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Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2013 Article ID 252140 9 pageshttpdxdoiorg1011552013252140

Research ArticleModeling of the ORNL PCA Benchmark Using SCALE60 HybridDeterministic-Stochastic Methodology

Mario MatijeviT Dubravko Pevec and Krešimir Trontl

University of Zagreb Faculty of Electrical Engineering and Computing Department of Applied Physics Unska 3 10000 Zagreb Croatia

Correspondence should be addressed to Kresimir Trontl kresimirtrontlferhr

Received 30 May 2013 Accepted 29 August 2013

Academic Editor Valerio Giusti

Copyright copy 2013 Mario Matijevic et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Revised guidelines with the support of computational benchmarks are needed for the regulation of the allowed neutron irradiationto reactor structures during power plant lifetime Currently US NRC Regulatory Guide 1190 is the effective guideline forreactor dosimetry calculations A well known international shielding database SINBAD contains large selection of models forbenchmarking neutron transport methods In this paper a PCA benchmark has been chosen from SINBAD for qualificationof our methodology for pressure vessel neutron fluence calculations as required by the Regulatory Guide 1190 The SCALE60code package developed at Oak Ridge National Laboratory was used for modeling of the PCA benchmark The CSAS6 criticalitysequence of the SCALE60 code package which includesKENO-VIMonteCarlo code aswell asMAVRICMonaco hybrid shieldingsequence was utilized for calculation of equivalent fission fluxesThe shielding analysis was performed using multigroup shieldinglibrary v7 200n47g derived from general purpose ENDFB-VII0 library As a source of response functions for reaction ratecalculations with MAVRIC we used international reactor dosimetry libraries (IRDF-2002 and IRDF-90v2) and appropriate cross-sections from transport library v7 200n47gThe comparison of calculational results and benchmark data showed a good agreementof the calculated and measured equivalent fission fluxes

1 Introduction

Calculational methods for determining the neutron fluenceare necessary to estimate the fracture toughness of the reactorpressure vessel (RPV) materials which is one of the keyrequirements in determining operational limits and lifetimeof nuclear power plantsThis area of research is of a particularimportance in the era of plant lifetime extension demandsand possible financial savings which could be achieved byapproving the extensions Any developed or analyzed cal-culation methodology requires comprehensive verificationand validation against evaluated reference data A largedatabase of benchmarks aimed at validation of computercodes and nuclear data used for radiation transport andshielding problems is ldquoShielding Integral Benchmark Archiveand Database (SINBAD)rdquo [1] One of the most widely usedSINBAD benchmarks for qualification of radiation transportmethods and evaluation of appropriate nuclear data used fortransport as well as for dosimetry calculations in Light WaterReactors (LWR) is the ldquoPool Critical Assembly PressureVessel Facility Benchmarkrdquo (PCA benchmark) [2]

The purpose of the benchmark was to validate thecapabilities of the calculational methodology to predict thereaction rates in the region outside the reactor core whenthe neutron source material compositions and geometry arewell defined Over the years a number of PCA benchmarkstudies have been conducted Their classification is possiblebased on the type of neutron transport calculation (discreteordinates method orMonte Carlomethod) as well as nucleardata libraries used either for neutron transport or dosimetrycalculations

Benchmark original calculational results obtained by dis-crete ordinates synthesis transport method through DORTand DOTSYN codes and BUGLE-93 SAILOR-95 andBUGLE-96 nuclear data libraries for transport calculationand CROSS-95 library for dosimetry calculations wereimproved by Fero et al [3] using full 3D discrete ordi-nates transportmethod andBUGLE-96 library Improvementof calculated to measured ratio (CM) was observed andattributed to full 3D approach Lee [4] used 3D TRIPOLI-43 Monte Carlo code with continuous energy ENDFB-VI4

2 Science and Technology of Nuclear Installations

and JEF 22 nuclear data libraries for neutron transport andIRDF-90 IRDF-90v2 RRDF-98 and JENDLD-99 as well asENDFB-VI4 and JEF 22 nuclear data libraries for dosimetrycalculationsThe author finds the IRDF-90 file generally goodfor RPV dosimetry calculations but recommends 103Rh(nn1015840)103mRh and 237Np(n f)137Cs dosimetry cross-sectionsfrom RRDF-98 and JENDLD-99 libraries

