1H(n,el) as a Cross Section Reference in a White Source Neutron Beam With the fissionTPC
N. I. Walsh, J. T. Barker, N. S. Bowden, K. J. Brewster, R. J. Casperson, T. Classen, N. Fotiadis, U. Greife, E. Guardincerri, C. Hagmann, M. Heffner, D. Hensle, C. R. Hicks, D. Higgins, L. D. Isenhower, A. Kemnitz, K. J. Kiesling, J. King, J. L. Klay, J. Latta, W. Loveland, J. A. Magee, M. P. Mendenhall, M. Monterial, S. Mosby, G. Oman, S. Sangiorgio, B. Seilhan, L. Snyder, C. L. Towell, R. S. Towell, T. R. Towell, K. T. Schmitt, S. Watson, L. Yao, W. Younes
aa r X i v : . [ nu c l - e x ] A p r H(n,el) as a Cross Section Reference in a White Source Neutron Beam With thefissionTPC
N. I. Walsh a, ∗ , Barker, J. T. d , Bowden, N. S. a , Brewster, K. J. d , Casperson, R. J. a , Classen, T. a , Fotiadis, N. b , Greife,U. c , Guardincerri, E. b , Hagmann, C. a , He ff ner, M. a , Hensle, D. c , Hicks, C. R. d , Higgins, D. b , Isenhower, L. D. d ,Kemnitz, A. e , Kiesling, K. J. d , King, J. f , Klay, J. L. e , Latta, J. c , Loveland, W. f , Magee, J. A. a , Mendenhall, M. P. a ,Monterial, M. a , Mosby, S. b , Oman, G. e , Sangiorgio, S. a , Seilhan, B. a , Snyder, L. a , Towell, C. L. d , Towell, R. S. d ,Towell, T. R. d , Schmitt, K. T. b , Watson, S. d , Yao, L. f , Younes, W. a ,(The NIFFTE Collaboration) a Lawrence Livermore National Laboratory, Livermore, CA 94550, United States b Los Alamos National Laboratory, Los Alamos, NM 87545, United States c Colorado School of Mines, Golden, CO 80401, United States d Abilene Christian University, Abilene, TX 79699, United States e California Polytechnic State University, San Luis Obispo, CA 93407, United States f Oregon State University, Corvallis, OR 97331, United States
Abstract
We provide a quantitative description of a method to measure neutron-induced fission cross sections in ratio to elastichydrogen scattering in a white-source neutron beam with the fission Time Projection Chamber. This detector hasmeasured precision fission cross section ratios using actinide references such as
U(n,f) and
U(n,f). However, byemploying a more precise reference such as the H(n,el) cross section there is the potential to further reduce the eval-uation uncertainties of the measured cross sections. In principle the fissionTPC could provide a unique measurementby simultaneously measuring both fission fragments and proton recoils over a large solid angle. We investigate onemethod with a hydrogenous gas target and with the neutron energy determined by the proton recoil kinematics. Thismethod enables the measurement to be performed in a white-source neutron beam and with the current configurationof the fissionTPC. We show that while such a measurement is feasible in the energy range of 0 . ∼
10 MeV,uncertainties on the proton detection e ffi ciency and the neutron energy resolution do not allow us to preform a fissionratio measurement to the desired precision. Utilizing either a direct measurement of the neutron time-of-flight for therecoil proton or a mono-energetic neutron source or some combination of both would provide a path to a sub-percentprecision measurement.
1. Introduction
The Neutron Induced Fission Fragment Tracking Ex-periment (NIFFTE) collaboration constructed the fis-sion Time Projection Chamber (fissionTPC) to measurefission cross section ratios of the major actinides ( U, U, Pu). The aim of the experiment is to provideratio measurements with sub-percent uncertainties. Inthe original design both actinide (n,f) and H(n,el) crosssection references were considered [1]. To accommo-date either option the detector is capable of detectingboth fission fragments and proton recoils. A description ∗ Corresponding author
Email address: [email protected] (N. I. Walsh) of a cross section measurement in ratio to an actinidereference can be found in Ref. [2].As the precision of ratio measurements are improved,the uncertainty on the cross section reference becomesan important factor. The recent ENDF-B / VIII-0 eval-uation lists nine neutron cross section standards [3],with H(n,el) having the smallest uncertainty above1 MeV. For example at 2 MeV the evaluated H(n,el)cross section uncertainty is 0 .
