t-+-i Wllnlnm r-1 Nwm ...... ,-4 U2 u d t-m Cwlf-lm o“x 0. r-l .C.C.C : Qm i? t-ire.vi tu 33 Days 50 1(M 150 200 250 m 350 I I 1 I 1 1 L — L -1 — -r 0 2oixl 4000 Do Houm Fig. 15. CINDERhistogramcore powerhistory,Three Mile IslandUnit 2. !?pY~~ ,n, 10+10410-’10- 10 10 10’ 10’ 10’ I Fig. 16. Totalcore decaypower from actinidesand fissionproducts. ThreeMile Island,Unit 2. 34 @YfJ . 10+ 104 1O-”10410 10 10’ 10*10’ 108 ~ —Fimlon Product8 * 10’ ...... s ...... , g10° Actinidea—’”. “. \ ... 8 ; \ ; ! ‘; ‘; 1 ~ 10-~ ;t g \;, \: :..,,...... ~ rvmlq—mmq11~ IJnm ml,,n:o:mel.$m10’ 10=1041 Fig. 17. Actinideand fission-productdecaypower components. ThreeMile IslandUnit 2. G. Decay SpectralComparisons (T. R. Englnad,N. L. Whittemore,and D. George) Oak RidgeNationalLaboratory(ORNL)(J. K. Dickens)has supplieddetailed 239 time-dependentgammaand beta decay spectrafor Pu followingthermalfission for 1, 5, and 100 s periods. We have run CINDER-10calculationsfor each case and reinstatedcodesnecessaryfor comparisonsbetweencalculationand experiment. These comparisonswill be suppliedto ORNL for use in a joint report. More than 40 spectraof each type are being compared,each involving150 or mc)reenergy points. Calculationsare complete,but comparisonplotshave not been made. H. CINDER-10Code [T. R. England;N. L. Whittemore;and R. Wilczynski(Bettis AtomicPower Laboratory)] Work has resumedon modificationsof CINDER-10to reducestoragerequire- ments and runningtimes. Exceptfor data librariesand selectedroutines,the work is being done jointlywith BettisAtomicPower Laboratory. REFERENCES 7 1. G. M. Hale and D. C. Dodder,“R-Matrixhalysis of the Li system,” in “Ap- plied NuclearData Researchand Development,Januaryl-March31, 1977,”Los Alamos ScientificLaboratoryreportLJi-6893-PR,p. 1 (1977). 35 2. D. C. Dodder,G. M. Hale, S. D. Baker,and E. K. Biegert,“ChargeSymmetric R-MatrixAnalysisof the Seven-NucleonSystem,”in “AppliedNuclearData Re- searchand Development,July l-September30, 1978,”Los AlamosScientific LaboratoryreportLA-7596-PR,p. 1, (1978). 3. G. M. Hale, “FusionReactions,?’in ‘AppliedNuclearData Researchand De- velopment,Octoberl-December31, 1978,”Los Alamos ScientificLaboratory reportLA-7722-PR,p. 1 (1978). 4. G. M. Hale and D. Dodder,“ReactionRates for 6Li(p,a)3He,”in Brookhaven NationalLaboratoryreportBNL-NCS-26133,p. 128 (1979). 5. D. C. Dodderand G. M. Hale, “Applicationsof ApproximateIsospinConserva- tion in R-MatrixAnalyses,”Proc.of Intnl.Conf.on Neutron Physicsand NuclearData,Harwell,p. 490 (1978). 6. A. J. Elwyn,ArgonneNationalLaboratory,personalcommunication(1979). 7 7. G. M. Hale, “R-MatrixAnalysisof the Li System,”Proc. Intn’1.Specialists Symposiumon NeutronStandardsand Applications(NBSSpecialPublications 493),p. 30 (1977). 