Neutron Induced Fission Fragment Angular Distributions, Anisotropy, and Linear Momentum Transfer Measured with the NIFFTE Fission Time Projection Chamber
D. Hensle, J.T. Barker, J.S. Barrett, N.S. Bowden, K.J. Brewster, J. Bundgaard, Z.Q. Case, R.J. Casperson, D.A. Cebra, T. Classen, D.L. Duke, N. Fotiadis, J Gearhart, V. Geppert-Kleinrath, U. Greife, E. Guardincerri, C. Hagmann, M. Heffner, C.R. Hicks, D. Higgins, L.D. Isenhower, K. Kazkaz, A. Kemnitz, K.J. Kiesling, J. King, J.L. Klay, J. Latta, E. Leal, W. Loveland, M. Lynch, J.A. Magee, B. Manning, M.P. Mendenhall, M. Monterial, S. Mosby, G. Oman, C. Prokop, S. Sangiorgio, K.T. Schmitt, B. Seilhan, L. Snyder, F. Tovesson, C.L. Towell, R.S. Towell, T.R. Towell, N. Walsh, T.S. Watson, L. Yao, W. Younes
NNeutron Induced Fission Fragment Angular Distributions, Anisotropy, and LinearMomentum Transfer Measured with the NIFFTE Fission Time Projection Chamber
D. Hensle, ∗ J.T. Barker, J.S. Barrett, N.S. Bowden, K.J. Brewster, J. Bundgaard, Z.Q. Case, R.J.Casperson, D.A. Cebra, T. Classen, D.L. Duke, N. Fotiadis, J Gearhart, V. Geppert-Kleinrath, U. Greife, E.Guardincerri, C. Hagmann, M. Heffner, C.R. Hicks, D. Higgins, L.D. Isenhower, K. Kazkaz, A. Kemnitz, K.J. Kiesling, J. King, J.L. Klay, J. Latta, E. Leal, W. Loveland, M. Lynch, J.A. Magee, † B. Manning, M.P. Mendenhall, M. Monterial, S. Mosby, G. Oman, C. Prokop, S. Sangiorgio, K.T. Schmitt, B. Seilhan, L.Snyder, F. Tovesson, C.L. Towell, R.S. Towell, T.R. Towell, N. Walsh, T.S. Watson, L. Yao, and W. Younes (NIFFTE Collaboration) ‡ Colorado School of Mines, Golden, Colorado 80401, USA Abilene Christian University, Abilene, Texas 79699 Oregon State University, Corvallis, Oregon 97331 Lawrence Livermore National Laboratory, Livermore, California 94550 Colorado School of Mines, Golden, Colorado 80401 University of California, Davis, California 95616 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 California Polytechnic State University, San Luis Obispo, California 93407 (Dated: January 28, 2020)The Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) collaboration has per-formed measurements with a fission time projection chamber (fissionTPC) to study the fissionprocess by reconstructing full three-dimensional tracks of fission fragments and other ionizing radi-ation. The amount of linear momentum imparted to the fissioning nucleus by the incident neutroncan be inferred by measuring the opening angle between the fission fragments. Using this measuredlinear momentum, fission fragment angular distributions can be converted to the center-of-massframe for anisotropy measurements. Angular anisotropy is an important experimental observablefor understanding the quantum mechanical state of the fissioning nucleus and vital to determiningdetection efficiency for cross section measurements. Neutron linear momentum transfer to fissioning U, U, and
Pu and fission fragment angular anisotropy of
U and
U as a function ofneutron energies in the range 130 keV–250 MeV are presented.