36% compared to 1 . U(n,f) and
U(n,f) [4].While other experiments have measured a fissioncross section relative to hydrogen elastic scattering,most relied on separate systems to detect fission frag-ments and protons (e.g. Ref. [5]). This potentially intro-duces a systematic uncertainty from uncontrolled di ff er- Preprint submitted to Elsevier April 25, 2019 nces in beam scattering between the two targets. Oneexperiment that made such a measurement in the sameapparatus was performed in a mono-energetic beam [6].A back-to-back target design was used which signif-icantly reduces beam scatter between the two targets.However, the proton measurement was limited in solidangle and separate detectors were used for fragmentsand protons.A ratio measurement with the fissionTPC is uniqueas it can simultaneously detect both fission fragmentsand protons over a large solid angle with the same de-tector. In this work we examine one possible implemen-tation of this measurement using a hydrogenous gas tar-get and a determination of the neutron energy based onthe proton recoil kinematics. To perform this measure-ment over a broad neutron energy spectrum we exam-ine the outcome using a beam source such as the 90Llocation at Los Alamos Neutron Science Center (LAN-SCE) Weapons Neutron Research (WNR) facility [7].We have made this choice of energy reconstruction andbeam source as they do not require significant modifica-tion to the detector or signal processing compared to anactinide-to-actinide ratio measurement [2].While this work is motivated in the context of a pre-cise fission measurement, the method presented is appli-cable to neutron flux and spectrum measurements per-formed with a TPC. Specifically we describe in detail acharged-particle detection e ffi ciency and neutron energyresolution which are relevant to, for example, measure-ments of a neutron beam flux [8], directional neutronimaging [9, 10], and cosmogenic neutron flux measure-ments [11].
2. The fissionTPC
The fissionTPC is a two-volume ionization cham-ber with a common cathode and two highly-segmentedanode planes. A negative bias is applied to the cen-tral cathode causing ionization electrons to drift to-wards the anode. The charge is amplified with a MI-CROMEGAS [12] and read out from approximately3000 conductive pads on each anode plane. The tar-get, typically an actinide deposited on aluminum or athin carbon foil, is placed in the center of the cathode.Depending on the backing thickness, one or both fissionfragments induce a current on the cathode which is ca-pacitively coupled to a current amplifier. This providesthe signal used to measure the incident neutron time-of-flight (ToF) in fission measurements. A schematic of thedetector with the relevant structures labeled is providedin Fig. 1. A more detailed description of the design isfound in Ref. [1].
Figure 1: A simplified schematic of the fissionTPC detector. The neu-tron beam impinges from the left passing through the upstream vol-ume, the actinide target, and the downstream volume. Both upstreamand downstream volumes are 5.4 cm in length and each instrumentedwith approximately 3000 conductive pads at the anode plane for read-out. A charged particle track (represented by the red arrow) ionizesthe gas and the charge is drifted towards the segmented anode. Thetrack is reconstructed using the pad’s location and the relative time ofarrival of the charge.
The fissionTPC captures the following informationon charged particle tracks: the vertex, direction, length,total charge, and ionization profile. Two of the track’sspatial dimensions ( x , y ) are reconstructed from the lo-cation of the anode pad. The relative length along thedrift axis ( z ) is determined for all tracks by the time dif-ference between the start and end of a track as measuredon the anode. The absolute position along the drift axisrequires using the drift speed and the time di ff erencebetween the cathode signal and anode signal. In prac-tice however, all fission fragments are assumed to haveoriginated from the center cathode plane. Most protonrecoils, especially those further from the cathode, donot deposit enough energy to be detected on the cath-ode. Therefore, this work assumes only the z -length ofa proton track is known. Track energy and ionizationprofile are determined from the charge collected in thepads. For this analysis, we reduce 2-dimensional ion-ization profile information to a maximum dE / dx value(Bragg peak). These track parameters (energy, length,and Bragg peak) are used to distinguish between typesof particles. An example of the distribution of lengthvs. energy for the di ff erent particle species in the fis-sionTPC is shown in Fig. 2.
