A RESPONSE-MATRIX METHOD FOR THE CALCULATION OF NEUTRON PULSE HEIGHT DISTRIBUTIONS IN MCNP

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1 Internatonal Conference on Mathematcs and Computatonal Methods Appled to Nuclear Scence and Engneerng (M&C 2011) Ro de Janero, RJ, Brazl, May 8-12, 2011, on CD-ROM, Latn Amercan Secton (LAS) / Amercan Nuclear Socety (ANS) ISBN A RESPONSE-MATRIX METHOD FOR THE CALCULATION OF NEUTRON PULSE HEIGHT DISTRIBUTIONS IN MCNP S. Prasad *, S. D. Clarke, S. A. Pozz, E.W.Larsen Department of Nuclear Engneerng and Radologcal Scences, Unversty of Mchgan, Ann Arbor, MI 489 *shkhap@umch.edu ABSTRACT We apply the Response-Matrx Method for the calculaton of neutron pulse heght dstrbuton (Response-Matrx PHD) n order to compute PHD effcently by reducng computaton tme and mnmzng varance. The PHD calculatons and ther assocated uncertanty are compared for polyethylene-shelded and lead-shelded setups wth a 252 Cf source. These comparsons are made for three cases: laboratory measured PHD, Response-Matrx PHD Source Based, and fully analog MCNPX-PolM PHD. It s found that the Response-Matrx PHD greatly mproves the fgure of mert when compared to the fully analog case. The Response-Matrx PHD Source Based method utlzes the source basng method whch s the most applcable gven the source energy spectrum of the 252 Cf. Fnally, dfferent smulatons of source-sheld confguraton are compared wth ther laboratory measured results and show very good agreement thereby valdatng the computatonally robust Response Matrx method. Keywords: pulse heght dstrbuton, varance reducton, lqud scntllators, MCNPX-PolM, nonprolferaton, measurement 1. INTRODUCTION Detecton of shelded specal nuclear materal (SNM) s sgnfcant n nuclear nonprolferaton. The neutron energy spectrum s a sgnature that s useful n dentfyng and characterzng SNM whch may be obtaned usng lqud scntllaton detectors. Smulatons are needed n order to desgn an effectve scntllaton-based measurement system; these are most commonly performed usng the Monte Carlo method. Pulse heght dstrbutons (PHD) neutron detector response for lqud scntllators unvel nformaton about the neutron energy spectrum and are thus useful n dentfyng and characterzng sources. However, the wdely used MCNP code does not have the ablty to calculate scntllator neutron detector responses. In the past, these dstrbutons have been computed usng specalzed algorthms to process MCNP output [1, 2]. The method proposed here utlzes a sngle detector response matrx whch operates on the ncdent neutron energy to calculate the detector pulse heght dstrbuton. Ths method s general, and can be appled to any source-sheldng confguraton; one only needs to tally the neutron energy spectrum ncdent on the detector face. Any standard MCNP varance reducton technques may be appled to calculate the ncdent neutron energy dstrbuton. In the