I. INTRODUCTION
Nuclear fission data is an important input into manyapplications including nuclear reactors, stockpile stew-ardship, and astrophysics [1]. Neutron induced fissioncross sections are of particular importance, but are diffi-cult to measure with the precision required for some ap-plications [2]. Thus, the Neutron Induced Fission Frag-ment Tracking Experiment (NIFFTE) collaboration hasbuilt a time projection chamber, the fissionTPC, de-signed specifically to study the fission process [3]. ThefissionTPC has the ability to perform three-dimensionalreconstruction of ionizing radiation in the detector vol-ume. By leveraging this three-dimensional tracking abil-ity, the fissionTPC has the capability to explore cross sec-tion systematics not accessible by other fission detectionmethods [4]. Concurrently with cross section measure-ments, fission fragment angular distributions and linearmomentum transfer from the incident neutron to the tar-get nucleus are measured.Bohr first introduced the idea of a fissioning nucleus ∗ [email protected] † Currently at Stonehill College ‡ http://niffte.calpoly.edu/ being thermodynamically cold due to all of the energybeing stored in the deformation of the nucleus [5], allow-ing the fissioning nucleus to be described by a discreteangular momentum state. Fission fragment angular dis-tributions can be calculated from analytical expressionsbased on the angular momentum state of the fissioningnucleus [6, 7]. At high excitation energies, these discreteangular momentum states are expected to turn into acontinuous regime [8, 9]. Experimentally, a sum of dif-ferent angular momentum states contributes to the mea-sured angular distribution of fission fragments at eachincident neutron energy.Fission fragment angular distributions can be used toinfer the angular momentum state of the fissioning nu-cleus. These results provide useful empirical inputs toMonte Carlo fission reaction codes such as TALYS [10]and EMPIRE [11]. Conversely, comparison of the mea-sured angular distributions with the outputs from thesecodes provides a benchmark for the included in reactionmodels. Angular anisotropy is also included in cross sec-tion measurements to fully understand detector efficiency[4].Due to the linear momentum transfer of the incidentneutron to the target nucleus, the emission angles of fis-sion fragments in the center-of-mass frame are focusedforward in the lab frame. Fission fragments also gain a r X i v : . [ nu c l - e x ] J a n additional kinetic energy in the direction of the neutronflight path. Consequently, more fission events are di-rected downstream of the target and fewer fission frag-ments are detected in the upstream volume, thus affect-ing the detector efficiency as a function of neutron energyin any cross section measurement [4]. Other fission ob-servables such as fragment energies and masses must alsotake this kinematic boost into account [12].In this paper, we present measurements of fission frag-ment angular anisotropy for U and
U as well asmean neutron linear momentum transfer to fissioning U, U, and
Pu in the neutron energy range 130keV – 250 MeV.
II. BACKGROUND
Fission fragment angular distributions are fit with Leg-endre polynomials of even order to conserve forward-backward symmetry [6]. An anisotropy parameter is thenreported to display this information as a function of inci-dent neutron energies and is typically defined as the ratioof counts parallel to the beam to counts perpendicular tothe beam. This anisotropy parameter is expressed as A = W [cos θ c.m. = 1] W [cos θ c.m. = 0] = W (0 ◦ c.m. ) W (90 ◦ c.m. ) (1)where, in the case of this work, W (cos θ c.m. ) = a + a L (cos θ c.m. )+ a L (cos θ c.m. ) (2)and θ c.m. is the fission fragment polar angle in the center-of-mass frame.Because the anisotropy parameter is defined in thecenter-of-mass frame, a conversion from the lab frameto the center-of-mass frame is needed. Past experimentshave accounted for this correction by averaging upstreamand downstream results [13], assuming full momentumtransfer [14], or treating it as a negligible correction [15].A necessary input parameter to make this correctionwithout these approximations is the amount of linear mo-mentum the fissioning nucleus has actually acquired fromthe incident neutron, but, to the best of our knowledge,no such measurement for neutron-induced fission exists.Above neutron energies of a few MeV, new reactionmechanisms arise that complicate the simple picture ofcomplete neutron capture followed by fission. Direct re-actions and pre-equilibrium particle emission [16] becomeintermediate steps between incident neutron interactionand scission. These reaction mechanisms result in lightparticles (primarily neutrons and protons) being emittedin the direction of the neutron beam [17] and necessarilytake away some of the available linear momentum car-ried by the incident neutron. By measuring the openingangle of the fission fragments, the amount of linear mo-mentum transfer occurring as a function of incident neu-tron energy can be extracted and used to convert fissionfragments from the lab frame to the center of mass frame FIG. 1. Schematic drawing of the fissionTPC hardwareshowing two gas volumes, each with a highly segmented an-ode, separated by a central cathode. The actinide targets areplaced on the central cathode. – a method first proposed by Sikkeland et al. [18] andexpanded upon in this paper.
