Investigating the anisotropic scintillation response in anthracene through neutron, gamma-ray, and muon measurements
IIEEE TRANSACTIONS ON NUCLEAR SCIENCE 1
Investigating the anisotropic scintillation response inanthracene through neutron, gamma-ray, and muonmeasurements
Patricia Schuster,
Member, IEEE,
Erik Brubaker,
Member, IEEE
Abstract —This paper reports a series of measurements thatcharacterize the directional dependence of the scintillation re-sponse of crystalline anthracene to incident DT neutrons, DDneutrons, Cs-137 gamma rays, and, for the first time, cosmicray muons. The neutron measurements give the amplitude andpulse shape dependence on the proton recoil direction over onehemisphere of the crystal, confirming and extending previousresults in the literature. In similar measurements using incidentgamma rays, no directional effect is evident, and any anisotropywith respect to the electron recoil direction is constrained to havea magnitude of less than a tenth of that present in the protonrecoil events. Cosmic muons are measured at two directions, andno anisotropy is observed. This set of observations indicates thathigh dE/dx is necessary for an anisotropy to be present for agiven type of scintillation event, which in turn could be usedto discriminate among different hypotheses for the underlyingcauses of the anisotropy, which are not well understood.
I. I
NTRODUCTION O RGANIC scintillator materials have long been usedfor radiation detection. They are particularly useful fortheir ability to detect both neutrons and gamma rays and todistinguish between them using pulse shape discrimination(PSD). Organic scintillators exist in plastic, liquid, and crystalforms. Compared to liquids, the solid plastic and crystalscintillators are easy to work with because they are subject toless thermal expansion and there is no risk of leaks. However,crystal scintillators are fragile, limited in size, and exhibit adirectional variation [1]. For these reasons, many users opt touse liquid and plastic materials.There is renewed interest in organic crystal scintillatorsfollowing a new growing method that produces large crystalswith excellent light output and neutron-gamma PSD [2]. Still,the directional variation remains as a limit to the performance.When a heavy charged particle deposits energy in an organiccrystal scintillator, the light output and pulse shape may de-pend on the direction of the particle with respect to the crystalaxes. This degrades the energy resolution and widens thedistribution of pulse shapes produced in these materials whenheavy charged particles (e.g. nuclear recoils from neutroninteractions) interact at many angles in the crystal axes.For some applications, this serves as an obstacle, and thesematerials would serve better if one could correct for the direc-tional dependence or synthesize new materials that eliminate
P. Schuster is with the Department of Nuclear Engineering, University ofCalifornia, Berkeley, CA, USA e-mail: [email protected]. Brubaker is with Sandia National Laboratories, Livermore, CA, USA.Manuscript received October 30, 2015. it. Other applications exist in which the directional dependencecould be exploited for a compact directional detection system.In this case, it may be preferred to use materials with alarge directional dependence, or synthesize new materials withan enhanced directional dependence. For either application,a greater understanding of the mechanism that produces thedirectional dependence is important to correct for, exploit,enhance, or eliminate the effect.In order to contribute to the understanding of these systems,a new characterization has been performed on the directionaldependence of proton recoil events from neutron interactionsin anthracene. These measurements serve to augment andconfirm similar measurements made previously at a range ofneutron energies.Thus far, no directional dependence has been observed inelectron recoil events produced by gamma-ray interactions,but no quantitative measurements have been published todemonstrate this. The mechanism that is responsible for thedirectional dependence in heavy charged particle interactionsis not fully understood, but it has been hypothesized toresult partly from preferred directions of molecular excitationtransport in the crystal [3]. Such a mechanism may producea smaller but non-zero directional dependence for electronrecoil events. Thus, a characterization has been performed onthe directional response to electron recoil events produced bygamma-ray Compton scatter interactions in anthracene. Thesemeasurements will serve either to demonstrate that there is adirectional dependence and measure its magnitude, or, if noeffect is observed, to set an upper bound on its magnitude.Heavy charged particle recoils differ from electron recoilsin that they deposit their energy with a high stopping power dE/dx in a straight path. Electron recoils interact with rel-atively low dE/dx and do not travel along a straight path.Energetic cosmogenic muons are minimum ionizing particlesthat like electrons deposit energy with low dE/dx , but likeprotons travel in a straight path. Measurements of cosmicmuons were therefore obtained to test for a directional depen-dence. The presence or absence of a directional dependence incosmic muon interactions will probe whether a high stoppingpower dE/dx or straight trajectory is necessary for producinga directional dependence.II. G
ENERAL T ECHNIQUES
A. Excitations and Light Emission in Anthracene