8. S. D. Baker,E. K. Biegert,D. C. Dodder,and G. M. Hale, “Low Energy 6 Li(p,3He)4HeCross Section,”submittedto Astrophys.J. (1979). 9. P. G. Young and L. Stewart,“EvaluatedData for n + ‘Be Reactions,”Los Alamos ScientificLaboratoryreportLA-7932-MS(ENDF-283),(1979). 100 D. M. Drake,G. F. Auchampaugh,E. D. Arthur,C. E. Ragan,and P. G. Young, “Double-DifferentialBerylliumNeutronCross Sectionsat IncidentNeutron Energiesof 5.9, 10.1, and 14.2 MeV,N Nucl. Sci. Eng.—63, 401 (1977). 11. H. H. Hogue,P. L. Von Behren,D. H. Epperson,S. G. Glendinning,P. W. Lisowski,C. E. Nelson,H. W. Newson,F. O. Purser,W. Tornow,C. R. Gould, and L. W. Seagondollar,“DifferentialElasticand InelasticScatteringof 7- to 15-MeVNeutronsfrom Beryllium,”Nucl. Sci. Eng.& 38 (1978). 12. E. D. Arthur,“Calculationof NeutronCross Sectionson Isotopesof Yttrium and Zirconium,”Los Alamos ScientificLaboratoryreportLA-7789-MS(1979). 13. C. H. Johnson,A. Galonsky,and C. N. Inskeep,“CrossSectionsfor (P,n)Re- actionsin Intermediate-WeightNuclei,”Oak RidgeNationalLaboratoryre- port ORNL-291O(1960)(Unpublished). 1 14. Leona Stewart,‘HydrogenScattering Cross Section, H(n,n)lH,”Los Alamos Alamos ScientificLaboratoryreportLA-7899-MS(1979). 15. Computertapesand additionalinformationon ENDF/B-Vcan be obtainedfrom the NationalNuclearData Centerat BrookhavenNationalLaboratory,Upton, New York 11973. 36 16. E. M. Bohn,R. Maerker,B. A. Magurno,F. J. McCrosson,and R. E. Schenter, Eds., “BenchmarkTestingof ENDF/B-IV,Vol. I,” BrookhavenNationalLabor- atory reportBNL-NC5-21118(ENDF-230)(March1976),Chap. IV. 17. C. I. Baxmanand P. G. Young,“AppliedNuclearData Researchand Development April l--June30, 1977,”Los AlamosScientificLaboratoryreportLA-6971-PR (1977), p. 21. 18. C. I. Baxmanand P. G. 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Stamatelatos,“The Applicationof a Libraryof ProcessedENDF/B-IVFission-ProductAggregate Decay Data in the Calculationof Decay-EnergySpectra,”Los AlamosScien- tificLaboratoryreportLA-7483-MS(September1978). 23. R. J. LaBauve,T. R. England,and W. B. Wilson,“AbsorptionEffectson De- cay Heat and SpectralPulse Kernels,”Trans.Am. Nucl. Soc.~, 739 (1979). fiUS. Government Rintin90ffice: 1979 -t.j77_013/,13~ 37 Pnntcdinthcllnitcd Statcsof Amcrlu. Abaihhlchom t40tionolTcchnicdl I“formtio” Scrwc.. CSDeprtmcnl of (bmmuw S18S P(M NO)d Road Spin@Wd. VA 22161 Mimolichc S3.00 001425 4.00 126-150 7..25 2S1-275 10.75 376-400 13.00 501.525 1s.25 0264350 4.50 151.175 H.OIJ 276-300 11.00 4014?5 I3.?5 S26-SS0 1s.50 0s1-07s .5.25 176.200 9.00 301-325 I1.75 4?64S0 14.00 SSI-57S 16..ss 076.100 6.00 ?01-?2s 9.2s 326.3s0 12.00 45{475 14.50 576-600 16.S0 101.125 6,50 2.76.2.w9.51) MI-375 I~.so 476.501J 1500 bol-up NUIC:AddS2,50I“twUIdt additional 100-PJPL. inm!!wnt lrom 6471 IWC, up.