3. Measurement Method
A cross section of reaction x measured in ratio to ref-erence r is given by σ x σ r = C x − B x C r − B r · N r N x · Φ r Φ x · ǫ r ǫ x (1)2 Uncalibrated Energy [arb. units]
Leng t h [ c m ] p* p α FF Figure 2: Data from the fissionTPC taken at the LANSCE-WNRneutron beam. From left to right the labeled features are protons thatdo not stop in the detector (p*), contained protons (p), alphas ( α ), andfission fragments (FF). Particles traversing the entire drift volume areat least 5.4 cm in length and produce a visible feature in the plot atthat length. where C represents the number of measured reactionproducts, B the number of background counts in thatsignal, N the number of target atoms, Φ the beam flu-ence, and ǫ the detection e ffi ciency. With the exceptionof the target atom number, each term is a function ofneutron energy. The fluence ratio in the fissionTPC isvery close to one, with the sub-percent correction com-puted via simulation. The number of actinide targetatoms is determined from a measurement of the alphaactivity and scaled by half life data. The remainingterms, including the number of hydrogen targets, e ffi -ciency, background, and neutron energy, depend on thespecific experimental conditions.Both a hydrogenous gas target and a solid target arecandidates for a measurement with the H(n,el) refer-ence. While the quantitative result for the e ffi ciency andbackground depends on the precise choice of the solidor gaseous target, the evaluation method itself is simi-lar. In a precision measurement with the fissionTPC, theuniformity of the target is necessary to avoid systematice ff ects arising from beam non-uniformities. A solid tar-get like polystyrene can be spin coated to high unifor-mity on smooth silicon wafers. The thickness, density,and uniformity can be measured with the required ac-curacy with a combination of atomic force microscopy,ellipsometry, and X-ray reflectometry. However, com-plications of depositing an actinide an the same backingor having to remove the polystyrene from the backing(to avoid the large Si(n,p) background) without chang-ing the uniformity are left to further studies. On theother hand, hydrogenous gases like isobutane are usedregularly in the detector and are intrinsically uniform.The detector volume and gas properties such as pres- sure, temperature, and composition can be characterizedto the required accuracy with commercially availableequipment.In the fissionTPC the cathode signal provides neutronToF used for fission reactions. A full width at half max-imum (FWHM) timing resolution of 2 ns or better pro-vides su ffi cient resolution for precise fission cross sec-tion ratio measurements [2, 13]. Extracting an accuratetiming signal from protons is significantly more compli-cated and is not possible in the current fissionTPC setup.One of the complicating factors is the pile-up from mul-tiple proton tracks, which is further compounded by thehigh rate of alpha tracks when measuring against a Putarget. In addition, the cathode detection e ffi ciency de-creases rapidly for proton tracks generated farther awayfrom the cathode. Therefore, we have chosen to inves-tigate a kinematic method of reconstructing neutron en-ergy using a gas target in the fissionTPC. In the kine-matic reconstruction, the incident neutron energy ( E n )is related to the scattered proton energy ( E p ) and polarangle with respect to the beam axis ( θ p ), and is given by E n = E p / cos θ p (2)In the neutron energy range of interest ( <
10 MeV)the anisotropy is small so we assume the reaction isisotropic in the center-of-mass frame.To investigate the feasibility of using a gas targetand kinematic energy reconstruction, we have quanti-tatively evaluated the e ffi ciency, backgrounds, and en-ergy resolution. These results are based on MCNP [14],Geant4 [15, 16], and the current NIFFTE analysisframework [17]. The MCNP simulation uses the neu-tron fluence based on the 90L station at LANSCE-WNRto generate the neutron-induced charged particles thatenter the fissionTPC detector volume. These chargedparticles are recorded and the vertices are used as the in-put to a Geant4 detector simulation. The Geant4 simula-tion is interfaced with the NIFFTE analysis frameworkand together they account for the detector