In order to understand the mechanism that produces thedirectional dependence in organic crystal scintillators, one a r X i v : . [ phy s i c s . i n s - d e t ] O c t EEE TRANSACTIONS ON NUCLEAR SCIENCE 2 must consider the molecular excitations produced by radiationinteractions. A brief summary of relevant concepts is providedhere; more detailed treatment is available elsewhere, e.g. [4].After radiation deposits energy in an organic scintillator, thesystem quickly relaxes into singlet (antiparallel spin electrons)and triplet (parallel spin electrons) molecular excitations ofthe delocalized π -orbitals. These excitations may undergonumerous kinetic processes including de-excitation by lightemission. A de-excitation from the lowest singlet excitedstate to the ground state via light emission is known asfluorescence and occurs on the ns time scale. A de-excitationfrom the lowest triplet excited state to the ground state vialight emission is known as phosphorescence and occurs onthe µ s-ms time scale, which is longer than the time scaleof our measurement system so phosphorescence is essentiallyunobserved.Triplet energy may be observed on a shorter time scalethrough another kinetic process known as triplet-triplet annihi-lation [5]. In this process, two triplet states in close proximityinteract and annihilate into one singlet excited state and onesinglet ground state. The singlet excited state may then de-excite by fluorescence on the ns time scale. This emissionis known as delayed fluorescence, as the time of the lightemission is determined by the time required for the two tripletstates to travel through the material and annihilate. A higherrate of triplet-triplet annihilation will increase the amount oflight in the delayed regions of the pulse. Thus, the amountof delayed fluorescence produced by triplet-triplet annihilationwill depend on the density of triplet excitations in the materialand their mobility.Singlet excitations are also subject to interactive processesthat affect their light emission. One such process is singletionization quenching, in which two singlet states interact,leaving one in ground state and the other in a super-excitedsinglet state. The super-excited singlet may then de-excite bylight emission, halving the amount of light that could havebeen produced by the original two singlet excitations. Thus,the amount of prompt light produced by singlet fluorescencefrom the initial singlet population will be less for a systemin which singlet excitations are produced at a higher density,increasing the fraction of delayed light.The effects of these interactive processes are observedin the differences of the pulse shapes produced by neutronand gamma-ray events. Neutron interactions produce nuclearrecoils in the material, which deposit their energy with muchhigher dE/dx than the electron recoils produced by gamma-ray interactions. The higher dE/dx produces higher excitationdensities, more triplet-triplet annihilation, and more singletquenching. Thus, there is relatively more delayed light andrelatively less prompt light in the signal produced by neutroninteractions. Not only is the time distribution of light emitteddifferent, but the total amount of light emitted per energydeposited is different for neutron and gamma-ray events. Thedifference in the pulse shape allows for events to be identifiedas neutron or gamma-ray events through PSD.In crystals, the excitation density may depend on the di-rection of the recoil particle. Additionally, the rates at whichkinetic processes occur may have a directional dependence. Either of these effects could contribute to the anisotropyobserved in the scintillation output. B. Characteristics of Anthracene Crystal
Anthracene was chosen for this study because it has thelargest magnitude of pulse shape anisotropy of the organiccrystal scintillators that have been measured in the past [3].If there is a small anisotropy in the gamma-ray response, it ismore likely that a measurement system with a given sensitivitylevel could observe it in anthracene than in other materialsbecause the effect is larger in anthracene.The anthracene crystal used in these measurements is anolder sample with unknown history and considerable wear.Several minor cracks are visible within the crystal and thesurface has been polished numerous times. The crystal wasproduced using a melt growth technique, so it is unlikelyto be to a perfect monocrystal. The sample is a cylinderapproximately 0.75” tall and 1” diameter.The crystal axis directions within the sample are unknown,so an arbitrary set of axes has been established for thesemeasurements. The direction of the interacting particle will bedescribed in spherical coordinates using θ and φ . As shown inFig. 1a, θ represents the angle between the direction and thepositive z -axis, and φ represents the angle between the positive x -axis and the projection of the direction on the xy -plane.The arbitrary set of axes was maintained for all measurementsso that the ( θ , φ ) coordinates in all sets of measurements areconsistent.Because an interacting particle produces the same excita-tions in the forward and backward directions, only one hemi-sphere worth of interaction directions must be measured. Thedirections in the top hemisphere of space can be representedin two dimensions as shown in Fig. 1b. C. Equipment and Data Acquisition
The anthracene crystal was wrapped in teflon tape andmounted to the face of a 2” Hamamatsu H1949-50 photo-multiplier tube (PMT) assembly using V-788 optical grease.A plastic sleeve was placed over the crystal and wrapped inblack tape to block out external light. The coupling of thecrystal and PMT were fixed for all measurements to controlthe light collection efficiency.Events were recorded using a Struck SIS3350 500 MHz12-bit digitizer. The high voltage, gain, and offset were ad-justed so that the raw baseline of the negatively polarizedpulse, calculated as the average of the first 85 samples, wasapproximately 3965, and the largest amplitude events usedabout 80% of the dynamic range. For each event, 384 sampleswere recorded in digitizer channel units. Each raw pulsewas subtracted from its baseline to produce the baseline-subtracted pulse. Triggering was performed with a constantfraction discriminator set low with respect to events used inthe analysis.