An initial analysis of the applicability of SCALE60 [5]hybrid deterministic-stochastic methodology for the PCAbenchmark analysis was conducted by Vragolov et al [6]Only a preliminary averaged equivalent fission fluxes werecalculated and the results showed SCALE60 possibilitiesbut also raised issues that required further analysis Themain concern was the choice of nuclear data library used fordosimetry calculation

Recently Risner et al [7] used SCALE60 code packagefor validation of VITAMIN-B7 and BUGLE-B7 nucleardata libraries on a number of benchmarks including PCAbenchmark The overall results showed applicability of bothlibraries with SCALE60 sequences for PCA benchmarkanalysis with exception of 103Rh(n n1015840)103mRh and 115In(nn1015840)115mIn dosimetry cross-sectionsThe authors advice usageof IRDF-2002 library for named dosimeter reactions

We believe that additional investigation of SCALE60capabilities could be useful primarily in the context of directapplication of SCALE60 built-in fine-group data librariesfor neutron transport as well as for dosimetry calcula-tions Such an approach would speed up analysis and itwould avoid incorporation of external cross-section librariesinto SCALE60 sequences which is not a straight-forwardprocedure especially for inexperienced users Thereforewe conducted PCA benchmark analysis using SCALE60code package with built-in fine-group nuclear data librariesnamely v7 238 [5] for criticality calculation using CSAS6and v7 200n47g [5] for shielding calculations usingMAVRICsequence Dosimetry cross-section data were extractedfrom nuclear data library used for transport calculation(v7 200n47g) Sincewe faced similar problems as Risner et alwith data for 103Rh(n n1015840)103mRh and 115In(n n1015840)115mIn weused IRDF-2002 [8] and IRDF-90v2 [9] dosimetry librariesfor all dosimeters in order to examine the behavior of everyPCA benchmark dosimeter reaction with different library

The PCA benchmark is described in Section 2 Thedescription of the SCALE60 code package used formodelingof the PCA benchmark and calculational methodology aregiven in Section 3 The analysis of the PCA benchmarkincluding results of calculation and comparison of calculatedvalues with benchmark data is presented in Section 4 whilethe conclusions are given in Section 5 References are given atthe end of the paper

2 PCA Benchmark Facility Description

The main cause for limiting the PWR power plant lifetimeis the fast neutron fluence induced embrittlement of thereactor pressure vessel (RPV)With the advances of computercomputational power the reactor dosimetry calculations givebetter insight in radiation damage of RPV when exposed

to intense neutron flux Correlations can be made betweenneutron flux and irradiation of in-core and ex-core detectorstypically via displacements per atom (DPA)This is importantfor advanced nuclear material selection probing and scopingmaterial behavior in intense radiation environments forexample gas accumulations in reactor baffle plates by 58Ni(n120574)59Ni(n 120572) reaction sequence The current guideline forRPV dosimetry calculations is the USNRCRegulatory Guide1190 [10] which states that calculational methods used toestimate RPV fast fluence should use the latest version of theEvaluated Nuclear Data File (ENDFB) in fast energy range(01ndash15)MeV In accordance with this guideline we presentcalculational results for ORNL PCA Benchmark

The scope of PCA benchmark is to validate the capa-bilities of the calculational methodologies to predict thereaction rates in the region outside the core when theneutron source material compositions and relatively simplegeometry configuration are well defined and given The PCAbenchmark provides calculated and measured reaction rates(CM ratio) inside the simulated pressure vessel as well asin the water gap in front of the pressure vessel This allowsan assessment of the accuracy with which the calculationspredict the neutronflux attenuation inside the pressure vessel