response,electronic read-out, and track reconstruction. Inputs tothe simulations have been chosen to closely approxi-mate realistic detector conditions. The charge amplifi-cation gain and gas properties were chosen to enable sta-ble operation of the fissionTPC when operated in high-energy neutron environment [18]. The simulations areperformed using a gas mixture of neon and 5% isobu-tane and total pressures in the range of 550 to 1500 Torr.For each simulated pressure the electron di ff usion anddrift speed are estimated from MAGBOLTZ [19]. Thesimulated gains and thresholds are chosen to match theobserved length and energy distributions of data col-lected at 550 and 1000 Torr.3 . E ffi ciency The kinematic reconstruction of neutron energy re-quires the proton energy is fully deposited in the detec-tor volume. In a hydrogenous gas target, protons recoilsare generated throughout the volume and with a rangeof energies and angles. The likelihood of containmentcan be calculated because the direction and energy ofa proton recoil is described exactly by two-body kine-matics. We describe two e ffi ciencies, one based on thetruth-level information of whether or not a track is con-tained and the second on a selection criteria based onthe track-level information.The probability a proton recoil is fully contained inthe detector volume, the containment e ffi ciency , is afunction of neutron energy, proton kinematics, and startposition. Summing over all possible proton kinemat-ics and start positions, the e ffi ciency is simplified to afunction of only neutron energy. The containment e ffi -ciency can be computed numerically or by Monte Carloand is determined by the reaction kinematics, detectorgeometry, and stopping power. However in practice ananalysis of data requires a selection gate on some trackparameters to identify contained protons. This selectione ffi ciency depends on not just the stopping power butalso the detector performance, the tracking algorithms,and the selection criteria. ffi ciency The containment e ffi ciency is determined from thenumber of protons that stop in the detector relative tothe total number of H(n,el) interactions in the volume.At each neutron energy, the probability a proton is con-tained is calculated summing over all interaction ver-tices and scattering energies (therefore all angles). Inthe limit of low incident neutron energy, proton tracksare very short and almost always contained. In the otherlimit, when the proton length in the z -direction exceedsthe length of the detector, no vertex produces a con-tained proton. E ff ectively the number of target atomsavailable to produce a contained proton scales accord-ing to the recoil kinematics as ( Z tpc − L p cos θ p ), where Z tpc is the 5.4 cm-length of the drift volume. Assuminga beam radius ( r beam ) and a start vertex selection ( r start )not larger than the beam radius, the containment e ffi -ciency ( ǫ ) is given by, ǫ ( E n ) = (cid:16) π r start (cid:17) · R (cid:16) Z tpc − L p · cos θ p (cid:17) · d E p (cid:16) π r beam (cid:17) · Z tpc (3)A stopping power model is used to relate the protontrack length ( L p ) and energy ( E p ). Additionally, cos θ p C on t a i n m en t E ff i c i en cy Toy model/SRIM stopping powerGeant4 stopping power
Toy model calculationGeant4 Truth-level calculation
Figure 3: A toy Monte Carlo calculation of the containment e ffi ciencyfor H(n,el) recoil protons to be fully contained in a detector with ageometry like the fissionTPC. An e ffi ciency calculated with a SRIM-based stopping power model (red) is compared to the Geant4 stoppingpower (blue). The e ffi ciency is largest at lowest neutron energies asonly protons generated closest to the anode plane are long enough tonot be contained. At the higher neutron energies, only protons frommore glancing collision are contained. is a function of E p as given in Eq. 2. While this analyticform does not account for radial constraints of the detec-tor or other more complicated geometries, these e ff ectscan be calculated with a toy model Monte Carlo.We have validated the numeric calculation of contain-ment e ffi ciency with a toy Monte Carlo. In Fig. 3 weshow a comparison between a simple toy Monte Carlobased on the SRIM stopping power model [20] and aGeant4 simulation. Although the Geant4 