D. Calculating Light Output and Quantifying Pulse Shape
Each event in the detector produces a pulse with samplesof amplitude x i in baseline subtracted digitizer channel units, EEE TRANSACTIONS ON NUCLEAR SCIENCE 3 (a) Cartoon of 3D vector direction in top hemi-sphere represented in spherical coordinates with ◦ < θ < ◦ , ◦ < φ < ◦ . θ φ (b) 2D representation of the top hemisphere with φ increasing counter-clockwise and θ increasing radiallyoutward as r = √ − cos θ .Fig. 1. 2D and 3D visualization of directions in spherical coordinates. where i is the sample measured. The light output L is calcu-lated as the sum of the baseline subtracted pulse multiplied bya calibration factor C as shown in Eq. (1). L = C i =384 (cid:88) i =1 x i (1)The calibration factor C is determined using a Cs-137source producing monoenergetic gamma rays, and serves toconvert the light output from summed digitizer channel units tokeV-electron-equivalent (keVee). These units express the lightoutput in terms of the energy that an electron would depositin order to produce that number of optical photons.In order to quantify the pulse shape, the pulse shape value S is calculated as the fraction of light in a defined delayedregion of the pulse as shown in Eq. (2). S = (cid:80) i i x i (cid:80) i i x i (2)The samples i , i , and i define the beginning of the pulse,the beginning of the delayed region, and the end of the pulse,respectively. They are calculated as i = i P − , i = i P +∆ ,and i = i P + ∆ , where i P corresponds to the peak of thebaseline subtracted pulse after a smoothing filter is applied with a smoothing span of 11 samples. The smoothing accountsfor the jitter from fluctuations in photostatistics in order to pickout a consistent feature. ∆ and ∆ are selected via an iterativeprocess to maximize separation between the distribution of S values calculated for neutron and gamma-ray events. For thisanalysis on an anthracene detector using a digitizer measuringa sample every 2 ns, ∆ = 60 samples and ∆ = 160 samples.III. N EUTRON M EASUREMENTS
A. Purpose of Neutron Measurements
In order to confirm the directional dependence that hasbeen documented in anthracene [3], [6], [7], proton recoilevents from neutron interactions have been measured. Thedirectional dependence is characterized by measuring theexpected expected light output ˆ L and pulse shape ˆ S as afunction of the recoil direction for protons of a fixed energy.The measurements presented in this paper have been madewith digital pulse acquisition and processing, allowing fordetailed offline analysis. B. Neutron Interactions in Anthracene
One interaction between a neutron and anthracene thatproduces measureable signal is an elastic scatter of a neutronon a H nucleus, producing a proton recoil in the material. Theproton recoil travels with energy E recoil = E n cos α , where α is the angle between the initial direction of the neutron andthe proton recoil path. A proton that is scattered in the forwarddirection will travel with the full energy E recoil = E n . Thisis the only proton recoil energy that corresponds to a uniquedirection, as a proton recoil that travels at a non-zero anglemay be anywhere on the surface of a cone defined by thehalf-angle α about the incident neutron direction.As the proton recoil travels through the anthracene crystal,it deposits its energy in a quasi-straight path with a relativelylarge dE/dx compared to electron recoils or cosmic muons. C. Experimental Setup
In order to characterize the response of anthracene to protonrecoil events at different directions within the crystal, theenergy and direction of the proton recoil must be known. Thiswas accomplished by selecting full energy proton recoil eventsproduced by monoenergetic neutrons, fixing the proton recoilenergy as E recoil ≈ E n and the proton recoil direction as thatof the incident neutron. In order to change the direction of theproton recoil in the crystal axes, the anthracene crystal wasrotated to change its orientation with respect to the incidentneutron direction.A Thermo Electric MP 320 neutron generator was used toproduce neutrons via a DD (D+D → He+ n ; E n =2.5 MeV) orDT (D+T → He+ n ; E n =14.1 MeV) reaction. The anthracenedetector was mounted to a rotational stage, shown in Fig. 2,that is capable of positioning the detector at any angle in π with respect to the incident neutron direction. The stage hastwo motor-driven axes of rotation: 1) The circular turn tableon which the support is mounted can rotate ◦ around thevertical axis, and 2) the metal arm on which the detector is EEE TRANSACTIONS ON NUCLEAR SCIENCE 4
Fig. 2. Photo of anthracene detector on rotational stage used in neutronand gamma-ray measurements showing the two motor-driven axes of rotationaround 1) (blue) the vertical axis and 2) (red) the arm axis. mounted can rotate ◦ on its axis. For a given measurement,the incident neutron direction is calculated with respect tothe crystal axes given the rotation angles of the two stageaxes, the position of the generator, and the slight offsetbetween the detector and the intersection of the stage axes.The anthracene crystal was approximately 60” away fromthe neutron generator, controlling the incident angle of theneutrons on the detector within 2 ◦ .For the DT measurements, 76 proton recoil directionswere chosen to measure evenly across a hemisphere worthof directions. For the DD measurements, which are limitedby lower flux produced by the neutron generator, 34 evenlydistributed proton recoil directions were chosen. D. Data Analysis and Results
