LA-5949-MS

ZL3

Neutron

CIG14 REPORT COLLECTIONFIEPFKXNCTION

COPYUC-34CReporting Date: April 1975Issued: June 1975

Spectrum from an Oralloy Sphere

by

Charles E. RaganGeorge F. AuchampaughArthur Hemmendinger

Myron G. Silbert

hIosiialam

4 scientific laboratc)ryof the university of California

LOS ALAMOS, NEW MEXICO 87S444

/\

UNITED STATESENERGY RESEARCH AND DEvELOPMENT ADMINISTRATION’

CONTRACT W-7405 -ENG. 36

I

Printed in the United Slates of America. Available fromNational Technical Information Service

U S Department of CommerceS2E5 Port Royal Read

Springfield, VA 221S1Price: Printed Copy S4.M Microfiche $22S

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I

NEUTRON SPECTRUM FROM AN ORALLOY SPHERE

by

Charles E. Ragan, George F. Auchampaugh, Arthur Hemmendinger, and Myron G. Silbert

ABSTRACT

The neutron spectrum horn a 38-kg oralloy sphere, pulsed by acentrally located 14-MeV neutron source, has been measured usingtime-of-flight (TOF) techniques. The nearly isotropic source of 14-MeV neutrons was produced by bombarding a tritium gas targetwith low-energy deuterons. Neutrons in the 0.180- to 15.O-MeVemeizv range were detected at the end of a nartiallv evacuated, 39-

‘=- hi tlig-htpa~h by a NE-213 liquid scintillate; that &ed pulse shape~,

~: discrimination to distinguish neutron events from gamma-ray

:~zi.. events. Detector thresholds of ().15and 0.85MeV were used to cover9

3=— e ;:. the above ener~ range, and the detector efficiency was measured_l—.===~l __ over this range using monoenergetic neutrons from the T(p,n),<—-oz—

I&T(d,n), and D(d,n) reactions. Several measurements of the TOF

~~;:” ~ spectrum were used to determine the neutron flux at the detector,m= “–an-da comparison of this flux with the results of Monte Carlo9 -m

fire, calculations is presented. These calculations were performed with_— the code MCN using two cross-section sets, those from the= m ~“=:-Lawrence Livermore Laboratory (LLL) and those from the_

.—. . ENDF/B-IV library. The results calculated using the ENDF/B-IVcross sections are in excellent agreement with the measurements,especially in the 1- to 6-MeV energy region, where the uncertaintiesin both the calculated and experimental results are the smallest.

.—— ——— —.— —— ————

1. INTRODUCTION

The Los Alamos Scientific Laboratory’s (LASL)Theoretical Design Division has requested

measurements of fission densities as a function ofposition in various assemblies. 1 Thesemeasurements will be used as benchmarks inevaluating Monte Carlo calculations, and the con-clusions should be widely applicable. Common toeach assembly mentioned above is a hollow 38-kgoralloy (93.5% 235U, 6.5% 238U) sphere which will bethe component directly surrounding an ap-proximately isotropic source of 14-MeV neutrons.Knowledge of the neutron energy spectrum from thissphere is necessary to make accurate calculations of

fission densities in the specified assemblies.Therefore, as a first step in this program, a measure-ment of this spectrum was undertaken, and apreliminary report 2 on this measurement wasprepared for the Theoretical Design Division.

II. ACCELERATOR

Several accelerators capable of producing nearly Iisotropic pulses of 14-MeV neutrons exist at LASL.These accelerators are basically of two types:Cockcroft-Walton accelerators which produce 14-MeV neutrons from the T(d,n) reaction using 300- to400-keV deuterons and Van de Graaff accelerators

1

capable of producing neutrons with a wide range ofenergies from various reactions. At a pulse rate of 2.5MHz, one Cockcroft-Walton accelerator is capableof producing -5 x 108 neutronsls using a solidtritium-zirconium target, whereas the Van de Graaffaccelerators are capable of producing about 109neutrons/s from the T(d,n) reaction at approximate-ly this same pulse rate using a tritium gas target.From this standpoint, neither machine has an ob-vious advantage. High-resolution neutron time-of-flight (TOF) measurements require accurate timing(<1 ns) over a wide time interval. These re-quirement.. dictate the use of fast, sophisticatedelectronics for digitizing the data and the use of anon-line computer for data storage. Only the Van deGraaff accelerators in LASL’S Group P-9 areequipped in this manner; therefore, they werechosen for the TOF measurements.

The two Van de Graaff accelerators at P-9 are avertical, single-ended machine capable of providing1- to 6-MeV deuterons and a tandem FN acceleratorcapable of providing 4- to 18-MeV deuterons. As thedeuteron energy is increased above 110 keV, theyield from the T(d,n) reaction decreases substantial-ly, the neutron energy spread increases, and thedegree of isotropy decreases. Consequently, thedeuterons from either P-9 machine must be reducedin energy before interacting with the tritium. Thiscan be accomplished by using an entrance foil to thegas target of the appropriate thickness.