The PCA benchmark facility consists of the reactor coreand the components that mock up the reactor-to-cavityregion in light water reactors These components are thethermal shield (TS) the reactor pressure vessel simulator(RPVS) and the void box (VB) which simulates the reactorcavity An overall view of the PCA benchmark facility isshown in Figure 1 An aluminum plate referred to in Figure 1as the reactor window simulator was added to the facilityfor operational reasons The thicknesses of the water gapsbetween the aluminum window and thermal shield andbetween the thermal shield and pressure vessel are approx-imately 12 cm and 13 cm respectively Such configuration isknown as 1213 configuration The materials used for thecomponents outside the core were aluminum for the reactorwindow simulator stainless steel for the thermal shield andcarbon steel for the pressure vessel The facility is located ina large pool of water which serves as reactor core coolantand moderator and provides shielding The PCA benchmarkfacility core is a light water moderated enriched uraniumfueled critical assembly It consists of 25 material test reactor(MTR) plate type elements The standard MTR fuel elementand control element are depicted in Figure 2 The eight ver-tical experimental access tubes in which the measurementswere done were filled with appropriate material (steel inthe pressure vessel locations and Plexiglas in the in-waterlocations) in order to minimize the perturbations of theneutron field

Measured quantities used in PCA benchmark are givenin terms of the equivalent 235U fission fluxes which were cal-culated by dividing the reaction rates with the cross-sectionsaveraged over the 235U fission spectrum [2] All measuredquantities provided for comparisonwith calculated values aregiven per unit PCA benchmark facility core neutron sourceTherefore the calculated results need to be normalized tothe source strength of one fission neutron per second being

Science and Technology of Nuclear Installations 3

Void box(VB)

Thermalshield(TS)

Reactorwindow

simulator

PCAcore with

control rods

Reactor pressurevessel simulator

(RPVS)

A1A2A3

A4A5A6A7

Figure 1 SCALE60 model of PCA benchmark facility (water removed)

Figure 2 PCA standard MTR fuel and control element (waterincluded)

born in the whole PCA core The ratios of the calculated-to-measured (CM) equivalent fission fluxes for DORT librariesBUGLE-93 SAILOR-95 and BUGLE-96 are given in PCAbenchmark reference [2] Measurements were performed atcore midplane (119911 = 0) at several locations labeled in Figure 1as A1 to A7 To complete the PCA benchmark analysis theanalyst must determine the calculated-to-measured (CM)ratios of the equivalent 235U fission fluxes for all the locationsand all the dosimeters for which the measured values areprovided

The significance of the PCA Benchmark are experimentaldata measurements inside thick steel RPV in locations A4to A6 that is neutron flux gradient inside the pressurevessel which provides themeans for verification of calculatedneutron flux attenuation This is in contrast to availabledata from operating reactors which are typically addressingneutron flux for downcomer region internal to RPV andreactor cavity external to RPV wall [11]

3 SCALE60 Code Package

The SCALE60 [5] code system was developed for the USNRC to satisfy a need for a standardized method of analysisfor the evaluation of nuclear facilities and package designsIn its present form the system has the capability to performcriticality shielding radiation source term spent fuel deple-tiondecay reactor physics and sensitivity analyses usingwell established functionalmodules tailored to the SCALE60system

31 The CSAS6 Sequence The CSAS6 criticality sequence isdeveloped to provide automated problem-dependent cross-section processing followed by calculation of the neu-tron multiplication factor 119896eff The cross-section process-ing code BONAMI is used for the unresolved reso-nance range (Bondarenko factors) and either NITAWL orWORKERCENTRMPMC for the resolved resonance rangeKENO-VI a 3D multigroup Monte Carlo code is its func-tional module

32 The MAVRIC Sequence The MAVRIC shielding se-quence uses automated hybrid deterministic-stochasticmethodology to generate variance reduction (VR) param-eters forMonte Carlo calculationsMAVRIC uses 3Dneutrontransport code Monaco with integrated 119878