For each measurement, the following steps were taken tocalculate ˆ L and ˆ S , the expected L and S values for a full-energy proton recoil at the angle of interest.1) Neutron selection: An L vs. S distribution was pro-duced, as shown in Fig. 3. In this figure, the upperband with higher S values is populated primarily byneutron events, and the lower band with lower S valuesis populated primarily by gamma-ray events. The redlines indicate the light output threshold at 3000 keVeeand cutoff for separating the neutron and gamma-rayevents. Events above the red lines are selected for furtheranalysis.2) Neutron light output spectrum fit: To calculate the lightoutput at the spectrum endpoint, the energy spectrum ofthe selected events is fitted to the following function: f ( L ) = mL + b (cid:34) − erf (cid:32) L − ˆ Lσ √ (cid:33)(cid:35) − mσ √ π e − ( L − ˆ L )22 σ (3)This function represents a sloped distribution with a hardcutoff convolved with a Gaussian resolution function.The value ˆ L is the expected light output from a fullenergy proton recoil event, and σ is the fitted resolutionof the detector. A light output spectrum, along with itsbest-fit function, is shown in Fig. 4. Light Output (keVee) P u l s e S hape S Fig. 3. Density plot of L vs. S for the mixed radiation field produced bya DT neutron generator incident on anthracene at ( θ, φ ) = (8 . ◦ , . ◦ ) .The red lines are drawn to show the cutoff point for selecting neutron eventsabove 3000 keVee. Light output L (keVee) N u m be r o f c oun t s ˆ L ± σ Fig. 4. Light output spectrum for neutron events above 3000 keVee producedby a DT neutron generator incident on anthracene at ( θ, φ ) = (8 . ◦ , . ◦ ) .Black points are experimental data, the red line is the applied fit function, andthe range of full energy interactions ˆ L ± σ is indicated.
3) Full energy event selection: Events within the range ˆ L ± σ are selected as full-energy proton recoils. For thesemeasurements, this selection widens the range of protonrecoil directions to events within ◦ of the forwarddirection.4) Pulse shape distribution fit: A distribution of the S value for full energy proton recoil events is produced.A Gaussian fit is applied to this distribution to calculatethe centroid tail-to-total value ˆ S as shown in Fig. 5.For each measurement at a unique proton recoil direction,the ˆ L and ˆ S values for full energy proton recoils are calculated.Fig. 6 shows the ˆ L and ˆ S values produced by 14.1 MeV proton Pulse shape S N u m be r o f c oun t s ˆ S Fig. 5. S distribution for neutron events with L within ˆ L ± σ produced bya DT neutron generator incident on anthracene at ( θ, φ ) = (8 . ◦ , . ◦ ) .Black points are experimental data, the red line is the applied Gaussian fitfunction. EEE TRANSACTIONS ON NUCLEAR SCIENCE 5 (a) Light output ˆ L (keVee). (b) Pulse shape value ˆ S .Fig. 6. Response of anthracene crystal at various recoil directions to 14.1MeV protons. Black points indicate measurements and the colors represent asmooth interpolation between measurements. Length of vertical black bar oncolorbar indicates the statistical uncertainty. recoils produced by a DT neutron generator at 76 directions inanthracene. The distributions show smooth transitions betweenmaximum and minimum regions.Fig. 7 shows the same distributions for 2.5 MeV protonrecoils produced by a DD neutron generator at 34 directionsin anthracene. Although there is less resolution in these distri-butions due to fewer measurements, the features are consistentwith Fig. 6.To quantify the magnitude of the anisotropy at each energy,the ratio between the maximum and minimum observed valuesis calculated: A L = ˆ L max ˆ L min A S = ˆ S max ˆ S min These ratios for 14.1 MeV and 2.5 MeV proton recoil eventsin anthracene are shown in Table I. The errors are propagatedfrom the errors in the calculation of ˆ L and ˆ S as found by the fitfunction. These measurements demonstrate that the magnitudeof the light output anisotropy is greater at lower proton recoilenergies, while the magnitude of the pulse shape anisotropyis greater at higher proton recoil energies.These measurements of the magnitude of change in the lightoutput agree with past measurements made by others, as shownin Fig. 8. All measurements are consistent with the trend thatthe magnitude of change in the light output decreases as theproton recoil energy increases. (a) Light output ˆ L (keVee). (b) Pulse shape value ˆ S .Fig. 7. Response of anthracene crystal at various recoil directions to 2.5MeV protons. Black points indicate measurements and the colors represent asmooth interpolation between measurements. Length of vertical black bar oncolorbar indicates the statistical uncertainty.TABLE IM AGNITUDE OF A NISOTROPY M EASURED IN E XPECTED L IGHT O UTPUT ˆ L AND P ULSE S HAPE V ALUE ˆ S P RODUCED BY P ROTON R