The deuterons from the vertical accelerator needto be degraded in energy only slightly, thereby re-quiring a much thinner foil with less energy straggl-ing. This machine, however, has several unfavorablefeatures. (1) The energy resolution obtainable inTOF depends upon the length of the flight path.When this experiment was being planned. the con-struction of a 40-m flight path was under way at thetandem, and there were no provisions for a flightpath of this length on the vertical. (2) To detect low-energy neutrons, the time between pulses must besuch that these neutrons can reach the detectorbefore high-energy neutrons arrive from the nextbeam pulse. The pulse rate at the vertical machine isessentially fixed at 2.0 MHz, whereas the pulse rateon the tandem can be decreased in steps of two from2.5 MHz to 78.125 kHz. Therefore the tandemaccelerator was chosen for the spectrummeasurements, with the accepted disadvantage ofmore straggling in the entrance foil to the gas cell.

At the higher beam energies necessary on thetandem, a larger background of neutrons wasproduced in the entrance foil. This backgrounddecreased substantially with decreasing energy, butso did the beam current. At a beam energy of 4 MeV,

the available current was down by more than anorder of magnitude from the maximum. Thus, thechoice of the beam energy was a trade-off betweenbeam current and background, with the exact energydetermined by the entrance foil thickness.

After selecting the facility, it was necessary tocomplete the installation of the flight tube, installthe target and tritium gas handling system, deter-mine the characteristics of the neutron source, in-stall a detector system at the end of the flight tube,and construct a support for the oralloy sphere. Thedetails of this work are described in the followingsections.

HI. NEUTRON SOURCE

For a thin target, the peak cross section3-5 for theT(d,n) reaction occurs at approximately 110 keV. Atthis energy, the angular distribution of neutrons canbe calculated from the reaction kinematics, assum-ing an isotropic distribution in the center of mass.However, when a thick entrance window and targetare used, the angular distribution needs to be deter-mined experimentally.

Measurements of the source characteristics wereperformed on the R-2 beam leg of the tandemaccelerator. Figure 1 shows the experimental setup.The detector system was the same as used for thespectrum measurements, with the low-energythreshold set at approximately 0.85 MeV. The detec-tor and shield were placed on a cart that rotatedabout the center of the gas cell (Fig. 2), The pressureseal for the gas cell consisted of two iridium gasketsand a molybdenum foil. The cell was filled throughthe l.1-mm-diam hypodermic tubing and was in-sulated from the beam tube and from the gas handl-ing apparatus to allow current integration.

Measurements were made at a tritium pressure of0.204 MPa gauge (30 psig) using molybdenum en-trance foils of two thicknesses—50 and 63.5 ~m.These thicknesses correspond to the range of 4.6-and 5.3-MeV deuterons in molybdenum, respective-ly. Figure 3 shows the measured neutron yield fromthe T(d,n) reaction as a function of bombardingenergy at 90° to the beam for these two foils. Thepeak in the yield is caused by the 110-keV resonancein the T(d, n) cross section. At beam energies belowthe peak, the transmitted deuter(ms are below theresonance, and at beam energies above the peak, thedeuterons do not lose sufficient energy in the tritiumto reach the resonance from above. Most of theneutrons at the peak of the yield are thereforeproduced by 100 to 200-keV deuterons, and

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2S4 x12.7 cm --.>’.::-.NE- 213da?ector ‘:~;j }-,-jon RCA 2234 .-.....:.-photomultlpliwtubo ~. .

Fig. 1.Experimental setup used for determining theenergy and yield as a function of angle (0) forthe 14-Me V neutron source. The neutrons weredetected with a shielded NE-213 detectormounted (m an RCA-8854 photornultiplier tubeplaced 3.81 m from the source. The angle 0varied frotn O to 135°.

calculations indicate that the average deut eronenergy is approximately 150 keV.

Typical TOF spectra recorded at O and 90° to thebeam are shown in Fig. 4, and the T(d,n) neutronsare seen to be well separated from the background.The yield from the T(d,n) reaction varied onlyslightly with angle. However, the yield of thebackground neutrons was extremely forward peaked.The angular distributions of the neutrons in thebackground at incident beam energies of 5.05 and 5.6MeV, corresponding to the peak yields, are shown in

0.23mmtO.010In.)wall/01ainla9s olwl \

/Xndlum

\tic ~mp

seal(25 Mm)

Moibdanum1o11 HypodwmlclublrJ(50 pm- 63.5#m)

Fig. 2.Exploded view of the tritium gas targetassembly used as a source of 14--IWCVneutronsfrom the T(d,n) reaction. The deuteron beamenters from the left and passes through themo[.vbdenum foil before entering the gas. Thefoil is sealed between the two sets of flanges bythe iridium gaskets.

12

10

~~ 00

‘a 6

!’P”&

54)pm fdl 63.5pm foil

; (o.m2 In.) (0.00251n.l

04

2

Fig. 3.Plots of the counts per microcoulomb in the 14-MeV neutron peak for the 50-pm foil and forthe 63.5-pm foil as a function of deuteronenergy. The solid line is drawn to guide the eye.The yield is about the same for the two foilsand the peak yields occur at about 5.05 and,5.60 A4eV for the 50- and 63.5-pm foils, respec-tively.