III. DETECTOR
The fissionTPC, shown in Figure 1 and described indetail in [3], consists of two gas volumes separated by acentral cathode. Ionizing radiation strips electrons fromthe fill gas which are drifted to the anode pad planesby a static electric field of 500 V/cm. Each volume hasa highly segmented anode with 2976 hexagonal readoutpads, 2 mm in pitch, and a MICROMEGAS (MICROMEsh Gaseous Structure) metal mesh [19] held 75 μ mabove the pads for gas amplification to produce a gainfactor of approximately 40 [20]. The drift chamber, filledwith 95% argon / 5% isobutane at 550 torr [20], is 15 cmin diameter and each anode is 5.4 cm from the centralcathode. Each of the anode pads are connected to customelectronic readout cards with a sampling rate of 20 ns.The central cathode is used for neutron time of flightand has a sampling rate of one nanosecond [21].The fissionTPC operates at the Los Alamos NationalLaboratory’s Neutron Science Center at the WeaponsNeutron Research flight path 90L. An 800 MeV protonbeam impinges upon a tungsten target to create an un-moderated white neutron flux. The structure of the neu-tron beam is typically set to a 100 Hz macropulse struc-ture containing about 375 micropulses of 250 ps in width,each spaced by 1.8 μ s [22]. Neutron time of flight is usedto extract the neutron kinetic energy. The start signalis the proton pulse hitting the spallation target and thestop signal is fragment detection by the central cathode.Figure 2 shows the neutron time of flight spectrum fora U target. The peak at ∼
26 ns is due to photon in-
FIG. 2. Neutron time-of-flight spectrum for a
U targetwhere the red line represents the amount of neutron beamwraparound. The inset shows the peak at 26 ns resultingfrom photon induced fission and has a FWHM of about 3 ns,demonstrating the time-of-flight resolution of the fissionTPC. duced fission and is used to calibrate the time of flightspectrum as well as shows the time-of-flight resolution ofapproximately 3 ns FWHM.Due to the neutron beam micropulse separation of only1.8 μ s, neutrons from the subsequent pulse can pass theslowest neutrons from the previous pulse. These slowneutrons are then assigned the time of flight with respectto the most recent micropulse, not the micropulse fromwhich they originated. The amount of these wraparoundneutrons can be estimated by fitting the tail of the lastmicropulse and summing that fit over all micropulses.This procedure produces the red line in Figure 2 whichmust match the pedestal before the photo-fission peak asthese neutrons must be coming from wraparound eventsconsidering no neutrons can arrive before the gammaflash. IV. ACTINIDE TARGETS
Three actinides, U, U, and
Pu, have beenplaced in the fissionTPC and exposed to the neutronsource in a number of different target configurations, asshown in Figure 3. The first two targets consist of half-moons of the actinides placed on 100 μ g/cm carbon, al-lowing fission fragments and alpha particles emitted fromthe actinide deposit to be detected in both volumes. Allof the other targets are placed on aluminum backingswith a thickness of 0.5 mm which effectively separates theupstream and downstream gas volumes as fission frag-ments and alpha particles cannot pass through the alu-minum backing. In each of the thick target runs, the fis-sionTPC was rotated with respect to the beam such thateach side has the kinematic boost from the incident neu-tron flipped between the upstream and downstream datasets. Changing targets requires the entire fissionTPC to FIG. 3. List of targets used in this analysis. The first twotargets are placed on a thin carbon backing whereas the othertargets are on thick aluminum backings. be disassembled to gain access to the central cathode tar-get holder.One additional target of
Cf (not shown in Figure 3)was placed in the fissionTPC to calibrate the detector re-sponse to alpha particles and fission fragments without aneutron beam. This source provides isotropic emission offission fragments and alpha particles to demonstrate theability of the fissionTPC to accurately measure a knownangular distribution.
V. DATA RECONSTRUCTION
A large amount of processing must be done on the rawfissionTPC data in order to extract ionizing track param-eters. Voxels of charge are created which contain the x,y, z locations, and charge in units of uncalibrated Ana-log to Digital Converter (ADC) units. First, the anodepad signals undergo a differentiation process to extractthe amount of charge that was incident on the pad ateach individual time step. The pad position gives thex and y values for each voxel, and the z information isextracted by multiplying the electron drift speed by thedrift time relative to the start of the event. Because thefissionTPC cannot measure exactly when ionization oc-curs within the chamber, the z values are relative andnot absolute.Once all of the voxels are created, they are groupedtogether and fit with a straight line. Figure 4 showsan example event from a thin-backed target containingthe upstream and downstream fission fragments and aternary alpha particle [3].From each track fit, a number of track parameters canbe extracted including the start and end positions, polarand azimuthal angles, peak ionization value and loca-tion, length, and charge. In Figure 5, a plot of tracklength versus track energy shows how a common param-eter space is used to differentiate types of ionizing radia-tion [4]. Fission fragments are shorter and more energeticwhile alpha particles travel farther and deposit less en-ergy. Rough energy calibrations can be done using theknown energy of alpha particles from spontaneous decaysto convert from ADC to MeV.
FIG. 4. Visualization of reconstructed fission fragment andternary alpha particle charge clouds in the fissionTPC froman actinide target with a thin carbon backing allowing bothfission fragments to be detected. The color scale representsthe amount of charge in each voxel in uncalibrated ADC units[3].
In the context of fission fragment angular anisotropyand linear momentum transfer measurements, the polarangle of each track is the primary observable. However,corrections for electron drift speed and electron diffusionmust be applied to each fission fragment track to accu-rately extract these polar angles from the data.
A. Electron Drift Speed
The fissionTPC does not have the capability to directlymeasure the speed at which the electrons drift throughthe chamber. However, an accurate measurement of thedrift speed is needed in order to properly reconstruct thepolar angles of the ionizing radiation. The cosine of thepolar angle is determined bycos θ = ∆ zl (3)where ∆ z is the track length in the drift direction of thechamber and l is the total track length. Considering thez position of each charge voxel is determined by multi-plying the relative drift time by the electron drift speed,a larger drift speed produces a larger ∆ z and vice-versa. FIG. 5. Track length vs total track energy provides a com-mon parameter space which aids particle identification in thefissionTPC [4].