ECOIL E VENTSIN A NTHRACENE E recoil A L ± ± A S ± ± For a measurement in which the proton recoils travelthrough the crystal at a range of angles, this directionaldependence introduces additional variability into the lightoutput and pulse shapes produced by neutron interactionsin anthracene. A metric σ anis that quantifies the anisotropyin terms of this resolution effect is related to the observedstandard deviation σ obs of measured ˆ L and ˆ S values at a givenenergy. The contribution from statistical variance is subtractedin quadrature, e.g. σ anis = (cid:113) σ − σ , where σ is the average statistical variance from the setof measurements at different recoil directions. The relevantquantities for each group of datasets are given in Table II,normalized to the average measured value µ .Strictly speaking, σ anis includes both the anisotropy effectand other sources of systematic error. These systematic errorsinclude but are not limited to the width of the proton recoil EEE TRANSACTIONS ON NUCLEAR SCIENCE 6 A L : m ag n i t ud ec h a n g e i n ˆ L OliverBrooksThis Paper
Fig. 8. Magnitude of change in light output produced by proton recoil eventsin anthracene as a function of proton energy [3], [6].TABLE IIV
ARIABILITY IN P ULSE S HAPE AND L IGHT O UTPUT IN P ROTON R ECOIL E VENTS IN A NTHRACENE . E recoil
14 MeV 2.5 MeV ˆ L σ obs /µ σ stat /µ σ anis /µ ˆ S σ obs /µ σ stat /µ σ anis /µ direction selection window due to the physical size of thedetector and the range of energies selected at the endpoint,the possibility of several low energy interactions summingto a full energy event, the polycrystallinity that exists in thesample, and the approximation of the fit function to representthe distribution. Given efforts to limit these systematic biasesand the qualitative features in the angular distribution of ˆ L and ˆ S , it appears that σ anis for both ˆ L and ˆ S are dominatedby the anisotropy effect in proton recoil interactions.Other explanations for the observed directional dependencehave been considered, such as magnetic field effects on thePMT. However, any such external effect must be minimalcompared to the internal effect in the crystal because thisanisotropy is not observed for gamma-ray interactions, as willbe demonstrated in Sec. IV. E. Discussion
According to measurements made by previous groups, theproton recoil direction that produces maximum light outputin anthracene is along the c (cid:48) -axis, defined as the directionperpendicular to the ab -plane of the crystal, and the directionthat produces minimum light output is along the b -axis [3],[7]. This allows for the crystal axes of the anthracene samplemeasured in this paper to be inferred. According to Figs. 6and 7, the b -axis is at approximately ( θ, φ ) = (40 ◦ , ◦ ) and the c (cid:48) -axis is at approximately ( θ, φ ) = (60 ◦ , ◦ ) .These directions make an angle of approximately ◦ , as the b and c (cid:48) -axes should. This puts the a axis at approximately ( θ, φ ) = (65 ◦ , ◦ ) , which is roughly the position of the saddlepoint observed in the ˆ S distribution. These measurements alsoconfirm Tsukada’s findings that the saddle point in the lightoutput distribution occurs in the ac plane about ◦ from the a − axis [7]. Brooks has hypothesized that the directional dependence inheavy charged particle events is a result of preferred directionsof excitation transport in the crystal [3]. Excitation transportchanges the excitation density over time in the material. Inthe same way that the light output and pulse shape differ forneutron and gamma-ray events due to the gross differencesin the excitation densities that they produce, as describedin Sec. II-A, small changes in the excitation density dueto directionally dependent transport within the material mayaffect the light output and pulse shape at the levels observedin these measurements.The evolution of the excitation density depends on a numberof things, one of which is the initial distribution of excitationswith respect to the preferred directions of transport. If theexcitations are deposited along a direction with rapid trans-port, they are more likely to move within the initial path,maintaining the excitation density and the probability thatexcitations will meet and interact throughout their lifetime.If the excitations are deposited perpendicular to the directionwith rapid transport, the excitations more easily transport awayfrom the path during their lifetime, decreasing the excitationdensity and reducing the probability to interact.The overall light output ˆ L depends primarily on the rateof singlet quenching, while the pulse shape parameter ˆ S isaffected by both singlet quenching and triplet annihilation.As evident in Fig. 6 and Fig. 7, the proton recoil directionsthat produce higher light output correspond to regions thatproduce lower pulse shape values, and vice versa. This maylead one to conclude that a change in ˆ L is accompanied byan opposite change in ˆ S , but it is apparent from the differentpositions of the saddle points that the ˆ L and ˆ S values are notdirectly coupled. This correlation, but not fixed relationship,between the ˆ L and ˆ S distributions indicates that the physicalmechanisms