Fig. 5. These yields are plotted in counts permicrocoulomb without correction for the detector ef-ficiency to indicate the manner in which the yieldchanges with angle. The integrated background at

.

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.. ..

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.,

.%. . ..

.“ i.. . >. .‘: I

ChannelNumber

Fig. 4.S((mplc spectra obtained using the experimen-tal setup shown in Fig. 1 at a bombardingenergy of .5.0.5 Me V with a 50-pm-thick foil.Both spectra were recorded using 0.5-nschannel loidths. Spectrum (a) was recordedwith the d~tector at 0° to the beam and thebackground is much larger than in (b), whichI(WS recorded with the detector at 90°.

‘“’r—————l5.0 I\\,5L\

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i

Lo

t

A—A Ed95.05 MW(60 *m fall)

i.—. Ed=5.60 MeV

(63.5pm foil) -1

—

--‘-s----- -‘4

0.50I I 1 I I I 1

20 40 60 60 100 120 140

Detector Angle O (deg)

Fig. 5.Plots in counts per microcoulom b of theangular distribution of background neutronsobtained with two foil thicknesses and beamenergies. The data obtained at a deuteronenergy of 5.60 Me V (63.5-pm foil, .) are abouto factor of two higher than the data obtained ata bcarn energy of 5.05 MeV (5o pm foil, A).

5.6 MeV is larger than that at 5.05 MeV by ap-proximately a factor of two. Thus, a 50-pm entrancewindow and a 5.05-MeV beam energy were chosenfor the spectrum measurements. At this beamenergy the integrated background yield is 6[( of theintegrated yield of neutrons from the T(d,n) reac-t ion.

Figure 6 shows plots of the measured (•) andcalculated (A) energy and yield as a function of anglefor neutrons from the T(d,n) reaction at a deuteronenergy of 5.05 MeV, corresponding to the peak of theyield curve for the 50-~m molybdenum foil. Theenergy and yield were calculated from the reactionkinematics for a deutemn energy of 150 keV, and forthe yield calculations an isotropic distribution in the

– !4.8

– 14.6

– 14.4

~– 142 =!

~

– 14.0

– 13.8

Dstoctor Angle R (deg)

Fig. 6.Plots of the variation of energy (upper) and>’icld (lower) with angle for 14-Me V neutronsfrom the T(d, n) reaction at an effectivedeutcron energy of -150 keV. These neutronswere produced by 5. 05-MeV deuterons incidenton a gas cell with a 50-pm-thick molybdenumentrance foil. The A’s represent the valuescalculated from the reaction kinematics (seetext) and m-e in good agreement with them insured (a) values. The lines are drawn toguide the e.vc.

cent er of mass was assumed. These calculatedresults represent the measured values quite ac-curately. The yield appears to be antisymmetricabout 90° and changes by only 7.7°; in going from 90to OO.

For the actual spectrum measurements from theoralloy sphere, a tritium gas cell was mounted on aninsulated snout at the end of the 0° beam tube of thetandem accelerator. The hypodermic filling tubewas connect ed thmugh a ceramic insulator to auranium furnace containing approximately 100 cm 3of tritium trapped in the uranium. This furnace washeated to release the trit ium into the gas cell. Alsoconnected to the hypodermic tubing was apiezoresistive transducer with digital read(m t for

r

. I

,

measuring gas pressure. The pressure could bereproduced to l?ZOusing this device, and variations of0.1% during a run could be noted.

IV. MULTIPLYING ASSEMBLY

The hollow oralloy sphere designated MA-O isdetailed in LASL drawings 32Y-20935-C4, 5, and 8,and is shown schematically in Fig. 7. The sphere isparted along a diametrical plane, and in this planethere are three holes which accommodate parts ofthe target for the Cockcroft-Walton accelerator.Each half of the sphere is composed of threehemispherical shells which fit together to form ahollow sphere with an inner radius of 2.225 cm, anouter radius of 7.799 cm, and a mass of 37.764 kg.

For the spectrum measurements, the hemisphereswere positioned with the largest radial hole aroundthe insulated snout and with the gas cell in thecenter of the spherical cavity. The hypodermic fill-ing tube passed through the radial hole in the sphereat right angles to the largest one. Electrical tape wasused”to ensure that the sphere did not touch any por-tion of the target, which would have shorted out thecurrent integrating system. A pneumatic liftmechanism detailed in LASL drawing 713Y-157044-D1-5 and shown in Fig. 8 was used to support andassemble the two hemispheres. Also shown in Fig. 8are the two cadmium-clad hemispheres positionedaround the tritium target with the lift mechanism inthe down position.

A.----../.

B /-..-.,

L .“ ““ .’-...+-, :

v4=,.-”:A

.—.--

w +Beom

“ES” View

C!!9+Beom

‘A A“ View

Fig. 7.Schematic of the 37.764-kg oralloy sphere. Thesphere is parted along a diametrical plane andthe three holes in this plane are to accom-modate parts of the target for the Cockcroft-Walton accelerator.

Fig. 8.Photograph showing the oralloy sphere and thepneumatic lift mechanism. The tophemisphere is suspended in place, and the bot-tom hemisphere Ls lowered to show the tritiumgas cell in the central cavity.