result also in-cludes scattering in the gas and a more realistic beamprofile, the largest di ff erence between these e ffi cienciesis from the stopping power. The di ff erence in e ffi cien-cies shows that before a precision measurement can beperformed, an accurate stopping power model should beidentified and the uncertainties evaluated. ffi ciency The selection e ffi ciency is determined by the track-level identification of contained protons. It is sensitiveto detector e ff ects, the choice of tracking algorithms,and particle selections. In this analysis we consider onerealization of these tracking and selection choices.The 3-dimensional tracking and ionization profile in-formation enables the separation of protons from otherparticles and the separation of contained protons fromthose not contained. A distribution of length vs. energyin Fig. 4 shows the neutron-induced protons, alphas,and ion recoils as simulated and reconstructed. Con-tained protons are selected using a range of the max-imum dE / dx consistent with the proton Bragg peak.4 Uncalibrated Energy [arb. units]
Leng t h [ c m ] p* p α r Figure 4: Simulated neutron-induced charged particles in the down-stream volume of the fissionTPC for the LANSCE-WNR neutronbeam. The track length is plotted as a function of detected charge.The main features of the plot from left to right are uncontained protons(p ⋆ ), contained protons (p), alphas ( α ), and ion recoils (r) dominatedby carbon and neon. The 5.4 cm length of the drift volume accountsfor the horizontal feature at that length. This Bragg peak distribution and the resulting length vs.energy distribution after such a Bragg peak selection areshown in Fig. 5. Additional selections on length, polarangle, vertex, and energy further improve the identifica-tion of neutron-induced contained protons.Based on the proton selection criteria applied to thesimulation, we have computed the selection e ffi ciencyas a function of neutron energy. As shown in Fig. 6, abroader range of neutron energies is accessible by oper-ating the fissionTPC at multiple pressures. At the lowerneutron energies the selection e ffi ciency does not followthe containment e ffi ciency because a minimum lengthcut eliminates recoils from low energy neutrons. Weapply a polar angle selection of θ < ◦ which limits themaximum neutron energy that can generate a containedproton. The selection e ffi ciency is subject to several sourcesof uncertainty related to the physics of stopping pow-ers and electrons drifting in the gas. Specifically it de-pends on the gas mixture, gas pressure, electron dif-fusion, drift speed, charge multiplication, and triggerthreshold. These are all included in the Geant4 model-ing of the detector, but each would need to be calibratedfor a precision measurement.The models for electron di ff usion, drift and stoppingpower can be calibrated to mono-energetic alpha decaysof an actinide target. A calibration to protons directlycould be achieved in two ways. The first is to use asource of mono-energetic neutrons such as from a DDgenerator. A second option is to use a neutron filter such Bragg Peak [arb. units]
Leng t h [ c m ] (a) p* p α Uncalibrated Energy [arb. units]
Leng t h [ c m ] (b) p d α Figure 5: Distributions of light charged particles as simulated in thefissionTPC showing (a) the Bragg peak (maximum dE / dx ) and (b) theenergy distribution after a selection on the Bragg peak for protons. Aselection of the proton Bragg peak between the dashed lines in (a) isused to generate the length-energy distribution in (b). Additional cutslike a minimum length and a 2-dimensional cut on the proton length-energy band are used to improve the selection of contained protons.The labels indicate features due to uncontained protons (p ⋆ ), protons(p), deuterons (d), and alphas ( α ). Neutron Energy [MeV] S e l e c t i on E ff i c i en cy
550 Torr1500 Torr
Figure 6: The selection e ffi ciency computed from a simulation of thefissionTPC with a neon-isobutane gas mixture at 550 and 1500 Torr.This e ffi ciency is based on a selection applied to the proton Braggpeak dE / dx value to identify fully-contained protons from the H(n,el)reaction. This selection includes a minimum track length of 1 cm anda minimum polar angle of θ< ◦ . Error bars are statistical only.