Thus, changing the electron drift speed changes the re-constructed track polar angle.In order to find the correct electron drift speed in thefissionTPC, the spontaneous alpha emission from the ac-tinide target is used. Because the spontaneous alphaemission must be isotropic, the cos θ distribution must beflat. Thus, the electron drift speed in the reconstructionprocess is adjusted to achieve a flat polar angle distribu-tion.Using this technique, a drift speed for each target ineach configuration is found with an associated uncer-tainty of 0.01 cm/ μ s. Because electron drift speed is de-pendent on gas temperature and pressure, as well as theapplied drift voltage, the drift speed measurement be-tween the targets used in this analysis varies from 2.75to 3.09 cm/ μ s [23]. B. Electron Diffusion
After setting the electron drift speed to reproduceisotropic emission of alpha particles, an additional po-lar angle correction for electron diffusion is needed forthe fission fragments. Because the fission fragments havea much higher ionization density than the alpha parti-cles, electron diffusion manifests more strongly in the fis-sion fragments. If the electron diffusion coefficients aredifferent between the radial and drift directions of thefissionTPC, then a polar angle distortion takes place.By treating the electron diffusion as a Gaussian distri-bution with different widths in the radial and drift direc-tions of the fissionTPC, a correction to the polar angletakes the form [23] δ cos θ = sin θ cos θ (cid:82) a q ( a ) da/Q < l > ( σ r − σ z ) (4)where a is the length along the track with respect to thecenter of the charge cloud, Q is the total charge in thetrack, q ( a ) is the charge per unit length along the track, σ r ,z are the electron diffusion coefficients in the radialand drift directions, respectively. The average electrondrift length is given by < l > = 1 Q (cid:90) l ( a ) q ( a ) da (5)where l ( a ) = 5 . − a · cos θ and 5.4 cm is the lengthof the fissionTPC in the drift direction. Due to the largeamount of data needed to save the complete Bragg curvefor each fission fragment, q ( a ) is estimated by treatingthe Bragg curve as having a Gaussian start and a lineartail where the two functions meet at the Bragg peak andthe slope of the linear tail is such that (cid:82) q ( a ) da = Q .Thus, since q ( a ) is estimated using only three points –start and end positions, and the Bragg peak – the datarequirements in the processing step are greatly reduced.Fission fragments emitted perpendicular to the neu-tron beam direction, i.e. with 0 < cos θ < .
05, havewidth projections along the drift direction or the radialdirection of the fissionTPC. By stacking many fragmentcharge clouds on top of each other, the standard devia-tions of the charge cloud projections, σ r and σ z , can becalculated. These charge cloud widths are related to thediffusion coefficients by the drift distance they traveled σ r,z = σ r ,z < l > (6)where < l > = 5 . σ z ranging from 0.126 to0.141 cm and values of σ r ranging from 0.152 to 0.161 cmwith an uncertainty of 0.001 cm. This produces a 10%uncertainty on the overall diffusion correction. The dif-fusion correction uncertainty associated with modifyingBragg curve parameters was negligible when compared tothe uncertainty caused by the diffusion coefficients [23]. C. Californium-252 Calibration Source
To ensure the electron diffusion and electron driftspeed corrections successfully reproduce fragment angu-lar distributions, a source of
Cf was placed in the fis-sionTPC to provide a simultaneous source of isotropicfission fragments and alpha particles. This measure-ment of the track widths resulted in σ r = 0 .
156 cm and σ z = 0 .