119873code Denovo

and it is based on CADIS (Consistent Adjoint DrivenImportance Sampling) [12] and FW-CADIS methodology[13] Denovo is used in forward and adjoint mode toapproximate space-energy flux and adjoint functionrespectively These solutions are utilized to calculate spaceand energy dependent biasing parameters that is biased


source and transport importance map to be used as a VRin Monaco CADIS is used to optimize results in localizedregions of phase-space while FW-CADIS tends to obtainglobal uniform statistical uncertainty by weighting of theadjoint source with expected detector response approximatedwith forward Denovo solution CADIS and FW-CADIS arebased on the adjoint function [14] (ie solution of the adjointBoltzmann equation) which has long been recognized as theimportance function for some objective function of interestDetector response is found by integrating the product ofthe detector cross-section 120590

119889( 119903 119864) and flux over detector

volume

119877 = int119881119863

int119864

120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)

Alternatively if we approximate adjoint scalar flux with quickDenovo solution where the adjoint source is set as 119902dagger( 119903 119864) =120590119889( 119903 119864) then the detector response is found by integrating

over source volume

119877 = int119881119878

int119864

119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)

The biased source distribution [15] which minimizes thevariance of user-desired response is given as

119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)

119877 (3)

where 120601dagger( 119903 119864) 119902( 119903 119864) and 119877 are the scalar adjoint functionthe source emission probability (forward source) and totaldetector response from (2) respectively For transport biasingthe weight window technique is employed that is space-energy dependent geometric splittingroulette Biased sourceand weight-window lower bounds are consistent so thesource particles are created with statistical weight withinweight windows

119908 ( 119903 119864) =119902 ( 119903 119864)

119902 ( 119903 119864)=

119877

120601dagger ( 119903 119864) (4)

Inverse relationship between particle statistical weight andadjoint functionmust be emphasized Since PCA Benchmarkinvolves calculation of near and far detector reaction ratesthis FW-CADIS methodology is highly desirable choice

33 Cross-Section Libraries There are several multigroupcross-section libraries distributed within SCALE60 for criti-cality safety analyses and shielding calculations For criticalitysafety analyses the v7-238 library [5] was used while for theshielding calculations v7-200n47g library [5] was used Theyare based on ENDFB-VII0 data [16] For shielding part ofcalculations it was imperative to use fine structure libraryv7 200n47g because high-energy threshold for all reactionscould not be correctly accounted for if broad shieldingv7 27n19g library was used

4 Analysis of the PCA Benchmark

The calculational models of the PCA benchmark withinCSAS6 and MAVRIC sequences of SCALE60 code package

have been determined The results of the calculations that isequivalent fission fluxes using the established models havebeen compared with the PCA benchmark data

41 CSAS6 Results The initial CSAS6KENO-VI criticalityeigenvalue calculation of the PCA benchmark facility wasperformed using 550 batches and 2000 neutrons per batchwith first 50 batches skipped in order for the fission sourcedistribution to converge to eigenmode Critical control rodpositions were validated and obtained effective multiplica-tion factor of the system was 119896eff = (099856 plusmn 000071)This result was tested with MCNP5 code [17] Shannonentropy check for source stationarity was successful andsimilar 119896eff was obtained 119896eff = (099911 plusmn 000051) ThisCSAS6KENO-VI calculation was then rerun with betterstatistics (2150 batches10000 neutrons per batch) for thegeneration of mesh-based fission source distribution (ldquoCDS= YESrdquo option) to be used as a criticality source in the subse-quent MAVRIC calculations This approach in SCALE60 isknown as CAAS (Criticality Accident Alarm Systems)

42 MAVRICMonaco Results The MAVRIC shielding se-quence was run with the mesh-based source from criticalityeigenvalue run FW-CADIS methodology provides consis-tentweightwindows (ie importancemap) and biased sourcedistributions for transport of the PCA core neutrons to thelocations of interest detectors in experimental access tubesA1ndashA7

The equivalent fission fluxes in PCA report were cal-culated by dividing the reaction rates by the cross-sectionsaveraged over the 235U fission spectrum That fast neutronfluence calculation was reasonable approach in the time ofPCA Benchmark calculation with DORT but full spectrumcalculation nowadays with modern Monte Carlo code is notprohibitive So our calculations were conducted with fullneutron spectrum in accordance with SCALE60 multigroupweighting function (spectrum) [2] defined as