5s boron or carbon to e ff ect a known distortion in theneutron spectrum (and therefore the proton spectrum).This second method provides the ability to directly cal-ibrate in a white source of neutrons.The predicted selection e ffi ciency may be validatedwith ratio measurements performed at multiple gaspressures and mixtures. Each gas configuration has adi ff erent stopping power and therefore a di ff erent selec-tion e ffi ciency. Each measurement is corrected for thee ffi ciency and the di ff erent number of target atoms, withthe flux normalization being obtained from an actinide(n,f) reaction and its cross section.This validation relies on the assumption that the e ffi -ciency for detecting fission fragments does not changeas a function of pressure. This is justified because thefission fragment source is localized along the z-axis andthe primary driver for fission fragment e ffi ciency is tar-get thickness and neutron kinematics [2].
5. Backgrounds
In this analysis tracks that pass the selection criteriathat are not protons from H(n,el) reactions in the gas,including particles mis-identified as protons, are con-sidered to be backgrounds. The dominant backgroundsarise from other neutron induced reactions with a protonin the final state. Most such backgrounds are thresholdreactions like (n,p) which have neutron energy thresh-olds of around 5 to 10 MeV. These reactions producetrack angles and energies that do not preserve the in-cident neutron energy information. Without a time-of-flight to verify the kinematic reconstruction, these in-elastic reactions are indistinguishable from elastic pro-ton recoils.Beam-induced background protons originate fromthe detector vessel, target backing, anode planes, andthe non-hydrogenous gas components. The upstreamside of the fissionTPC is useful as a veto of tracks thatpass through part of the upstream volume, through thecathode, and stop in the downstream volume. Thesetracks are identified and removed if they are coincidentand co-linear. Another potential background sourceis back-scattered protons from the downstream anodeplane. These are rejected based on their direction.The remaining background sources are protons createdin the central portion of the cathode (the target back-ing) and the downstream gas components. Reducingthe target-backing mass greatly impacts the backgroundrate. In this work a thin 100 µ g / cm carbon foil was cho-sen. After applying these selections, the resulting back-ground rates (Fig. 7) relative to H(n,el) are expected tobe less than 1% below reconstructed neutron energies of 3 MeV. Corrections approaching 10% are required up to8 MeV. The dominant background is the Ne(n,p) reac-tion. − − − −
10 1 B a ck g r ound / S i gna l
550 Torr1000 Torr 1500 Torr 550 Torr1000 Torr 1500 Torr
Figure 7: Simulated background rates relative to the H(n,el) reac-tion assuming a kinematic neutron energy reconstruction. These re-sults are based on the fissionTPC with a neon-isobutane mixture op-erated in the LANSCE-WNR neutron beam. Error bars are statisticalonly. The main backgrounds are (n,p) reactions caused by neutronsof higher energies than as reconstructed assuming an elastic collision.Below 3 MeV the background is less than 1% of the signal. At higherenergies, corrections of up to 10% are required.
6. Neutron Energy Resolution
In the kinematic reconstruction of the incident neu-tron energy, the energy resolution is determined by thecombined proton energy and angular resolutions. Theseresolutions ultimately depend on the specific experi-mental parameters such as electron drift speed, electrondi ff usion, gain, and thresholds. We evaluate these res-olutions with the Geant4 simulation using a combina-tion of estimated and measured parameters for the fis-sionTPC.While the simulation provides information about thedetector e ff ects, we have not explicitly evaluated the ef-fects of calibration uncertainties on the proton energyand angle. In the simulation the proton energy is de-termined with a linear scaling of the collected charge.In data this relation is determined using mono-energeticalphas of known energies such as those emitted from anactinide target. The polar angle calibration is directly re-lated to that of the drift velocity. The drift velocity is setto a value that reconstructs the polar angle distributionof spontaneous alpha decay as an isotropic distribution.The uncertainty is determined from a combination ofstatistics and variations from the fit range used to evalu-ate the polar angle isotropy. In a previous measurementwith a U alpha source, the drift velocity was deter-mined with an uncertainty of 0.3%.6 .1. Proton Energy Resolution