133 cm. Notice that the closer σ r is to σ z , thesmaller the correction in Equation 4. A completely sym-metric electron diffusion would have σ r = σ z , thus lead-ing to no correction. The magnitude and shape of thecorrection can be seen in Figure 6 where the two bandsresult from the light and heavy fragments.Polar angle distributions for the fission fragments andalpha particles from the Cf source after the electrondrift speed and electron diffusion corrections can be seen
FIG. 6. Values calculated by Eq. 4 showing the magnitudeof the electron diffusion correction for the
Cf source. Thetwo bands are from the light and heavy fragments which haveslightly different correction magnitudes due to their differentionization densities. in Figure 7. This plot demonstrates the fissionTPC’sability to reconstruct the polar angles of fission fragmentsover an angular range from about 0 . < cos θ < . θ is due to the fragments andalpha particles losing energy and ranging out in the tar-get material, and the bump at high cos θ is due to thesaturation of the readout electronics for pads that havea large number of electrons deposited on them in a shortamount of time. All the charge from a fission fragmentthat is emitted perpendicular to the anode will be col-lected on a few number of pads, causing saturation. Dueto the differentiation step in the processing from pad sig-nals to voxels of charge, no charge is assigned to thosevoxels after saturation occurs, effectively creating a holein the center of the charge cloud. Because the fittingof the charge clouds is weighted by the ADC value ineach voxel, a hole in the center of the charge cloud skewsthe angle in such a way that the saturation creates the“bump” seen at high cos θ in Figure 7 [23]. VI. LINEAR MOMENTUM TRANSFER
Before a measurement of the anisotropy can take place,a measurement of linear momentum transfer is needed toconvert from the lab frame to the center-of-mass frame.The amount of linear momentum that is transferred fromthe incident neutron to the target nucleus shows up in theopening angle of the fission fragments [18]. By placingthe actinide deposits on a thin carbon foil, both frag-ments can be detected in the fissionTPC, allowing fissionfragment opening angle measurements. Coincident fis-sion fragment pairs are selected and the angle betweenthe two fission fragments is calculated after the driftspeed and electron diffusion corrections are applied.Figure 8 shows the opening angle measurement be-tween fission fragments that were produced by incident
FIG. 7. Area normalized fission fragment and alpha particlepolar angle distributions from the
Cf source after electrondrift speed and electron diffusion corrections are applied. Thered lines are the fits demonstrating the reproduction of theisotropic emission of fragments and alphas.FIG. 8. Fission fragment opening angles for 10 to 12 MeVincident neutrons on a
U target. Mean opening angles aretaken from the solid line fit after the contribution from thedashed Gaussian that corrects for the wraparound neutronsis subtracted. neutrons with energy between 10 and 12 MeV, wherethe solid red line is a Gaussian fit to the data andthe dotted red line is the wraparound Gaussian that issubtracted from the distribution to account for eventsfrom wraparound neutrons. The wraparound Gaussiandistribution has an amplitude equal to the number ofwraparound events in each energy bin as determined inFigure 2 and is centered at 180 degrees. After perform-ing the wraparound subtraction, the mean opening anglefor each measured target and actinide can be plotted asa function of neutron energy, as shown in Figure 9.In order to extract the amount of linear momentumneeded to reproduce these opening angles, a Monte Carlo
FIG. 9. Measured fission fragment opening mean angles afterwraparound subtraction. No momentum transfer would resultin a mean opening angle of 180 degrees. simulation was used as the fissionTPC does not have thenecessary information or precision to extract the linearmomentum transfer on an event by event basis.A fission event is generated using the GEF code (Ver-sion 2017/1.1) [24] to get fission fragment masses andcenter of mass energies, and an initial downstream cos θ is selected from the measured downstream cos θ distribu-tion. Sampling from the measured angular distributionis necessary because the opening angle is dependent onboth the amount of linear momentum transferred and theemission angle of the fragments. An easy way to demon-strate this dependence is to consider fission fragmentsthat are emitted along the axis of the incident neutronbeam – no matter how much linear momentum is trans-ferred to these fragments, the opening angle will alwaysbe 180 degrees in the lab frame.Next, that initial downstream cos θ is converted fromthe lab angle to the center of mass angle viacos θ c.m.d,u = (cid:115) − E Ld,u E c.m.d,u (1 − cos θ Ld,u ) . (7)where the fragment energy in the lab frame can be cal-culated by [23] E Ld = E c.m.d + m d p n m CN (cid:18) cos θ Ld − (cid:19) + m n p n cos θ L m CN (cid:115) E c.m.d m CN m d + p n (cid:0) cos θ Ld − (cid:1) (8)for a given neutron momentum transfer p n , mass of thecompound nucleus m CN , and downstream center of massfragment energy E c.m.d and mass m d . E c.m.d is computedaccording to the total kinetic energy value and massessampled from the GEF output. m CN = A + 1 and theupstream mass is m u = m CN − m d . Treating fissionas a two-body decay, in order to conserve momentum, FIG. 10. Simulated average opening angle for 3.4 MeV inci-dent neutrons as a function of applied momentum transfer.See the text for more details. the upstream center-of-mass angle must be the same asthe downstream center of mass