2 Prasad et al. paper Response-Matrx PHD method s appled wth varance reducton technques to shelded neutron sources and compared to analog MCNPX-PolM data. 2. NUMERICAL METHOD The Response-Matrx PHD method makes use of an MCNPX-PolM calculated response matrx to calculate the pulse heght dstrbuton. It s also requred to know the neutron energy spectrum ncdent on the detector. Ths energy spectrum may be calculated usng any standard varance reducton technque applcable to the problem. The formulaton of the method s descrbed below: 2.1 MCNPX-PolM Response Matrx The response matrx used n the calculaton of Response-Matrx PHD contans nformaton about the EJ-309 lqud scntllator s ntrnsc effcency. The rows of the matrx correspond to energes rangng from 0.2 MeV to 15 MeV wth ncrements of 20 kev (741 energy bns) whle the columns correspond to lght output rangng from 0.01 MeVee to.07 MeVee wth ncrements of kevee (07 lght output bns). The sum of all lght outputs (or columns) for a gven energy (row) gves the total ntrnsc detecton effcency at that energy. Thus, more generally for m energy rows and n lght output columns the response matrx s: R R R E1, L1 Em, L1 R R E1, Ln Em, Ln The response matrx s created usng analog MCNPX-PolM smulatons to calculate the energy deposted whch were converted to lght usng approprate coeffcents; here a separate MCNPX- PolM case was run for each energy bn n the matrx. The neutrons smulated are monodrectonal. 2.2 Pulse Heght Dstrbuton Formulaton Snce a response-matrx element represents the ntrnsc effcency for an ncdent energy E and lght output L, ts product wth the number of ncdent neutrons at a gven energy E yelds the total number of neutrons detected for E at lght output L. Thus, f these products are summed over all ncdent energes as n Eq. (1), one obtans the total number of counts for the lght output bn L. Smlarly counts can be obtaned for all lght output bns yeldng a complete pulse heght spectrum. The formula governng ths method usng MCNP s gven as followng: 2/14

3 Response-Matrx PHD m N ( L) nˆ J ( E ) A R( E, L) 1 E (1) N(L) = total counts for a gven lght output L L = a gven lght output bn E = th energy bn nˆ = vector normal to the detector face J + = partal current towards detector face A = area of the detector R( E, L) = response matrx element at E E and L = energy bn wdth about E The F1 tally n MCNP counts the number of partcles crossng a user specfed surface. Thus, the number of partcles enterng the detector face s calculated by the F1 tally and has the followng relatonshp [4]: F1 ( E ) nˆ J A E (2) MCNP Substtutng Eq. (2) n Eq. (1) we obtan the smple relatonshp for counts n a lght output bn: N( L) m 1 F1 MCNP ( E ) R( E, L) The Response-Matrx PHD method utlzes Eq. (3) to calculate the pulse heght dstrbuton. The assumpton here s that there s no overlap of neutrons n a pulse. The MCNP F1 tally used n ths result can be calculated usng MCNP5, MCNPX or MCNPX-PolM. The F1 tally does not need to be run n analog mode and can therefore make use of applcable varance reducton technques. 2.3 Radal Leakage Correcton Factor (3) As mentoned n secton 2.1 the response matrx has been constructed for neutrons that travel monodrectonally and perpendcular to the detector face. However, the neutrons comng out from the shelded 252 Cf sotropc source are not monodrectonal and perpendcular to the detector face. These neutrons have a greater chance of leakng out of the lateral sdes of the detector and n general wll have a shorter pathlength or a smaller lkelhood to scatter n the scntllator detector, and thus get detected. As a result the PHD calculated wth the Response- Matrx PHD method wll be an overestmate snce the response matrx underestmates lateral leakage through the sdes. For larger dstances (more than half a meter source detector dstance n the gven setup) ths effect wll be mnmal snce the angle subtended between the source and the edge of the detector wll be small and thus the partcle drecton wll be closer to a perpendcular monodrectonal beam. However, as the source gets closer to the detector the spread of a partcle s ncdent drecton wth respect to the detector face ncreases and thus ths effect becomes more domnant as shown below n Fg. 1(a) for a cm source detector dstance wth 5.08 cm (2 nches) of polyethylene sheld. 3/14