responsible for the directional dependence mayaffect singlet and triplet state evolution in related but differentways. The singlet and triplet excitations undergo transport andinteractions via different mechanisms, so they may or may nothave the same preferred directions of transport or the samerelative change in transport likelihood in different directions.The same may be true of other kinetic processes. This meansthat singlet and triplet excitations will experience differentchanges in their densities throughout their lifetimes.It is possible that the magnitude of change in the excitationdensity due to preferred directions of transport is only sig-nificant among a high excitation density like that producedby neutron events. This hypothesis will be tested throughmeasurements of gamma-ray and cosmic muon interactionsin the following sections.IV. G AMMA -R AY M EASUREMENTS
A. Purpose of Gamma-Ray Measurements
So far, no directional dependence has been documented ingamma-ray interactions in organic crystal scintillator detectors.Brooks’ characterization of the heavy charged particle scintil-lation anisotropy noted that electron recoil events producedby gamma-ray interactions are not subject to a directionaldependence [3], however, this was not quantified and nomeasurement details were provided.
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According to the working hypothesis on the mechanismsthat cause the directional dependence, the excitation densityproduced by gamma-ray events may be so low that direction-ally dependent changes are not significant compared to theoverall density. However, it is also possible that the effectis just much smaller for gamma-ray events than for neutronevents, and a smaller anisotropy may be observable witha more sensitive measurement. In order to investigate this,electron recoils produced by gamma-ray interactions have beenmeasured at different directions in anthracene.
B. Gamma-Ray Interactions in Anthracene
Gamma rays of energies typical of radioactive sourcesinteract primarily via Compton scattering in anthracene. For anincident gamma ray of energy E γ , the highest energy electronrecoil that can be produced occurs in the head-on collisionin which the photon scatters at angle θ = π from its initialdirection and the recoil electron departs the interaction in theforward direction. Although the initial direction of the electronis fixed for such a Compton edge event, the electron undergoeswide angle scattering as it travels through the crystal, so it doesnot travel in a straight path as it deposits its energy. C. Experimental Setup
Measurements were made with a Cs-137 source that wasplaced 38” from the detector, controlling the incident gamma-ray direction within 3 ◦ . The 662 keV gamma ray from Cs-137 produces a Compton edge electron recoil with energy E e − = 478 keV. In order to control the energy and initialdirection of electron recoils produced in anthracene, Comptonedge electron events were selected. The same rotational stagewas used for the gamma-ray measurements as was describedin Sec. III-C for the neutron measurements. This provided thecapability to change the initial direction of the electron recoilin the crystal axes by rotating the anthracene crystal withrespect to the incident gamma-ray direction. Measurementswere made at the same 72 recoil directions in the anthracenecrystal as were measured in the DT neutron measurements. D. Data Analysis and Results
For each event, the L value was calculated in summeddigitizer channel units using Eq. (1) with a dimensionless C = 1 . In this analysis, no conversion to keVee was made.In order to build a fit function, MCNP5 was used to producea simulated detector response. The energy spectrum producedby 662 keV gamma rays incident on anthracene in MCNP5was smeared with a Gaussian detector response function withresolution σ , which was adjusted until the smeared spectrummatched the shape from measured light output spectra, asshown in Fig. 9. This simulated spectrum showed that theamplitude of the energy spectrum at 478 keV was equal to N = 0 . ∗ N CE , where N CE is the amplitude of theenergy spectrum at the peak corresponding to the Comptonedge.For each measurement, the following three steps were takento calculate ˆ L and ˆ S , the expected L and S values for a 478keV electron recoil at the angle of interest. Light output L (digitizer channel units) × N u m C oun t s M ea s u r ed R e l a t i v e N u m E v en t s × -6 N N CE ˆ L ± σ Fig. 9. Light output spectrum for Cs-137 gamma-ray events incident onanthracene. The red curve and axes correspond to an MCNP5 simulation. Theblack data points and axes correspond to a measurement. N and N CE asfound in the fit function are indicated, which produce a final ˆ L value for thelight output in summed digitizer channel units of a 478 keV electron recoilevent. Pulse shape value S N u m be r o f c oun t s ˆ S Fig. 10. Distribution of S values for events with light output in the range ˆ L ± σ produced by Cs-137 gamma rays incident on anthracene at ( θ, φ ) =(50 ◦ , ◦ ) . Black points are experimental data with statistical error bars.The red line is the applied Gaussian fit function.