angle, i.e. cos θ c.m.d =cos θ c.m.u . Converting this upstream center-of-mass angleback to the lab frame is done by inverting Equations 7and 8 using the appropriate fragment masses and energies[23]. The final step is to then take the opening anglebetween these upstream and downstream fragments andadd a Gaussian smearing with a sigma of 3.8 degrees tomatch the angular resolution of the data.Repeating this process produces a set of opening anglesfor a particular incident neutron energy bin and neutronmomentum transfer p n . The amount of neutron momen-tum transfer can be extracted by plotting the mean open-ing angles as a function of neutron momentum transferand matching the measured opening angle to the sim-ulation. Figure 10 demonstrates this procedure for aparticular incident neutron energy bin and shows thatthe mean opening angle changes linearly as a functionof applied neutron momentum transfer. The horizontaldashed lines are the statistical uncertainty bounds fromthe measurement of the opening angle (from Figure 9),and the vertical dashed lines are where the opening anglemeasurement intersects with the linear fit in red. Com-plete linear momentum transfer for this particular neu-tron energy bin is denoted by the solid vertical red line.Thus, in using this Monte Carlo simulation, theamount of linear momentum transferred from the inci-dent neutron to the fissioning nucleus can be extracted;however, one additional normalization step is needed. Inorder to reproduce full momentum transfer at low inci-dent neutron energies, the electron drift speed differenceapplied between the upstream and downstream volumesis modified to create a less than 0.2 degree shift in themeasured opening angles such that the weighted averageis one in Figure 11 for all incident neutron energy binsbelow 2 MeV. This normalization procedure accounts forthe uncertainties in the electron drift speed and electrondiffusion corrections between the upstream and down- FIG. 11. Fraction of the total momentum transfer as mea-sured by the fissionTPC. A normalization procedure was ap-plied in order to achieve a weighted average of full momentumtransfer for all neutron energy bins below 2 MeV.FIG. 12. Average neutron linear momentum transfer as mea-sured by the fissionTPC along with published measurementsof linear momentum transfer for proton [25–28], deuteron [26],and alpha [25, 26] induced fission. stream volumes [23].Since
U has a fission threshold of about 1.2 MeV,the photofission peak from this actinide is not contam-inated by wraparound neutrons. After performing thecomplete normalization procedure, measuring the open-ing angle from these photon induced fission events gives179 . ± .
14 degrees, which is consistent with the negli-gible momentum transfer expected from photons.The final results of average linear momentum transferas a function of incident neutron energy after the nor-malization procedure are shown in Figure 12.
A. Uncertainty Analysis
The error bars shown in Figures 11 and 12 include bothstatistical and systematic uncertainties. An example un-certainty budget is shown in Figure 13 for the
U halfof the U/ U target measurement.Statistical uncertainties from the fit of the measuredopening angle are displayed in Figure 9. The magnitudeof these statistical uncertainties propagated through thesimulation can be seen directly in Figure 10 where therange of the opening angle measurement is equated to arange in the evaluated momentum transfer. Statisticaluncertainty is the dominant uncertainty, particularly atlow incident neutron energies where the opening anglemeasurement requires fractions of a degree resolution.Many systematic uncertainties were also consideredand a sensitivity study was performed for each of theseto estimate their potential magnitude.The contributions due to the neutron beamwraparound uncertainty is found by subtracting adifferent amplitude for the wraparound Gaussian shownin Figure 8 in accordance with the wraparound error andpropagating the modified result through the simulationresults. The uncertainty on the percentage of neutronbeam wraparound in each energy bin is calculated fromthe uncertainty on the fit that is integrated to getthe neutron beam wraparound percentage.
U hasno need for the wraparound correction because of itsroughly 1.2 MeV fission threshold. Thus, the agreementbetween
U and U/ Pu provides validation thatthe neutron beam wraparound is handled correctly.Opening angle measurements and propagation throughthe Monte Carlo simulation were redone using differentelectron drift speed and electron diffusion values. Elec-tron drift speeds were varied by ± .
03 cm/ μ s and theelectron diffusion correction was varied by ± FIG. 13. Uncertainty budget on the linear momentum trans-fer result for each systematic variation considered for the
Uhalf of the U/ U target. tribution from GEF would average out much more thantaking the mass exclusively from the upstream or down-stream fragment.For all of these considered systematic variations, anindependent linear momentum transfer result was com-puted. The uncertainty associated with each parame-ter variation was taken as the difference between the re-sult when varying that parameter and the primary mo-mentum transfer result. These uncertainties were thentreated independently and added in quadrature to get atotal uncertainty, which includes both the statistical andsystematic uncertainties. Some parameters not having alinear relationship to the momentum transfer or an un-even parameter range (taking 5 amu from the compoundnucleus for example), produces slightly asymmetric errorbars. The largest of the asymmetric uncertainty contri-butions for each incident neutron bin are shown in Figure13.