4 Counts Counts Prasad et al Response-Matrx PHD Analog PHD 0000 Response-Matrx PHD Analog PHD Lght Output [MeVee] Fgure 1(a): Response-Matrx PHD wthout radal leakage correcton compared to analog Lght Output [MeVee] Fgure 1(b) Response Matrx PHD wth radal leakage correcton compared to analog. As seen n Fg. 1(a) the dscrepancy s sgnfcant between the Response Matrx PHD whch uses the response matrx constructed usng monodrectonal neutrons and the MCNPX-PolM PHD whch correctly models the ncdent angle of the neutron and the subsequent nteractons. In order to correct for ths dscrepancy caused due to ncdent angle of the neutrons we formulate a radal leakage correcton factor: ζ = Φ unmodfed / Φ beam (4). Snce we obtan hgher counts usng the Response Matrx PHD due to larger ntrnsc effcences, the correcton factor should correctly account for greater leakage from the detector sdes to reduce the ntrnsc effcences. In order to accomplsh ths task we need to calculate the factor by whch the rate of the pathlength creaton dffers n the case where the partcles are not ncdent n a perpendcular beam. A rato ζ, of the volumetrc flux (rate of pathlength creaton n a gven volume [4]) for the gven setup wth unmodfed partcle drecton, Φ unmodfed, to the case where the partcles n setup are made monodrectonally ncdent on the detector face, Φ beam s calculated. Ths rato gven n Eq. (4) s calculated for each energy group. Each lght output s ntrnsc effcency n an energy group s multpled by ts correspondng ζ to yeld the correct ntrnsc effcency as: ε corrected (E m, L n )= ε beam (E m, L n ) ζ(e m ) (5). As seen n Fg 1(b) after ncorporatng the radal leakage correcton factors the agreement between the Response Matrx PHD and analog MCNPX PolM PHD s excellent. 4/14

5 Response-Matrx PHD 2.4 Varance Reducton Technques Analog Monte Carlo smulatons can be long and tme consumng. In order to ncrease the usefulness of Monte Carlo, varance reducton technques are used to reduce the uncertanty and complete smulatons n shorter run-tmes. There are varous varance reducton optons avalable n MCNP such as source basng, geometry splttng, pont detectors, DXTRAN, to name a few. It s mportant to choose the optons that effcently reduce uncertanty, whle mnmzng smulaton run-tmes [4]. A typcal fsson spectrum has fewer neutrons towards hgher energes, thus an F1 tally wll tend to have greater uncertanty n these regons. Nonetheless, hgher energes are mportant snce bgger lght pulses are caused due to hgher energes deposted. Therefore, t s mportant to reduce uncertanty of the F1 tally towards hgher energes. Hence, for the method we have appled the source basng technque to obtan a unform varance dstrbuton. In the source basng method the user specfes the desred probablty dstrbuton, pˆ or the bases. Based on these bases new weghts, ŵ are calculated such that the product of orgnal weght w 0 and probablty p 0 are preserved: w p wˆ pˆ 0 0 (6) In order to obtan a unform dstrbuton throughout the spectrum nstead of low varance n certan regons and hgher n the others, a flat dstrbuton s nput as the desred probablty densty dstrbuton, the new weghts are then calculated accordng to Eq. (6). Thus, gven that w 0 s unty, t can be gleaned that ŵ must follow the spectral shape of p 0 (f pˆ s a flat dstrbuton) such that the product wˆ pˆ s preserved as shown n Eq (6). Ths relatonshp s demonstrated usng MCNP results as dscussed n the Secton LABORATORY MEASUREMENTS Measurements were performed to valdate smulaton results as shown n Fg. 2. A strong 252 Cf source emttng nearly neutrons per second placed 30 cm from detector was shelded wth dfferent thcknesses of polyethylene and lead shelds. The measurements were performed at the Detecton for Nuclear Nonprolferaton Group Laboratory (DNNG), Unversty of Mchgan. A 137 Cs source was used for calbraton. A 12-bt dgtzer was used. The threshold for detecton was determned to be 70 kevee. 5/14