1) Light output spectrum fit: A light output spectrum of allevents in a single measurement is shown in Fig. 9. Thelight output corresponding to N was recorded as ˆ L .2) Compton edge event selection: Events within the range ˆ L ± σ were selected as Compton edge electron recoils.This widened the range of electron recoil directions toevents within half-angle ρ = 18 . ◦ around the forwarddirection.3) Pulse shape distribution fit: A distribution of the S valuefor Compton edge electron recoil events was produced.A Gaussian fit was applied to this distribution to estimatethe expected pulse shape value ˆ S as shown in Fig. 10.In order to estimate the statistical error in the calculationof ˆ L in each measurement, a bootstrapping method wasapplied. 100 light output spectra were generated based onPoisson fluctuations about the light output spectrum from eachmeasurement, simulating a resampling of the data. The ˆ L valuewas calculated for each bootstrap-generated spectrum, and thestandard deviation in the 100 ˆ L values served as an estimatefor the statistical error in the measurement of ˆ L .The light output and pulse shapes produced in anthracenehave a temperature dependence that proved to be the largestsource of systematic bias in the gamma-ray measurements.Therefore, the dependence was characterized and a correctionwas applied. A separate set of 10-min long measurements of EEE TRANSACTIONS ON NUCLEAR SCIENCE 8
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Measurement temperature (C) ˆ L r e l a t i v e t o t h a t a t ◦ C Fig. 11. ˆ L produced by a Cs-137 source at a fixed position at temperatures22-28 ◦ C relative to that at 25 ◦ C.
22 23 24 25 26 27 28
Measurement temperature (C) ˆ S r e l a t i v e t o t h a t a t ◦ C Fig. 12. ˆ S produced by a Cs-137 source at a fixed position at temperatures22-28 ◦ C relative to that at 25 ◦ C. a Cs137 source at a fixed angle with respect to the detectorwere taken over six days as the temperature in the lab variedwith the weather. The ˆ L and ˆ S values were calculated for eachmeasurement and plotted vs. temperature as shown in Fig. 11and Fig. 12. Linear fits to these data were used to correct the ˆ L and ˆ S values in the directional measurements to 25 ◦ C.Fig. 13 shows the ˆ L and ˆ S values measured for 478 keVelectron recoil events in anthracene at different electron recoildirections. The length of the black line on the colorbar isthe average statistical uncertainty in the measurement. Threemeasurements were omitted in which the motor system wasbetween the source and the detector, causing considerablymore environmental scattering and producing outlying valuesfor ˆ L and ˆ S .Although there are variations in these measurements greaterthan the statistical uncertainties, there is not a distinct patternof high and low regions in angle space as there are in theproton recoil measurements shown in Sec. III-D. Since thevariation has no order, it appears that there is no measurabledirectional dependence, but rather there are other sources ofvariation.Following the method explained in Sec. III-D, Table IIIshows the relative standard deviations due to statistical un-certainty and other effects. Compared to the neutron measure-ments in which it was concluded that the anisotropy was thedominant effect in the variability of ˆ L and ˆ S , the qualitativefeatures on the angular distributions of ˆ L and ˆ S indicate thatthe variability in the gamma-ray measurements is dominatedby sources of bias and not an anisotropy. For that reason, thisvariability will be named σ other . Several sources of bias existin these measurements. First, as the rotational stage changes (a) Light output ˆ L .(b) Pulse shape value ˆ S .Fig. 13. Response of anthracene crystal at various recoil directions for478 keV electron recoils. Black points indicate measurements and the colorsrepresent a smooth interpolation between measurements. Length of verticalblack bar on colorbar indicates average 2- σ statistical error. its position, the position of the detector relative to the sourceand environment change, so the scattering environment differs.This may be significant for a gamma-ray source among thehigh-Z materials in the laboratory equipment. Second, thetemperature correction is not a perfect method because thetemperature sensor is outside of the detector and provides ameasurement of the room temperature rather than the tem-perature in the crystal. Third, the light output window in thegamma-ray measurements produces a wider selection of recoilangles than in the neutron measurements. TABLE IIIV
ARIABILITY IN P ULSE S HAPE AND L IGHT O UTPUT IN E LECTRON R ECOIL E VENTS IN A NTHRACENE . E recoil ˆ L σ obs / µ σ stat / µ σ other / µ ˆ S σ obs / µ σ stat / µ σ other / µ However, if a conservative assumption is made that theanisotropy is the dominating effect, an upper limit on themagnitude of the anisotropy from 478 keV electron recoilsmay be approximated as σ other . Even under this assumption, EEE TRANSACTIONS ON NUCLEAR SCIENCE 9 the anisotropy effect in electron recoil events is still less thanone tenth of that for the proton recoil interactions (cf. Table I).