V. NEUTRON DETECTOR AND ELEC-TRONICS

Neutrons were detected with a 2.54-cm-thick by12.70-cm-diam NE-213 liquid scintillator mountedon an RCA-8854 photomultiplier tube. A schematicof the detailed electronics is shown in Fig. 9. The fastoutput (anode) from the tube base was shaped by aconstant fraction discriminator to provide startsignals from the detector. Stop signals were providedby a delayed pulse obtained from a capacitativebeam pickoff. Each start-stop pair was converted todigital time information using a 62.5-MHz EG&Gclock with a timing resolution of 0.125 ns. This timeinformation was stored in the SDS-930 on-line com-puter with 8-ns channel widths. By using thedifferent rise-time characteristics of the ~E-213scintillator for neutrons and gamma rays, a tagpulse was generated for each detector pulse. Thesetags were used to route the neutron and gamma-rayTOF spectra to different portions of memory in thecomputer. At the end of each run the spectra in thecomputer were written onto magnetic tape for lateranalysis using the CDC-6600 computer.

I

5

-1

r–––II N~u,rOn

delectw1~

—— —— . . ._ __ —— —— .—I

I 1 1 —— I

IDynode 1 Constont 0.5-ps delayAnode

●fraction

Idiscriminator

— 1.8-Ps deloy

L_–-!v__––––l– –__ _’

TAC

StapIStart

n-tag

I

1,1 I

——

Sfort Time Volid stop

Beam stopb

digitizerY-1ag

pick-of f +

n-tag4

To computer

Fig. 9.Electronics setup used in the measurement-of the spectrum from the oralloy sphere. Theanode output was used to provide a fast timing pulse, and the dynode output was used withthe anode output to form a tag signal to identify the anode signal as a neutron or gamma ray.This distinguishing signal came from the time-to-amplitude converter (TAC) and originatedbecause the NE-213 scintillator has different rise times for neutrons (slow) and gamma rays(fast). The electronics within the dashed line were positioned near the detector and theremainder were near the computer.

To unfold the spectrum shape from the measurednumber of counts, it is necessary to know the ef-ficiency of the detector as a function of energy. Theshape of this curve without n,-y discrimination canbe calculated because it depends on the neutron-proton cross section, the detector thickness, and thedetector bias or low-energy threshold. However, theeffectiveness of the n,-y discrimination is a functionof energy; therefore the efficiency must be deter-mined experimentally.

Saturation effects in the n,~ discrimination circuitcause some high-energy neutrons to be tagged asgamma rays, thereby limiting the dynamic range ofthe system. The pulse height output of NE-213 is notlinear in neutron energy,7 and the energy range from0.2 to 17 MeV represents a dynamic range of ap-proximately 600. Therefore, this energy range wascovered in two steps by using two different highvoltages on the photomultiplier tube. A bias of–2100 V was used to cover the range from ap-proximately 1.4 to 17.0 MeV and a bias of –2600 Vwas used for the range <0.2 to -5.0 MeV. Therelative detector efficiency was measured at bothvoltages over the above energy ranges.

This efficiency was measured using monoenergeticneutrons produced by charged particle reactions

6

with knowns’g cross sections. The tandemaccelerator provided monoenergetic neutrons withenergies z3.5 MeV at 0° from the T(p,n), T(d,n),and D( d,n) reactions. The efficiency measurementsat these neutron energies involved only determiningthe relative number of counts in the neutron peakand normalizing to the cross section and to the in-tegrated beam current after correcting for dead time( <5”;). In these measurements the beam stragglingin the 10.6-mg/cm2 molybdenum entrance windowto the gas target was small. For neutron energiesbelow 6.0 MeV, the efficiency was measured usingthe vertical accelerator. The two sets ofmeasurements were normalized in the overlap regionfrom 3.5 to 6.(I MeV. In the 1- to 6-MeV energyrange, the T(p, n) reaction at 0° was used as amonoenergetic neutron source. Neutrons below 1MeV were obtained from the T(p,n) reaction atangles other than 0°. The detector efficiency was ex-tracted from these measurements by normalizingthe counts in the neutron peak to the integratedcurrent and to the T( p,n) cross section at the ap-propriate angle. In the measurements at low inci-dent energy there was a considerable spread in theneutron energy due both to straggling in themolybdenum entrance foil and tritium gas, and to

kinematic broadening. These effects introduced un-certainties in the efficiency measurements, and theywere amplified by the rapidly changing detector ef-

7 ficiency near threshold, where small changes in theenergy or drifts in the electronics introduce largeerrors in efficiency.

b Figure 10 shows plots of the relative efficiency ‘curves at the two photomultiplier high voltages usedin the spectra measurements. The efficiency nearthreshold showed small drifts during the time re-quired to complete the spectra measurements(several months). For this and the above-mentionedreasons, larger errors have been assigned to theselow-energy points.. (See Sec. VIII.)