(1) Maxwellian spectrum (peak at 300K) from 10minus5 to0125 eV

(2) a 1119864 spectrum from 0125 eV to 674 keV(3) a fission spectrum (effective temperature at 1273

MeV) from 674 keV to 10MeV(4) a 1119864 spectrum from 10 to 20MeV

Equivalent fission fluxes thus are defined as

120601eq =int119864120590119894(119864) 120601 (119864) 119889119864

int119864120590119894(119864) 120593 (119864) 119889119864 int

119864120593 (119864) 119889119864

=reaction rates

120590119894

(5)

where 120590119894(119864) 120601(119864) and 120593(119864) are the dosimetry cross-sections

for the reactions being considered the Monte Carlo flux atthe dosimetry location and weighting spectrum functionrespectively The spectrum averaged cross-sections (120590

119894) were

taken from Table 16 from PCA report [2] for consistencysince they are in very good agreement with calculated valuesfrom our libraries


For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology

The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g

Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology

Two different approaches for the MAVRIC source distri-bution were

(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case

(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890

minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case

The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878

119873

mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875

3for Legendre order of scattering

cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup

1E16

1E15

1E14

1E13

1E12

1E11

1E10

1E09

minus50

minus100

50

x axis (cm) 0

Neu

tron

forw

ard

flux

(nc

m3 s

)

Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)

1E minus 02

1E minus 03

1E minus 04

1E minus 05

1E minus 06

1E minus 07

1E minus 08

1E minus 09

1E minus 10

minus50

minus100

50

0x axis (cm)

Neu

tron

adjo

int fl

ux (n

cm

2s

)

Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)

neutron fluxes reaction rates and finally equivalent fissionfluxes

The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8

The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results


127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09

Sampled neutronsTotal sampled neutronsValues

Figure 5 Biased source distribution (front half removed)

Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06

256E-07 minus 727E-07727E-07 minus 207E-06

899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08

Group 1Neutron target

Figure 6 Mesh-based importance map (front quarter removed)

Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13

240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13

568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08

236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07

Neutron fluxTotal neutron flux

Figure 7 Neutron flux mesh tally (front quarter removed)

5 Discussion of Results

All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under

prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering


000076

000001

14ndash7

19ndash7

26ndash11

Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)

08

085

09

095

1

10511

Detector position (cm)

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002

SCALE6 IRDF-90v2DORT BUGLE-93

DORT SAILOR-95DORT BUGLE-96

10 15 20 25 30 35 40 45 5550 60

Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors

on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections

Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na

An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it

08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95

DORT BUGLE-96

Detector position (cm)10 15 20 25 30 35 40 45 5550 60

Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors

11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)

Incident energy (MeV)

Figure 11 Inelastic scattering on iron [19]

takes to achieve a given level of uncertainty in Monte Carlocalculation

FOM =1

1198771198642sdot 119879

(6)

where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations

6 Conclusion

The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results


Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0

664sdot10minus6plusmn113

099


lowast507sdot10minus6plusmn068

090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic

tometastablerdquoiso

mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)

Figure 12 FOM factors for IRDF-2002 (CAAS case)

of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful

References

[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011

[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997

[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001

[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003

[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009

[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010

[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011

[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006

[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993

[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001

[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997

[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998

[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007

[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970

[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997

[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006

[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003

[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011

[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


and JEF 22 nuclear data libraries for neutron transport andIRDF-90 IRDF-90v2 RRDF-98 and JENDLD-99 as well asENDFB-VI4 and JEF 22 nuclear data libraries for dosimetrycalculationsThe author finds the IRDF-90 file generally goodfor RPV dosimetry calculations but recommends 103Rh(nn1015840)103mRh and 237Np(n f)137Cs dosimetry cross-sectionsfrom RRDF-98 and JENDLD-99 libraries

An initial analysis of the applicability of SCALE60 [5]hybrid deterministic-stochastic methodology for the PCAbenchmark analysis was conducted by Vragolov et al [6]Only a preliminary averaged equivalent fission fluxes werecalculated and the results showed SCALE60 possibilitiesbut also raised issues that required further analysis Themain concern was the choice of nuclear data library used fordosimetry calculation