In the fissionTPC the charged particle energy resolu-tion is impacted by variations in the charge-to-energygain in each anode pad due to variations in the pream-plifiers and the MICROMEGAS structure. Some of thisvariation is reduced by calibrating the pad gains for eachrun. Using data from mono-energetic alphas, the chargevoxel from each pad is first re-binned relative to the al-pha track charge cloud axis. Each pad is then comparedto the volume-averaged distribution of each bin to pro-vide an estimate of the gain correction. Pad gain vari-ations of 5% to 10% are typical in the data while thevariations were found to be stable to less than 1%. Thestability allows for a reliable correction to be applied.For reference, at a pressure of 550 Torr the energy reso-lution of 4 . . ff ects areincluded and provide a reasonable estimate of the res-olution. The same selection of contained protons as inthe previous sections is used to determine the proton en-ergy resolution (Fig. 8(a)). The FWHM of the distribu-tion ranges from ∼
8% at a gas pressure of 550 Torr to ∼
4% at 1500 Torr.The distribution is nearly symmetric except for asmall tail where the reconstructed energy is less thanexpected. We find these tail events are due primarily toat least one of three possible reasons. One reason is theproton is nearly contained but after depositing energycorresponding to its Bragg peak, the remaining energyis not deposited in the gas volume. A second reason ischarge is lost because of di ff usion. While the chargecloud drifts towards the anode, it spreads out and atthe edges the charge falls below the trigger threshold ofthe pad. The amount of energy lost increases with theamount of di ff usion and therefore also with drift dis-tance. A third scenario which a ff ects both the lengthand energy of the track, occurs at the beginning of thetrack where the stopping power is lowest and the chargedeposited falls below the pad threshold. Some of thesee ff ects can be minimized by operating at pressures anddrift fields that reduce the di ff usion or by increasing thegain of the MICROMEGAS. The angular resolution is computed by comparing thepolar angle from the reconstructed track to the initial di-rection as determined from the H(n,el) kinematics. Thisresolution is given in term of cos θ p as this scales withthe neutron energy. Unlike proton energy resolution,the angular resolution does not depend strongly on gas pressure. For example, at 1000 Torr and with a θ < ◦ selection, the angular resolution, shown in Fig. 8(b), hasa FWHM of 8%.The intrinsic few-degree scattering of protons stop-ping in a gas is the dominant contributor to this resolu-tion. The impact of this is more significant at larger θ due to the cosine function. The angular resolution im-proves to 5% FWHM with a selection criteria of θ < ◦ and to 3.5% FWHM with θ < ◦ . This cut improves theangular resolution but at the expense of a reduced se-lection e ffi ciency and narrower accessible range of neu-tron energies. Additionally, we identify tracking biasesthat arise due to the asymmetric value of electron dif-fusion parallel and perpendicular to the drift field. Thise ff ect can be measured and corrected for in the track-ing algorithm. Using an ad hoc correction to adjustthe cos θ bias removes the skew in the resolution dis-tribution, however this correction does not change theFWHM of the distribution. We compute the reconstructed neutron energy reso-lution with respect to the truth incident neutron energy.The resolution for the fissionTPC detector is shown inFig. 8(c). The FWHM of the neutron energy resolutionvaries from 12% at 1500 Torr to 16% at 550 Torr. Aselection of forward polar angles ( θ < ◦ ) improves theresolution to 7%. A distribution of the truth neutron en-ergy versus the reconstructed energy in Fig. 9 displaysthe impact this resolution has on reconstructing the cor-rect energy. Similarly Fig. 10 shows the energy reso-lution after applying a forward angle selection cut of θ < ◦ . Even with the coarse binning shown in the fig-ures and a forward angle selection the e ff ect of the res-olution is substantial. Events not along the diagonal ofthese plots would be events placed in the wrong energybin.Compared to the ToF method in the fissionTPC with a2 ns FWHM timing resolution, the ∼