VI. FLIGHT TUBE

The flight path for measuring the spectrum usingTOF techniques is 38.87 m from the center of the gascell to the {enter of the detector. An evacuated 30.5-cm-diam iron pipe covers approximately 29 m,whereas air fills the remaining distance. The win-dows for the pipe consist of 125-pm Kapton(C16HSOANZ, p = 1.42 gcm-3); Figure 11 is aphotograph of one end of the iron pipe showing thewindow.

Two 1.2-m-long collimators were installed in thepipe. These collimators consist of 2.5-cm-wall ironpipes, with 15.24- and 16.51-cm inside diameters.The smaller collimator, located approximately 7.3 m

0.28I I I I I I I I

A I

p I I I 1 I 1 I 1 I0246010 12141G~

E#kV)

Fig. 10.Plots showing the relative efficiency of thedetector as a function of neutron energy. Theseefficiencies were measured at photomultipliervoltages of –2100 and –2600 V and correspondto thresholds of 0.85 and 0.15 Me\< respective-ly.

.—.

Fig. 11,Photograph showing the end of the evacuatedflight pipe nearer the detector with a stretchedI.%-pm Kapton window. The vacuum in thepipe was maintained at less than 60x 10-3torr.

from the source, defined the viewing area for the12.70 -cm-diam detector. Each collimator waslocated where the flight tube passes through a 0.9-m-thick concrete wall. The hole in the wall around thepipe was fdled with lead, iron, and polyethyleneshielding material. A schematic of the flight path isshown in Fig. 12. The entire pipe was aligned tobetter than 3 mm using a laser, and the collimatorswere positioned to an accuracy of 1 mm.

At the end of the flight tube, the detector andassociated electronics were housed in a portablebuilding (Fig. 13). The beam enters the buildingthrough a 125-pm-thick clear-polystyrene window. Atraveling telescope mounted about 2 m behind thedetector was used h locate the center of the beam.With the detector centered within 1 mm of the beamcenter, the collimating system allowed the detectorto view a circular source with a diameter onlv 3 mmgreater than that of the oralloy sphere. -

VII. EXPERIMENTAL PROCEDURE

Three separate sets of measurements of theneutron spectrum from the oralloy sphere were per-formed on May 7, June 11, and August 29, 1974. Foreach set of measurements the two oralloy

7

Od&

hlv!@luJ&r

“*Fig. 12.

Flight path from the source to the detectorshowing the collimating system for limiting thedetector field of view. Notice the scaledifferences in the two directions.

I

Fig. 13.Portable building containing the detector (inthe window) and the electronics within thedashed line of Fig. 9. Also shown a.t the left arethe signal cables from the detector to the com-puter area.

hemispheres were transported in separate containersfrom the vault at LASL Group A-2 to LASL GroupP-9. Each hemisphere was removed from its con-tainer, in the presence of an H-Division monitor, andwas fitted inside a 0.76-mm-thick cadmiumhemishell, which was used as a shield from thermalroom-return neutrons.

Before beginning each series of runs, the low-energy threshold and n,-y discrimination propertiesof the detector were checked using 137CSand Pu(Be)sources, respectively. The target cell was filled withhelium to check for pressure stability while the beamwas being tuned on target. After making thesechecks, the gas cell was filled to 0.218 MPa gauge (32psig) of tritium by heating the uranium furnace, anda spectrum of the bare source was recorded for aspecified integrated current of incident deuterons.This run was also used to assure that the electronicswere working properly.

The sphere was then positioned around the targetusing the assembly shown previously. As a precau-tion, when the two hemispheres were being assembl-ed, the gamma-ray activity was monitored by detec-tors with an audible alarm. The parting plane of thesphere was tipped about 10 from horizontal so that itwas not in line with the detector. In the May 7 runs,the sphere was not tilted and a 0.5-mm separationbetween the two hemispheres was responsible for ananomalously large number of source neutronsreaching the detector. However, the other portion ofthe spectrum was not affected by the separation. Inthe other runs, the separation between thehemispheres was less than 0.05 mm.

For each set of runs, several spectra were recordedwith and without the oralloy sphere surrounding thetritium-filled gas cell. These runs provided ameasurement of the transmission of 14-MeVneutrons, as well as a measure of the shape of thespectrum from the sphere. The gas cell was thenevacuated and filled with helium gas to a pressure of0.218 MPa gauge, and the time-of-flightmeasurements were repeated with and without thesphere. These spectra were used to measure theneutrons associated with the Mo(d, n) and otherbackground reactions. For the May 7 and August 29measurements, spectra were recorded with detectorthresholds of approximately 0.15 and 0.85 MeV. Forthe June 11 measurements, spectra were recordedusing only the 0.85-MeV threshold; however, fivepairs of sphere-on and sphere-off runs were recordedto obtain an accurate measure of the transmissionfor 14-MeV neutrons. These five pairs of runsrepeated within statistics, indicating accuratecurrent integration and reproducibility in position-ing the sphere.

.

.