Recently Risner et al [7] used SCALE60 code packagefor validation of VITAMIN-B7 and BUGLE-B7 nucleardata libraries on a number of benchmarks including PCAbenchmark The overall results showed applicability of bothlibraries with SCALE60 sequences for PCA benchmarkanalysis with exception of 103Rh(n n1015840)103mRh and 115In(nn1015840)115mIn dosimetry cross-sectionsThe authors advice usageof IRDF-2002 library for named dosimeter reactions

We believe that additional investigation of SCALE60capabilities could be useful primarily in the context of directapplication of SCALE60 built-in fine-group data librariesfor neutron transport as well as for dosimetry calcula-tions Such an approach would speed up analysis and itwould avoid incorporation of external cross-section librariesinto SCALE60 sequences which is not a straight-forwardprocedure especially for inexperienced users Thereforewe conducted PCA benchmark analysis using SCALE60code package with built-in fine-group nuclear data librariesnamely v7 238 [5] for criticality calculation using CSAS6and v7 200n47g [5] for shielding calculations usingMAVRICsequence Dosimetry cross-section data were extractedfrom nuclear data library used for transport calculation(v7 200n47g) Sincewe faced similar problems as Risner et alwith data for 103Rh(n n1015840)103mRh and 115In(n n1015840)115mIn weused IRDF-2002 [8] and IRDF-90v2 [9] dosimetry librariesfor all dosimeters in order to examine the behavior of everyPCA benchmark dosimeter reaction with different library

The PCA benchmark is described in Section 2 Thedescription of the SCALE60 code package used formodelingof the PCA benchmark and calculational methodology aregiven in Section 3 The analysis of the PCA benchmarkincluding results of calculation and comparison of calculatedvalues with benchmark data is presented in Section 4 whilethe conclusions are given in Section 5 References are given atthe end of the paper

2 PCA Benchmark Facility Description

The main cause for limiting the PWR power plant lifetimeis the fast neutron fluence induced embrittlement of thereactor pressure vessel (RPV)With the advances of computercomputational power the reactor dosimetry calculations givebetter insight in radiation damage of RPV when exposed

to intense neutron flux Correlations can be made betweenneutron flux and irradiation of in-core and ex-core detectorstypically via displacements per atom (DPA)This is importantfor advanced nuclear material selection probing and scopingmaterial behavior in intense radiation environments forexample gas accumulations in reactor baffle plates by 58Ni(n120574)59Ni(n 120572) reaction sequence The current guideline forRPV dosimetry calculations is the USNRCRegulatory Guide1190 [10] which states that calculational methods used toestimate RPV fast fluence should use the latest version of theEvaluated Nuclear Data File (ENDFB) in fast energy range(01ndash15)MeV In accordance with this guideline we presentcalculational results for ORNL PCA Benchmark

The scope of PCA benchmark is to validate the capa-bilities of the calculational methodologies to predict thereaction rates in the region outside the core when theneutron source material compositions and relatively simplegeometry configuration are well defined and given The PCAbenchmark provides calculated and measured reaction rates(CM ratio) inside the simulated pressure vessel as well asin the water gap in front of the pressure vessel This allowsan assessment of the accuracy with which the calculationspredict the neutronflux attenuation inside the pressure vessel

The PCA benchmark facility consists of the reactor coreand the components that mock up the reactor-to-cavityregion in light water reactors These components are thethermal shield (TS) the reactor pressure vessel simulator(RPVS) and the void box (VB) which simulates the reactorcavity An overall view of the PCA benchmark facility isshown in Figure 1 An aluminum plate referred to in Figure 1as the reactor window simulator was added to the facilityfor operational reasons The thicknesses of the water gapsbetween the aluminum window and thermal shield andbetween the thermal shield and pressure vessel are approx-imately 12 cm and 13 cm respectively Such configuration isknown as 1213 configuration The materials used for thecomponents outside the core were aluminum for the reactorwindow simulator stainless steel for the thermal shield andcarbon steel for the pressure vessel The facility is located ina large pool of water which serves as reactor core coolantand moderator and provides shielding The PCA benchmarkfacility core is a light water moderated enriched uraniumfueled critical assembly It consists of 25 material test reactor(MTR) plate type elements The standard MTR fuel elementand control element are depicted in Figure 2 The eight ver-tical experimental access tubes in which the measurementswere done were filled with appropriate material (steel inthe pressure vessel locations and Plexiglas in the in-waterlocations) in order to minimize the perturbations of theneutron field