10% energy resolu-tion from this method is, for example at 2 MeV, 10 timesworse. Ultimately the impact from the energy resolutionon a cross section ratio depends on the bin width and theslope and structure of the cross section ratio. A mea-surement with only the kinematic method of energy re-construction precludes using the H(n,el) cross section asa reference in a precision (n,f) measurement. However,in other cross section measurements or neutron imagingexperiments this resolution may be su ffi cient.7 .4 − − p / E p E δ (a) − − θ / cos θ cos δ (b) − − n / E n E δ (c) Figure 8: Resolution on the reconstruction of (a) proton energy, (b) cosine of the polar angle squared, and (c) neutron energy generated froma simulation of neon-isobutane gas at 1000 Torr in the fissionTPC. Contained protons are identified by selections that include a minimum length( > θ< ◦ ), and a Bragg peak selection. The FWHM of the E p resolution is 5%, the cos θ FWHM is 8%, and the E n FWHM is12%. A polar angle selection of θ< ◦ improves the angular and neutron energy resolution by nearly a factor of two. [MeV] n Reconstructed E [ M e V ] n T r u t h E Figure 9: Distribution showing the spread of the truth neutron energyvs. the reconstructed neutron energy using the kinematic method in asimulation of the fissionTPC. [MeV] n Reconstructed E [ M e V ] n T r u t h E Figure 10: Distribution of truth and reconstructed neutron energysimilar to Fig. 9 but with a narrower selection of polar angles ( θ< ◦ ).The few events in the tail of the distribution (truth energy greater thanreconstructed energy) are from background (n,p) reactions. . Discussion and Conclusion This work provides a quantitative assessment of amethod to apply the precisely known H(n,el) cross sec-tion as a reference in a neutron-induced fission crosssection ratio measurement. We evaluate the e ffi ciency,background, and energy resolution as they are all crit-ical to the ratio measurement. The decision to use agaseous hydrogenous target and the kinematic energyreconstruction is motivated by the desire to operate thefissionTPC with minimal detector development while ata white-source neutron beam. The method presented isalso relevant for neutron imaging experiments and neu-tron flux measurements performed with other TPCs.We show that without knowing the absolute z -position of the proton, we are able to compute a pro-ton selection e ffi ciency as a function of neutron en-ergy. From our simulations, we show the ionizationprofile can be used to identify fully contained protonsand based on a selection of this ionization profile wehave calculated a selection e ffi ciency. The estimatedbackground contribution assuming a thin-carbon back-ing and a hydrogenous gas target has a minimal e ff ectbelow 3 MeV, with small corrections needed at higherenergies. The energy resolution has been evaluated andseveral systematic e ff ects were identified. Ultimatelythe energy resolution of this method is limited by the in-trinsic few-degree scattering of protons stopping in thegas.Although this measurement is feasible, it would notprovide a su ffi ciently precise reference for a fissioncross section ratio. The precision is limited by the neu-tron energy resolution and a reliance on simulation forbackground and e ffi ciency corrections. Developing arobust method to extract neutron ToF from the protonrecoil would greatly improve the neutron energy reso-lution. A fast ToF signal would also eliminate the lowenergy background as a direct measurement of the inci-dent neutron energy would make them distinguishablefrom signal protons where the kinematic method can-not. Furthermore, a ToF measurement would removethe requirement that the proton be fully contained whichwill significantly reduce the complexity of the e ffi ciencycorrection.A measurement at a mono-energetic neutron facilityis also an option towards a precision measurement. Amono-energetic beam would eliminate the high-energy(n,p) backgrounds. This would then allow for measure-ments to be made with a thick silicon target backing onwhich a solid hydrogenous target could be mounted. Asolid target at a fixed location in z rather than gaseoustarget also simplifies the e ffi ciency correction.
8. Acknowledgments
The neutron beam for this work was provided byLANSCE, which is funded by the U.S. Department ofEnergy and operated by Los Alamos National Security,LLC, under contract DE-AC52-06NA25396. This workperformed under the auspices of the U.S Departmentof Energy by Lawrence Livermore National Laboratoryunder contract DE-AC52-07NA27344. This materialis based upon work supported by the U.S. Departmentof Energy, National Nuclear Security Administration,Stewardship Science Academic Alliances Program, un-der Award Number de-na0002921.
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