8

The spectrum data were obtained at threedifferent beam pulse rates. All of the data recordedwit h a detector threshold of approximately 0.15 MtIVwere obtained at a pulse rate of 78.125 kHz, withbeam currents of 40 to 50 nA. Most of the datarecorded with a detector threshold of about 0.85MeV were obtained at a pulse rate of 0.3125 MHzand with beam currents of 180 to 200 nA, but someruns with this threshold were obtained at the lowerpulse rate. The data used to determine the transmis-sion of 14-MeV neutrons were obtained at a pulserate of 1.25 MHz with beam currents of 0.5 to 0.6 ~A.These pulse rates allowed the neutrons in the energyregion of interest to reach the detector before thenext beam pulse.

VIII. DATA REDUCTION AND RESULTS

Figure 14 shows typical spectra recorded with thesphere in place and with the cell lllled with tritiumand helium. These raw data in counts per channelwere reduced to neutrons fMeV-cm2 per source 14-MeV neutron to facilitate comparison with M(mteCarlo calculations and to remove errors associated

En(MeV)cm 10 12 15 2 345711t3

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103 .. T2in-II ‘ ‘~

t 1 I IA

1 1300 4m 500 ma m aoo

Channel Number

Fig. 14.Plots of the raw data in counts per channel as afunction of channel obtained with the sphere inplace and with tritium (.) and helium (A) inthe cell. These spectra were recorded with adetector threshold of 0.85 MeV with channelwidths of 8 ns. The integrated current for eachspectrum was 105 KC, but the helium run useda slightly larger beam current and thus ashorter time. For this reason, the time-independent background is less than in thetritium run. The neutron energy in MeV isgiven along the top of the graph.

with uncertainties in the absolute detector efficien-cy. This reduction was accomplished in the followingmanner. If Ni (E)dE is the number of neutronsdetected with energy E in the interval dE by a detec-tor of area A at the end of a flight path of length [during the ith run for Ci KC, then the number ofsource neutrons from an isotropic source permicrocoulomb in the energy interval dE is given by

WTt2Ni(E)dE

ni(E)dE =A CiEb(E) ‘

where ~b(E) is the detector efficiency for a thresholdb. Thus the number of 14-MeV source neutrons perMeV from a bare isotropic source is given by

ni(E) = -- ~ Ni(E) ,

A Ci <(14) 14’s

where the sum is over the neutrons in the 14-MeVpeak and where the average efficiency for 14-MeVneutrons ~b( 14) has been removed from thesummation. For an anisotropic source which is an-tisymmet ric about 90° with a(d) representing theratio of the number of neutrons per steradian at anangle Oto the average number emitted per steradian,the number of source 14-MeV neutrons is

WL2ni(E) = & & Ni(E) .

A Ci a(Q) ~

For the present source and detector, 8 = 0° anda(O”) = 1.07. Then for a run with the oralloy spherein place, the number of neutrons at the detector perMeV-cm 2 per source 14-MeV neutron is

N.(E) /[y(E)CjA]

nj(E) =41r~2 ~ Ni(E)/[A Cia(00)~(14)]

141=

N.(E) a(OO).

Y(E)> 4T~2 ~ Ni(~) _

i 14’s <(14)

9

where Nj (E) is the number of detected neutrons perMeV for Cj KC. This number is obtained from Nj(k),the net counts per channel in channel k, using therelation

Nj (E) = ~ Nj(k) =:~Nj (k) ,

where t is the flight time for neutrons of energy Eand T is the time per channel. The flight time andrelativist icallythe relations

(t = T Ik-kY

correct energy are talc-ulated using

)+-A ,

and

r

E = 939.505 [[I - [A,(A+ kkyi)]2]-1’2 - 1] s

where the gamma-ray flight time is A = 3.3356 I/rand ky is the gamma-ray channel.

The number of source neutrons

~ Ni (E)14’s

was obtained from the runs taken with the sphereremoved and with tritium in the cell by summing thecounts above a background obtained from a linearinterpolation under the peak.

For the jth run with the sphere in place, the netnumber of counts in the kth channel Nj(k) wasobtained from the raw data in the following manner.First, the raw data were corrected for “dead time”by multiplying the counts in each channel by theratio of the total number of start pulses to thenumber of start-stop pairs accepted by the com-puter. Then, two types of background were sub-tracted from the spectrum. A time-independentbackground not associated with the beam pulse wasobtained for each channel by averaging manychannels in the flat portion of the spectrumpreceding the gamma-ray bursts. This backgroundwas obtained to an a~curacy of a few percent andwas less than 5(’; of the counts per channel in mostcases. A time-dependent background was obtained

from the runs with helium in the cell and with thesphere in place. These spectra were corrected fordead time and time-independent background, nor-malized to the integrated current, and subtractedchannel by channel from the runs with tritium in thecell. This background was 1 to 570 of the totalnumber of counts per channel.

Sample listings of the raw data obtained onAugust 29, 1974, using a detector threshold of 0.85MeV with tritium or helium in the cell are given inTables I and II, respectively. Table III lists theresults obtained from these data for every fifthchannel. The channel number and energy are givenin columns 1 and 2. Column 3 gives the net spectrumafter dead time corrections, and column 4 listsefficiency-corrected values for the neutrons/MeV-cm 2/source neutron at the detector. The statisticalerror associated with each channel is given incolumn 5.