Measured quantities used in PCA benchmark are givenin terms of the equivalent 235U fission fluxes which were cal-culated by dividing the reaction rates with the cross-sectionsaveraged over the 235U fission spectrum [2] All measuredquantities provided for comparisonwith calculated values aregiven per unit PCA benchmark facility core neutron sourceTherefore the calculated results need to be normalized tothe source strength of one fission neutron per second being


Void box(VB)

Thermalshield(TS)

Reactorwindow

simulator

PCAcore with

control rods


(RPVS)

A1A2A3

A4A5A6A7









119873code Denovo





volume

119877 = int119881119863

int119864

120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)


over source volume

119877 = int119881119878

int119864

119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)


119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)

119877 (3)


119908 ( 119903 119864) =119902 ( 119903 119864)

119902 ( 119903 119864)=

119877

120601dagger ( 119903 119864) (4)













120601eq =int119864120590119894(119864) 120601 (119864) 119889119864

int119864120590119894(119864) 120593 (119864) 119889119864 int

119864120593 (119864) 119889119864

=reaction rates

120590119894

(5)



119894) were











119873




1E16

1E15

1E14

1E13

1E12

1E11

1E10

1E09

minus50

minus100

50

x axis (cm) 0

Neu

tron

forw

ard

flux

(nc

m3 s

)


1E minus 02

1E minus 03

1E minus 04

1E minus 05

1E minus 06

1E minus 07

1E minus 08

1E minus 09

1E minus 10

minus50

minus100

50

0x axis (cm)

Neu

tron

adjo

int fl

ux (n

cm

2s

)






127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09




256E-07 minus 727E-07727E-07 minus 207E-06







236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07







000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Void box(VB)

Thermalshield(TS)

Reactorwindow

simulator

PCAcore with

control rods


(RPVS)

A1A2A3

A4A5A6A7









119873code Denovo





volume

119877 = int119881119863

int119864

120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)


over source volume

119877 = int119881119878

int119864

119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)


119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)

119877 (3)


119908 ( 119903 119864) =119902 ( 119903 119864)

119902 ( 119903 119864)=

119877

120601dagger ( 119903 119864) (4)













120601eq =int119864120590119894(119864) 120601 (119864) 119889119864

int119864120590119894(119864) 120593 (119864) 119889119864 int

119864120593 (119864) 119889119864

=reaction rates

120590119894

(5)



119894) were











119873




1E16

1E15

1E14

1E13

1E12

1E11

1E10

1E09

minus50

minus100

50

x axis (cm) 0

Neu

tron

forw

ard

flux

(nc

m3 s

)


1E minus 02

1E minus 03

1E minus 04

1E minus 05

1E minus 06

1E minus 07

1E minus 08

1E minus 09

1E minus 10

minus50

minus100

50

0x axis (cm)

Neu

tron

adjo

int fl

ux (n

cm

2s

)






127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09




256E-07 minus 727E-07727E-07 minus 207E-06







236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07







000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















volume

119877 = int119881119863

int119864

120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)


over source volume

119877 = int119881119878

int119864

119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)


119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)

119877 (3)


119908 ( 119903 119864) =119902 ( 119903 119864)

119902 ( 119903 119864)=

119877

120601dagger ( 119903 119864) (4)













120601eq =int119864120590119894(119864) 120601 (119864) 119889119864

int119864120590119894(119864) 120593 (119864) 119889119864 int

119864120593 (119864) 119889119864

=reaction rates

120590119894

(5)



119894) were











119873




1E16

1E15

1E14

1E13

1E12

1E11

1E10

1E09

minus50

minus100

50

x axis (cm) 0

Neu

tron

forw

ard

flux

(nc

m3 s

)