B. Discussion
A few other sources of uncertainty were considered andwarrant discussion but are not included in the error bars.Most notably, fission is assumed to be a two body decayin the Monte Carlo simulation, but this ignores ternaryfission. Any ternary particle will certainly have an effecton the opening angle for that particular fission event,but we have found no published evidence that ternaryparticles have anisotropic emission with respect to theincident neutron beam direction. In the context of thisanalysis, this means that there is no overall shift of thecenter of the opening angle distribution. Additionally,ternary fission consists of less than 1% of all fission events[6], so any potential effect from an angular anisotropywith respect to the neutron beam would be minimal.Prompt neutron emission from the fragments can pro-duce slight changes in the fragment angle. In the restframe of the fragment, the angular distribution of theemitted neutrons is measured to be primarily isotropic.A small anisotropic component dependent on the angularmomentum state of the fission fragment might exist, butis debated [29]; therefore, the uncertainty from promptneutron emission is treated as negligible.One difference between the detection of fission frag-ments in the different detector volumes is that one of thefragments must travel through the carbon backing. Inorder to ensure no angular bias is introduced in the frag-ment traveling through the backing, the two targets usedin this analysis were placed in different orientations. The U/ U target has the actinides in the downstreamvolume, but the U/ Pu target has the actinides inthe upstream volume. However, the Monte Carlo sim-ulation samples from the downstream cos θ distributionfor both targets. Since there is good agreement betweenthese two targets, no detectable bias is introduced due tothe fragments traveling through the carbon backing.To the best of our knowledge, this is the first mea-surement of neutron induced fission momentum transfer,so the comparison with other data shown in Figure 12is with respect to proton, deuteron, and alpha inducedfission. VII. FISSION FRAGMENT ANISOTROPY
Measurements of neutron-induced fission fragment an-gular anisotropy are also presented here for
U and
U. By applying the electron drift speed and elec-tron diffusion corrections, the isotropic distribution ofalpha particles and fission fragments were successfullyreproduced for a specific angular range, demonstratedin Figure 7. No efficiency correction is therefore neededin the angular measurements of
U and
U angularanisotropy.The first step in the anisotropy measurement consistsof separating fission fragments from recoil ions. This isdone by introducing a cut on the Bragg peak value, whichprovides more separation between fission fragments andargon recoils compared to a selection on total energy.Track length versus Bragg peak is shown in Figure 14as well as the location of the cut for this data from the U/ U aluminum backed target.After selecting the fission fragments, they are sepa-rated into incident neutron energy bins and the electrondrift speed and electron diffusion corrections are applied.Their angles are then converted from the lab frame tothe center of mass frame using the average momentumtransfer as measured in Figure 12. Even order Legendrepolynomials up to fourth order are then used to fit theangular distributions. An example upstream and down-stream angular distribution is shown in Figure 15 fromthe
U side of the thick U/ Pu target that wasrotated with respect to the neutron beam.Extracting the measured anisotropy parameter from
FIG. 14. Track length versus Bragg peak showing separationof fission fragments from neutron recoils on detector materialsand gas particles. The vertical dashed line shows the locationof the fragment selection cut.FIG. 15. Example
U angular distributions for 6 to 7 MeVneutrons from upstream and downstream measurements ofthe thick aluminum backed
Pu/
U target. The angulardistributions are normalized such that the fit equals one ifextended to cos θ = 0. the Legendre polynomials is done via A meas = W (cos θ c.m. = 1) W (cos θ c.m. = 0) = a + a + a a − a / a / a n corresponds to the coefficient of the n-th Leg-endre polynomial. However, this measurement includesfission events from wraparound neutrons that do not be-long in this incident neutron energy bin. The measuredanisotropy is a combination of the real anisotropy and theanisotropy of the wraparound neutron events, or moreexplicitly, A meas = (1 − p wrap ) A real + p wrap A wrap (10)where p wrap is the percentage of wraparound neutronsin that incident neutron energy bin, as plotted in Figure0 FIG. 16. Anisotropy parameter, as defined by Eqn. 1, fromeach target and orientation of
U.FIG. 17. Anisotropy parameter, as defined by Eqn. 1, fromeach target and orientation of U.
2. With the assumption that the low energy wraparoundneutrons produce an isotropic distribution of fission frag-ments, A wrap = 1 and the real value of the anisotropy is A real = A meas − p wrap − p wrap . (11)Each of the different actinide targets depicted inFigure 3 were placed in the fissionTPC to measurethe anisotropy (with the exception of the thin-backed U/ Pu target). Each measurement had slightly dif-ferent operating parameters resulting in slightly differentcorrections for electron drift speed and electron diffusion.Measuring the anisotropy with many different targetsdemonstrates the reproducibility of the fissionTPC overthe course of the experiments.
U and
U anisotropyresults ( A real ) can be seen in Figures 16 and 17 for eachof the targets. FIG. 18. Uncertainty budget for
U anisotropy from thethick backed U/ Pu target.
A. Uncertainty Analysis
The uncertainty analysis procedure for the anisotropyresults is very similar to the procedure followed for thelinear momentum transfer results – parameters are variedand the difference between the primary anisotropy resultand that variation is taken as the uncertainty associatedwith that parameter.Statistical uncertainties on the anisotropy analysis arepropagated from Equation 9 where the uncertainties on a n are taken directly from the fit. Similarly, uncertaintyfrom neutron beam wraparound is propagated directlyfrom Equation 11 using the uncertainty on the percentof the wraparound counts in each incident neutron energybin.Electron drift speed values are varied by ± .
01 cm/ μ sand the electron diffusion correction is varied by ± ± .