These data were then averaged over the energybins in Table IV for comparison with Monte Carlocalculations. This averaging was performed by fin-ding the net number of neutrons per square cen-timeter for each energy bin and then dividing thissum by the energy bin width to giveneutrons/MeV/cm 2. The energies listed in Table IVare the upper bounded for each bin and were chosen,generally, to cover a wide enough energy to give goodstatistics. The bin boundary at 13.29 MeV waschosen because this represents the low energy pointfor the direct source neutrons in the 14-MeV peak.These are the neutrons that come out at back anglesand scatter into the detector. After averaging, thestatistical errors were reduced substantially,. and,when combined with the errors associated withbackground subtract ion, were less than 1% in theenergy interval 0.3 to 6.0 MeV. In the energy intervalbelow 0.3 MeV and from 6.0 to 13.29 MeV, thelargest error from these two sources occurs at 13.29MeV and is about 10’;. In the peak at 14 MeV, thecombined statistical error and that associated withbackground subtraction is about 4%. Over most ofthe energy range, the largest errors in the experimen-tal results are associated with uncertainty in thedetector efficiency. These efficiency-associatederrors are 5ri in the interval from 2 to 13.29 MeV,10Ci.in the interval from 1 to 2 MeV, and 15% below1 MeV. At 14 MeV the detector efficiency introducesno error.

The data obtained with a detector bias of ap-proximately 0.15 MeV were normalized to the dataobtained at a bias of approximately 0.85 MeV in theenergy region from 1.5 to 5.0 MeV. The compositespectrum obtained from all the data is presented in

v

.

.

L

10

.

TABLE 1IN cELL

RAW DATA OBTAINED WITH TRITIUM

. iz1215la9101*12229612101216II

131312iz12%3%211

98

129

12

141!1(

1

1

$;15121015221015

abo!iLz1871322*o6710*159213271376b12b97S32

ici23ioib111513

i2

}~” “37 “6811117920s2853533s5679

lb1012112i27●2SE92

~bti18726t319393462

12

l;~7273050

100I*6183272302398@69531550626

.iaSb35SE120187233z8b

8sLio180z2b27535*ko9505539600bt6627680661bo9573512k263672?4195115M26

#1$%059

1320215s~0715322723731a38i510553559bzg

1

38*6416925b9593636bb(lbbs67156a58*541.bb3s12761S6%29!5925

1::s

b36b57542580

518570639b60659“657b3b56055s

b3ibbi!

539624640

5bi609621659660607615S-2867737b296\b8129

76

635b~h563496*22

bbib71b81b9t5ot51t52153t561551S6i571

59362b608

.641bbb6156014*2

b21619660bOl5765554513983$9201i2768493335

317la1511i31918b9to11

b3t633b69632bi9535520b22357246159

915-13t23

605101212$0lb2962i%i2

5s162s

b50b535ab536522b3i331263j48

9962

35b2b2i7s97

44933*318183@

b244335b11i31710

7

4i93ob20@i29Loi

50323;

5b26

12Y?15121+it13t73b

Sz.i59160161162t63i .64165166167;b8i69i7ot71i72i73i7*1751761771781791

402s49

1115i215

9131%1320

132b

121222m711

30131115

1:97sbo

>

0

11

RAW DATA

Channel

TABLE II

OBTAINED WITH

Number Data

. 1:i?;31

M617181

1:;1111211311411s11611711811912312112212312412s12612712812913al3113213313bi3s1361371381391bat~11421631641651461●71681491sol511S21531541SS1S61571SalS91601611621,63;6*I6516616716816917017117217317417s1761771781791

HELIUM IN CELL

649569

1:35b8

1:11

8

1:

1!1411

s69

:9

109

1:8

!9e.799

1:15172313

21i724

%2716

::Ii?161622103

:9s

:

:6

;4a666

1:0

12

TABLE III

REDUCED DATA FROM TABLES I AND H

CHHNNEL

13

TABLE IV

MEASURED NEUTRON SPECTRUMFROM ORALLOY SPHERE

Neutrons/MeV-cm2/SourceNeutron at the

(l%e;) Detector x 10‘g

16.013.2910.08.06.04.03.02.52.01.81.61.41.21.00.90.80.70.60.50.40.30.20.18

—————————

0.980.0420.0890.3581.604.216.999.6

11.813.315.317.119.921.123.425.428.531.632.631.129.423.6

---

Error(90)

4151286555

1010101010151515151515162025---

defined by a 30.5-cm-diam cylinder from the sourceto the detecLor. When a neutron was scattered intothis volume outaide the cylinder, ita weight was setto zero and its path was no longer followed.

The measured energy and yield as a function ofangle (Fig. 6) were used in the source subroutine forthese calculations. The sphere geometry used in thecode is shown in Fig. 7. Neutrons per square cen-timeter were tallied in the energy bins of Table IVand then divided by the energy bin width to giveneut rons/MeV-cm2/source neutron. Statisticalerrors of 2% or less were acquired in several hours ofcomputer time for most energy bins, with the largesterror of approximately 5% occurring for the 10- to13.!29-MeV bin.