6 Prasad et al. 0.5 Tal Integral 0.4 Neutrons from Cf-252 Photons from Cs-137 Dscrmnaton Lne Fgure 2(a): Measurement setup wth 252 Cf source (left), 20.3 cm of polyethylene (mddle) and EJ-309 detector (rght) Total Integral Fgure 2(b): Pulse shape dscrmnaton between neutrons (blue) and gammas (red) for the setup wth no sheldng. Pulses sgnal the detecton of partcles. Acquston wndow s 0 ponts long where each pont s 4 ns wde. The pulses were dscrmnated between neutrons and gammas based on ther tal to total ntegrals as shown n Fg. 2(b). Neutrons nteract wth the nucle n the scntllator and thus result n larger tals compared to gamma-rays whch nteract wth electrons. Therefore, n Fg. 2(b) ponts correspondng to hgher tal ntegral values for the same total ntegral value of the pulse are from neutrons and are those ponts found above the dscrmnaton lne. 4. MONTE CARLO SIMULATIONS Fgure 3: Shelded 252Cf setup wth an EJ-309 lqud scntllator The measurement setup shown n Fg. 3 contans an sotropc 252Cf source placed 30 cm from the face of an EJ-309 lqud scntllaton detector. In addton to the features modeled n Fg.3 the ron table on whch the detector rests and the concrete floor are also modeled. The source s shelded by lead or polyethylene rectangular blocks that are 5.08 cm,.16 cm, cm and cm thck. The detector s a cylnder wth a radus of 6.34 cm and a length of cm. Its chemcal 6/14

7 Response-Matrx PHD composton s 54.8% hydrogen and 45.2% natural carbon by number of atoms. The 252 Cf source s modeled only to emt fsson spectrum smulated by the Watt spectrum. W e g h t s ŵ MCNP ŵ calculated ṕ nput Energy [MeV] 5.00E E E E E E E E E E E+00 Fgure 4: Source based new weghts, calculated new weghts and based new probablty As dscussed n the prevous secton descrbng varance reducton technques, source basng requres the user to nput a desred dstrbuton of source partcles, pˆ (shown n Fg. 4). Ths desred dstrbuton n our case s a unform dstrbuton of source partcles throughout the spectrum such that a unform uncertanty dstrbuton s obtaned n the F1 tally throughout the energy spectrum. Based on these based probabltes new weghts, ŵ are calculated such that the product of orgnal weght w 0 and probablty p 0 are preserved as gven by Eq. (6). In Fg. 4 both the MCNP new weghts ŵ and those calculated ndependently usng Eq. (6) are n good agreement. Snce pˆ s a flat dstrbuton t s expected that the spectral shape of ŵ wll be that of a Watt spectrum (as seen n Fg. 4) n order to preserve the orgnal probablty dstrbuton p 0 of the Watt spectrum. B a s e d P r o b a b l t y 7/14

8 No. of Source Neutrons No. of Source Neutrons Prasad et al. 5. RESULTS & ANALYSIS Ths secton s dvded n four subsectons. The frst subsecton presents the source-based F1 tally results that gve the neutron energy spectrum enterng the detector. Ths ncomng neutron energy spectrum s combned wth response matrx to yeld pulse heght dstrbutons. The next two subsectons dscuss the Response Matrx method results and ther statstcal uncertantes respectvely. Fnally, n the last subsecton comparsons of the smulaton results wth the measurement data are shown. 5.1 Incdent Current on Detector Face usng Source Basng Energy [MeV] Fgure 5(a): 252 Cf neutron spectrum from polyethylene Energy [MeV] Fgure 5(b): 252 Cf neutron spectrum from lead The F1 tally n MCNP was used to tally the neutron spectrum enterng the detector face after leavng the.16 cm (4 n) thck polyethylene or lead shelds as shown n Fg. 5(a) and 5(b). These cases were run for 7 source partcles but have been normalzed to the source strength n the laboratory measurements. As seen above, the spectrum from the polyethylene sheld has been heavly moderated and has lost ts orgnal Watt spectrum shape. Whereas the spectrum from the lead sheld has stll retaned most of the Watt spectrum shape. Polyethylene s a hghly hydrogenous materal and s thus very effectve n moderatng neutrons. Lead s made up of heavy nucle and s thus not as effectve n moderatng neutrons. However, lead has several resonances n ts elastc scatter crosssectons contrbutng to the fluctuatons seen n the peak of the spectrum n Fg. 5(b) [5]. The MCNP cases were performed wth and wthout varance reducton technques. The MCNP smulaton wth varance reducton utlzed source basng as dscussed n the prevous secton to produce unform uncertanty throughout the energy spectrum as shown n Fg. 6. It can be gleaned that the uncertanty n both cases s relatvely flat throughout the energy spectrum. The hgh uncertanty even for a large number of source partcles s expected snce each energy bn s only 20 8/14