03 cos θ , but when varying the fit upperbound by that same amount, large differences of up to4% arise. When changing the upper bound of the fit,the fit is affected by the bump at large cos θ from thedetector saturation effect discussed in Section V C. Thisis compounded by the fourth order Legendre componentalso having the most influence at larger cos θ . Due tothese compounding factors, the fit upper bound is actu-ally the largest uncertainty contribution for the majorityof incident neutron energy bins.1The location of the Bragg peak cut used to selectthe fission fragments shown in Figure 14 is varied by ±
50 ADC/mm. At very high incident neutron energies,this cut starts to dip down into the high energy recoilions which show up at large cos θ . These high energy re-coils lead to an increased uncertainty associated with thefission fragment selection, which can be seen in Figure13.The kinematic correction to convert from lab to cen-ter of mass angles is varied in accordance with the un-certainty from the linear momentum transfer result inFigure 12. B. Anisotropy Results and Discussion
In order to report a single anisotropy result from themany fissionTPC data sets seen in Figures 16 and 17,each measurement was combined with a weighted average¯ A = (cid:80) w i A i (cid:80) w i (12)where the squared weights are given by the inverse av-erage of the slightly asymmetric error bars for each datapoint w i = (cid:18) σ + i + σ − i (cid:19) . (13)The uncertainty reported on this weighted average is thegreater of the standard uncertainty expression for theweighted average σ ¯ A = 1 (cid:112)(cid:80) w i (14)or the weighted standard deviation σ ¯ A = (cid:115) (cid:80) w i ( A i − ¯ A ) N − ( N − (cid:80) w i (15)where N is the number of data points with non-zeroweight. The need to compare two different uncertaintiesarises from the limitations of each method. The typicalweighted average uncertainty (Eq. 14) does not includethe spread of the data points and the weighted standarddeviation (Eq. 15) produces an uncertainty of zero if allpoints lie on top of each other, regardless of the size ofthe error bars. Taking the largest uncertainty betweenthese two methods ensures that both the spread of thedata and size of the error bars are taken into account.Comparison of the anisotropy results to the other pub-lished data from EXFOR [30] shows generally good agree-ment for U, but not
U. All of the previously pub-lished
U data shown here use a normalization at lowincident neutron energies in order to determine their de-tection efficiency. This process was also used in a pre-vious measurement of the
U anisotropy by the fis-sionTPC, which shows good agreement with the pub-lished data [14]. However, with the additional electron
FIG. 19. Anisotropy results combining the
U data setscompared to available data in EXFOR [30].FIG. 20. Anisotropy results combining the
U data setscompared to available data in EXFOR [30]. drift speed and diffusion corrections applied, no normal-ization is needed for this work.Better agreement with the
U data can be explainedby the lack of low incident neutron energies being usedfor detector response calibration and efficiency. In partic-ular, the EXFOR entry for the
U Vorobyev data refer-ences a publication that assumes full detection efficiencyfor 0 . < cos θ < . U VorobyevEXFOR entry points to a reference which shows subse-quent calibration work with a
Cf source [13] demon-strating incomplete efficiency for 0 . < cos θ < .
0, thuspossibly explaining why the
U results show betteragreement than U. VIII. SUMMARY
The fissionTPC is studying fission in a novel way withthe use of its full three-dimensional tracking ability. This2ability requires an extensive reconstruction process totransform raw signals into individual track parameters,including finding the electron drift speed by flatteningthe spontaneous alpha polar angle distribution as well asapplying a correction to the fission fragment angles dueto the electron diffusion coefficients not being equal in thedrift and radial directions of the fissionTPC. By applyingthis reconstruction process, the polar angle distributionof spontaneous fission and alpha emissions from a
Cfsource was successfully shown to be isotropic.Placing actinide deposits on a thin-carbon backing al-lows for the detection of both the upstream and down-stream fission fragments in the fissionTPC. By measuringthe opening angle between the upstream and downstreamfission fragments and using a Monte Carlo simulation, thefirst measurement of linear momentum transfer from in-cident neutrons to the fissioning nucleus was performed.This linear momentum transfer measurement was thenapplied in the conversion of fission fragment angles fromthe lab frame to the center of mass frame to determinethe angular anisotropy of the fission fragments as a func-tion of incident neutron energies. Both the linear mo-mentum transfer and anisotropy measurements includedcareful attention to systematics whose exploration wasmade possible by the wealth of data for every fission eventdetected in the fissionTPC. Measurements of fission fragment angular anisotropyshow significant disagreement from published
U data.This might be explained via the detection efficiency pro-cedures used in previous analyses which assumed isotropyat low incident neutron energies. The
U angularanisotropy presented here agrees better with previouspublications where those detection efficiency procedurescannot be performed due to the fission threshold atroughly 1.2 MeV.
ACKNOWLEDGMENTS
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