Cross-section sets from LLL and ENDF/B-lv wereused to calculate the spectrum. These calculatedresults are presented in Table V. Figure 15 shows acomparison of the experimental results with thecalculated results using the two cross-section sets.The experimental results are plot ted at the midpointof each energy bin and the calculated results areshown as curves from the midpoint of one bin to thenext. Both sets of results are in reasonable agree-ment with the experimental results. However, theENDF/B-IV cross-section set does provide muchbetter agreement, and in the region from 1 to 6 MeVthe agreement is excellent. Both cross-section setsappear to predict a harder spectrum above 6 MeVthan is observed, and the worst agreement is in the10- to 13.29-MeV bin where the statistical errors,both for experiment al and calculational results, arethe largest. Future experiments are planned to covermore fully the region below a few hundred keV.

aUpper boundary of energy bin.

REFERENCESTable IV, along with the total experimental uncer-tainty for each energy bin. This uncertainty was ob-tained by simply adding the statistical uncertaintyin each energy bin to the uncertainty from thedetector efficiency.

IX. COMPARISON WITH MONTE CARLOCALCULATIONS

Monte Carlo calculations were performed byLASL’S Theoretical Design Division with the codeMCN. 10The detailed geometry shown in Fig. 12 wasused in these calculations with a point detectorpositioned at 0° to the beam at a distance of 38.87 mfrom the source. The effect of the collimating systemand concrete walls was simulated by setting the cellimportance to zero for those cells outside the volume

1. R. E. Hunter, Los Alamos Scientific Laboratory,private communication, March 4, 1974.

2. C. E. Ragan, LOSAlamos Scientific Laboratory,private communication, Sept. 27, 1974.

3. Lefma Stewart and Gerald M. Hale, “TheT(d,n)4He and T(t,2n) Cross Sections at LowEnergies, ” Los Alamos Scientific Laboratory reportLA-5828-MS (Jan. 1975).

4. ,John D. Seagrave, “D(d,n)HE3 and T(d,n)He4Neut mn Source Handbook, ” Los Alamos ScientificLilb(watory report LAMS-2162 (Nov. 1957).

14

TABLE V

CALCULATED NEUTRON SPECTRUMFROM ORALLOY SPHERE

Neutron/MeV-cm2/SourceNeutron x 10’9

LLLCross Sections

ENDF/B-IVCross Sections

16.013.2910.08.06.04.03.02.52.01.81.61.41.21.00.90.80.70.60.50.40.30.2

———_

0.860.0440.1250.411.553.75.87.89.6

11.013.015.018.021.522.525.028.031.534.034.531.5

0.940.0440.1400.481.584.16.59.1

11.313.515.016.520.021.523.525.527.029.530.531.027.5

aUpper boundary of energy bin.

5. H. V. Argo, R. F. Taschek, H. M. Agnew, A.Hemmendinger, and W. T. Leland, “Cross Sectionsof the D(T, n)He4 Reaction for 80- to 1200-keVTritons,” Phys. Rev. 87, 612 (1952).

6. See, for example, I. J. Taylor and J. Kalyna, ‘6AHigh Speed Pulse Shape Discriminator,’” Nucl.Instrum. Methods 88, 267 (1970).

7. V. V. Verbinski, W. R. Burrus, T. A. Love, W.Zobel, N. W. Hill, and R. Textor, “Calibration of anOrganic Scintillator for Neutron Spectrometry.”Nuc1. Instrum. Methods 65, 8 (1968).

8. H. Liskien and A. Paulsen, “Neutron Produc-tion Cross Sections and Energies for the ReactionsT(p,n)3He, D(d,n)3He, and T(d,n)4He,” Nucl.Data Tables 11, 569 (1973).

9,

,:&uJ+J_u&~10.0 20.0

En(M@V)

Fig. 15.Comparison of the experimental and calcu-lated spectrum from the 38-kg oralloy sphere atthe detector in neutronalcm2fMe Vfsourceneutron. The Monte Carlo code MCN was usedto obtain the calculated results, and in thesecalculations two sets of cross sections wereused—one from LLL and one from theENDFIB-IV library. The results from theENDFIB-IV calculation are in excellent agree-ment with the experiment and are a substan-tial improvement over the calculations usingthe LLL cross sections, especially in the 1-to 6-MeV energy region.

M. Drosg and D. M. Drake, “Absolute Differen-tial Cross Sections for Neutron Production by the2H(d n)3He Reaction with Ed from 6 to 17 MeV andby th’e 3H(p,n)3He Reaction with EP from 6 to 16MeV,” Los Alamos Scientific Laboratory report LA-5732-MS (Dec. 1974).

10. E. D. Cashwell, J. R. Neergaard, W. M. Taylor,and G. D. Turner, “MCN: A Neutron Monte CarloCt~de,” Los Alamos Scientific Laboratory report LA-4751 (Jan. 1972); E. D. Cashwell, J. R. Neergaard, C.J. Everett, R. G. Schrandt, W. M. Taylor, and G. D.Turner, “Monte Carlo Photon Codes: MCG andMCP,” Los Alamos Scientific Laboratory report LA-5157-MS (1972); R. G. Schrandt, “MCNG - RunningInstructions, ” Los Alamos Scientific Laboratory,private communication (1973).

15