1E minus 02

1E minus 03

1E minus 04

1E minus 05

1E minus 06

1E minus 07

1E minus 08

1E minus 09

1E minus 10

minus50

minus100

50

0x axis (cm)

Neu

tron

adjo

int fl

ux (n

cm

2s

)






127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09




256E-07 minus 727E-07727E-07 minus 207E-06







236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07







000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


























119873




1E16

1E15

1E14

1E13

1E12

1E11

1E10

1E09

minus50

minus100

50

x axis (cm) 0

Neu

tron

forw

ard

flux

(nc

m3 s

)


1E minus 02

1E minus 03

1E minus 04

1E minus 05

1E minus 06

1E minus 07

1E minus 08

1E minus 09

1E minus 10

minus50

minus100

50

0x axis (cm)

Neu

tron

adjo

int fl

ux (n

cm

2s

)






127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09




256E-07 minus 727E-07727E-07 minus 207E-06







236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07







000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















127E14 minus 264E14

613E13 minus 127E14

295E13 minus 613E13

142E13 minus 295E13

685E12 minus 142E13

330E12 minus 685E12

159E12 minus 330E12

765E11 minus 159E12

369E11 minus 765E11

178E11 minus 369E11

856E10 minus 178E11

412E10 minus 856E10

199E10 minus 412E10

956E09 minus 199E10

461E09 minus 956E09




256E-07 minus 727E-07727E-07 minus 207E-06







236E06 minus 998E06

422E07 minus 178E08998E06 minus 422E07







000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















000076

000001

14ndash7

19ndash7

26ndash11


08

085

09

095

1

10511


Aver

age C

M ra

tio

SCALE6 ENDFB-VII0

SCALE6 IRDF-2002



10 15 20 25 30 35 40 45 5550 60





08085

09095

1105

11115

12

Aver

age C

M ra

tio

SCALE6 ENDFB-VII0


DORT BUGLE-96



11

1

1

102

102

10minus4

10minus4

10minus2

10minus2

10minus10

10minus10

10minus5

10minus5

Cros

s sec

tion

(bar

ns)




FOM =1

1198771198642sdot 119879

(6)


6 Conclusion



Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Table1Eq

uivalent

fissio

nflu

xes(per1

PCAcore

fissio

nneutronpersecon

d(cmminus2 ))

Detector

locatio

nRe

spon

sefunctio

ndata

237 N

p(n

f)137 C

sCM

238 U

(nf)1

37Cs

CM

103 R

h(n

n1015840)103119898Rh

CM

115 In(n

n1015840)115119898Inloz

CM

58Ni(n

p)5

8 Co

CM

27Al(n

120572)2

4 Na

CM

A1

ENDFB-VII0


099



090


095


109

IRDF-2002


103



099


095


097


109

IRDF-90v2


098



099


095


098


113

A2

ENDFB-VII0




095


099


113

IRDF-2002





101


103


113

IRDF-90v2





101


103


117

A3

ENDFB-VII0


093



081


086


097

IRDF-2002


096




087


088


098

IRDF-90v2


090




087


088


101

A4

ENDFB-VII0


098


087


090


091


105

IRDF-2002


099


089


097


096


092


105

IRDF-90v2


097


092


097


098


094


108

A5

ENDFB-VII0


095


081


086


087


102

IRDF-2002


096


082


090


091


087


101

IRDF-90v2


096


085


092


093


090


104

A6

ENDFB-VII0


091


077


084


088


101

IRDF-2002


092


078


089


089


090


101

IRDF-90v2


092


082


091


093


093


103

A7

ENDFB-VII0


087





lowast

IRDF-2002


087






lowast

IRDF-90v2


088






lowast

lozEN

DFB-VI8

datawas

used

fore

xtractionof

crosssectio

nldquoin

elastic


mer

115 In(n

n1015840)115119898In

lowastEx

perim

entald

atan

otprovided

inPC

Abenchm

ark


0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0

20

40

60

80

100

FOM

fact

or


27Al(n 120572)103Rh(n n998400)

238U(n f)

115In(n n998400)58Ni(n p)

237Np(n f)



References
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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