9 Uncertanty n Counts Response-Matrx PHD kev n wdth. Furthermore, n the case of lead sheld the spectrum of neutrons has smaller uncertantes for smaller energes and then flattens out. For the purpose of ths paper, however, we are nterested n the pulse heght dstrbuton resultng from a combnaton of partcles n all energy bns and ther responses from the MCNPX-PolM calculated response matrx as dscussed next. % Lead 9% Polyethylene 8% 7% 6% 5% 4% 3% 2% 1% 0% Energy [MeV] Fgure 6: Percent uncertanty n source based neutron energy spectrum enterng detector 5.2 Pulse Heght Dstrbuton Comparson The F1 talles or the current of neutrons enterng the detector s combned wth the response matrx as shown by Eq. 3 to yeld pulse heght dstrbutons as shown n Fg. 7(a) and 7(b) for.16 cm (4 n) thck polyethylene and lead sheld respectvely. It can be gleaned from these fgures that the analog pulse heght dstrbuton obtaned from MCNPX-PolM case and ts postprocessor has extremely large varances. However, n the case of Response-Matrx PHD and Response-Matrx PHD Source Based the pulse heght dstrbutons are well converged. The fgures are shown only up to 2 MeVee snce for hgher energes the analog pulse heght spectrum has almost 0% uncertanty, moreover, the scntllator measurement data can be measured only up to 2 MeVee. For ths lght output range both the Response-Matrx PHD methods, wth and wthout source basng have very small uncertanty and are therefore dffcult to dfferentate. The dfferences between these methods are better llustrated by Fg. 8(a) and 8(b). It can also be observed n Fgure 7(a) and 7(b) that the lead pulse heght spectrum has hgher counts than the polyethylene pulse heght spectrum, ths behavor s expected gven the two energy spectra shown n Fgures 5(a) and 5(b): the lead-shelded spectrum s less moderated than the polyethylene-shelded spectrum. 9/14

10 Percent Uncertanty Percent Uncertanty Counts/s.MeVee Counts/s.MeVee Prasad et al.,000 1,000 Analog Response Matrx Response Matrx Source Based,000 1,000 Analog Response Matrx Response Matrx Source Based Lght Output [MeVee] Fgure 7(a): 252 Cf PHD from a polyethylene sheld Lght Output [MeVee] Fgure 7(b): 252 Cf PHD from a lead sheld 5.3 Pulse Heght Dstrbuton Uncertanty Comparson Ths secton dscusses the statstcal uncertanty n the calculaton of the pulse heght dstrbutons. The uncertanty n the pulse heght dstrbuton for.16 cm (4 n) thck polyethylene or lead shelds wth 7 source partcles obtaned by usng the three methods: analog PHD, Response-Matrx PHD and Response-Matrx PHD Source Based s shown n Fg. 8(a) and 8(b). The advantage of usng the Response-Matrx PHD s evdent from these graphs. The analog PHD results n uncertanty over % just about 500 kevee and reaches nearly a 0% about 2 MeVee. The Response-Matrx PHD method s a sgnfcant mprovement over the analog case where the uncertanty ranges between 1% and 2% both cases, however, t shows a gradually ncreasng trend whch crosses % around 5 MeVee. The Response-Matrx PHD Source Based, however, provdes the best mprovement. For ths method the uncertanty remans constant at about 1%, nearly three orders of magntude mprovement for lght output greater than 1 MeVee for the same number of source partcles and slghtly reduced runtme n MCNP. 0% 0% % % 1% 0% Analog Response Matrx Response Matrx Source Based Lght Output [MeVee] 1% 0% Analog Response Matrx Response Matrx Source Based Lght Output [MeVee] Fgure 8(a): Uncertanty n 252 Cf PHD from polyethylene Fgure 8(b): Uncertanty n 252 Cf PHD from lead /14

11 Response-Matrx PHD Table I: Fgure of Mert Improvement wth Response Matrx over the Entre Pulse Heght Dstrbuton Sheldng Materal 5.08 cm (2 n).16 cm (4 n) cm (6 n) cm (8 n) Polyethylene Lead FOM s calculated usng the standard MCNP conventon: FOM 1/(R 2 T) (7) Where, R s the sample relatve standard devaton of the mean, and T s the computatonal tme [4]. In Table I factors of mprovement n the fgure of mert (FOM) for the entre pulse heght dstrbuton range or over all lght output bns are shown. If one had to calculate FOM factors for ndvdual low lght output bns they would be close to the values lsted above but as we move towards hgher lght output bns the FOM mprovement factors ncrease by orders of magntude. The FOM mprovement factors lsted n Table I are manly representatve of FOM mprovement factors of the many low lght output bns because the number of counts n the hgh lght output bns are very few. The FOM mprovement factor s calculated as a rato between the FOM for the Response Matrx PHD method (no addtonal varance reducton used) to the analog PHD. The FOM mprovement s sgnfcant for polyethylene and lead shelds, however, t s substantally greater n the case of polyethylene shelds where t s over a factor of 8 for all thcknesses (except the 5.08 cm where t s 6.5). For the lead shelds t vares between a factor of 3 and 4. FOM mprovement factors for ndvdual lght output bns n the hgher end of the spectrum can be greater than three orders of magntude evdent from Fg. 8(a) and 8(b), however, n Table 1 when we dscuss the FOM mprovement over the entre PHD spectrum. Thus, the greatest advantage s attaned by the usng the Response-Matrx PHD Source Based method. The Response-Matrx PHD and the Response-Matrx PHD Source Based method are also dfferent from the analog PHD method because they do not need to post-process an addtonal data bank wth the nformaton about all collsons and the energy deposted. The detector response s already contaned n the MCNPX-PolM calculated response matrx. Furthermore, snce the response matrx has fxed dmensons (m by n) the number of floatng pont operatons performed to process the data (Eq. 3) s ndependent of the number of source partcles, t s always 2mn-n. Gven 741 energy bns and 07 lght bns for cases dscussed here, there are merely 1.5 mllon floatng pont operatons performed for any number of source partcles usng the Response Matrx PHD method. However, n the analog case the post processor wll do more work and run for longer tmes for a greater number of source partcles snce there wll be more collsons to follow. Addtonally, 11/14

12 Counts/s.MeVee Counts/s.MeVee Counts/s.MeVee Counts/s.MeVee Prasad et al. the analog case wll also consume greater storage space to save the data bank as the number of source partcles s ncreased. 5.4 Comparson of Response Matrx PHD wth Measured Data The computatonal advantage of the Response Matrx method wth and wthout standard MCNP varance reducton technques has been verfed above by comparng the results wth analog MCNPX-PolM cases. However, the true value of the technque s proven by comparng the results wth measured data. The measurement technque has been dscussed n Secton 3, here we dscuss the results.,000 1,000 Measured Response Matrx Method,000 1,000 Measured Response Matrx Method Lght Output [MeVee] Fgure 9(a): Lead sheld 5.08 cm (2 n) Lght Output [MeVee] Fgure 9(b): Lead sheld cm (8 n) As seen n Fg. 9(a) and 9(b) the smulated Response Matrx method results of lead shelded 252 Cf source agree very well wth the measured data. Ths agreement s even better for the case wth 5 cm of lead. For 20 cm of lead the smulated Response Matrx counts are slghtly lower than the measurement beyond 0.40 MeVee.,000 1,000 Measured Response Matrx Method,000 1,000 Measured Response Matrx Method Lght Output [MeVee] Fgure (a): Polyethylene sheld 5.08 cm (2 n) Lght Output [MeVee] Fgure (b): Polyethylene sheld cm (8 n) 12/14

13 Response-Matrx PHD In Fg. (a) and (b) measurements wth polyethylene shelds have been shown. The agreement n case of 5 cm of polyethylene s good but a lttle hgher than the measurement. The agreement n case of 20 cm of polyethylene s generally good but can be mproved to better smulate the measured spectrum. For the 20 cm case the smulated counts are lower below 0.3 MeVee. The dsagreement n ths low regon s very lkely due to the msclassfcaton of neutrons n the PSD process as shown n Fg 2(b). For low lght outputs gammas and neutrons can overlap n the PSD plot, ths overlap becomes more mportant when the sheld becomes ncreasngly moderatng and gves lower energy neutrons that yeld smaller lght pulses. A more general reason for the dscrepancy between the measured and the smulated could be the emprcally found lght converson coeffcents that convert the energy deposted n the detector nto the lght output. Work contnues to refne these coeffcents to acheve excellent agreement n varous measurement confguratons. 6. CONCLUSION Pulse heght dstrbutons are mportant for characterzng sources. They descrbe the energy deposton behavor of partcles. Monte Carlo codes such as MCNP5 cannot calculate neutron pulse heght dstrbuton for scntllators [4]. MCNPX-PolM and ts assocated post-processor can calculate pulse heght dstrbutons, however, calculatons can be done only n analog mode resultng n tme consumng runs and post processng. The method proposed here, Response-Matrx PHD utlzes a sngle detector response matrx whch operates on the ncdent neutron energy to calculate the detector pulse heght dstrbuton. The Response-Matrx PHD s also appled wth source basng as t s not requred to be run n the analog mode. The smulaton setup comprses of the 252 Cf source placed 30 cm away from the EJ-309 lqud scntllator detector wth a.15 cm (4 n) thck polyethylene or lead sheld n front of the source. A comparson of the three methods s made for 7 neutron source partcles. It s evdent that the Response-Matrx PHD method greatly reduces varance throughout the pulse heght spectrum. In general, a FOM mprovement by a factor of 8 s acheved n the case of polyethylene shelds and a factor of 3-4 tmes s acheved n the case of lead shelds over the entre PHD. These factors can be as much as a few orders of magntude for ndvdual hgh lght output bns. Furthermore, usng the Response-Matrx PHD Source Based not only decreases the varance even more but keeps t constant throughout the spectrum. The statstcal uncertanty n the source based case s usually constant about 1%, whereas n the analog case the uncertanty reaches nearly a 0% only at about 2 MeVee. Furthermore, the analog case requres storage of large data fles, and requres tme consumng post-processng of these fles. Comparsons wth DNNG laboratory measured data for 5.08 cm and cm polyethylene and lead shelds are also very promsng and show excellent agreement n general. Work contnues to refne the lght converson coeffcents that can further mprove the agreement between measured and smulated results. Future work on ths method wll 13/14

14 Prasad et al. nclude examnng other varance reducton technques such as DXTRAN and pont detector talles n addton to nvestgatng more demandng sheldng confguratons. 7. REFERENCES [1] S. A. Pozz, E. Padovan, M. Marseguerra. MCNP-PolM: A Monte Carlo Code for Correlaton Measurements, Nucl. Instr. Meth. A, 513, pp , [2] S. Pozz, E. Padovan, M. Flaska, and S. Clarke. MCNP-PolM Post-Processng Code Ver Oak Rdge Natonal Laboratory Internal Report, ORNL/TM-2007/33, [3] S. A. Pozz, S. D. Clarke, M. Flaska, and P. Peeran. Pulse Heght Dstrbutons of Neutrons and Gamma-Rays from Plutonum Oxde. Nucl. Instr. Meth. A 608, pp , [4] MCNP5 User s Manual, Volume 1. Los Alamos Natonal Laboratory, LA-UR , Aprl [5] Evaluated Nuclear Data Fles, ENDF VII, 14/14