E. Discussion
This analysis provides quantitative measurements that sup-port the claim made by previous groups that no directionaldependence has been observed in electron recoil events inanthracene [3]. Two reasons have been hypothesized as beingresponsible for the lack of directional dependence in electronrecoil events. First, Brooks attributed this lack of anisotropyto the non-straight path that electrons follow as they slowdown due to the large-angle scattering that they undergo [3].Electrons may not actually populate a directionally dependentexcitation distribution, and it is possible that an electron recoilevent, were it to travel in a straight path, could be subject to adirectional dependence, but the non-straight path traveled bythe electron washes out the effect. Second, electrons deposittheir energy with a much lower dE/dx than heavy chargedparticles, producing a lower excitation density. Changes in theexcitation density due to directional transport may be on toosmall a scale compared to the overall density to affect therelative rates of kinetic processes for the electron recoil. Thecosmic muon measurements presented in Sec. V provide a testof these hypotheses.V. C
OSMIC M UON M EASUREMENTS
A. Purpose
As demonstrated above, a directional dependence in an-thracene has been observed in heavy charged particle interac-tions but not in electron recoil events. In order to test whetherthe lack of directional dependence from the electron recoil isdue to its low dE/dx or due to its non-straight path, cosmicmuon events were measured. Muons are elementary particlessimilar to electrons but with mass of 105.7 MeV/c . Likeelectrons, muons interact with a much lower dE/dx thanheavy charged particles. However, due to their large masscompared to the electrons in the medium in which they areinteracting, muons are not subject to large-angle scattering andthus travel in a quasi-straight path.Since muons travel with lower dE/dx like the electronrecoil, but in a quasi-straight path like the proton recoil,the presence or lack of directional dependence in muoninteractions will provide information on whether a directionaldependence requires that a particle interact with high dE/dx or in a straight path. The goal of these measurements is tomeasure the anisotropy present in muon events in anthracene,or if no anisotropy is observed, set an upper bound on itsmagnitude. B. Muon Interactions in Anthracene
Cosmic muons reach sea level with approximately 4 GeVenergy. They interact as minimally ionizing particles, deposit-ing a minimal amount of energy per distance across the lengthof the material in which it interacts. In anthracene, muonsdeposit approximately 2.4 MeV/cm[8]. This is very close tothe dE/dx deposited by a 478 keV electron of 2.5 MeV/cm, and much less than the 166.7 MeV/cm deposited by a 2.5 MeVproton recoil[9]. Because a muon’s mass is so much greaterthan an electron’s mass, a muon experiences minimal changesin its direction as it interacts with electrons in the medium,producing a quasi-straight path.Since the energy deposited is proportional to the pathlength that the muon travels in the detector, the depositedenergy spectrum will be equal to the path length distributionmultiplied by a constant factor. If there were a light outputanisotropy in muon interactions in anthracene, it is expectedthat muons traveling at different angles would produce a differ-ent light output per energy deposited. Thus, the light outputspectra produced by muons traveling at different directionswould be equal to the path length distribution multiplied bydifferent constant factors, and any features in those spectrawould be shifted to different light output values.
C. Experimental Setup
Fig. 14 shows the detectors used in this measurement.The rectangular blocks are EJ200 plastic scintillator detectors,and the cylinder is the anthracene crystal. Only events thatexceeded the trigger threshold in all three detectors were usedin order to select muons that traveled within a set angle ρ fromthe vertical direction through the anthracene. As the distancebetween the anthracene and the plastic blocks is increased,the angle ρ decreases to select muons traveling within anarrower range of angles in the anthracene, and the count ratedecreases. The distance was chosen so that ρ was comparableto the range of proton recoil directions accepted in the neutronmeasurements. Each plastic block was placed 26.5” away fromthe anthracene detector, limiting the muon directions to withinthe half-angle ρ = 9 . ◦ of the vertical direction.In order to investigate muon interactions at different direc-tions within the anthracene crystal axes, measurements weretaken with the crystal at different orientations with respect toa vertical muon trajectory. Due to the requirement that thegeometry of the system be identical in the measurements inorder to preserve the path length distribution, only angles atwhich the height axis of the crystal was perpendicular to thevertical muon path, as shown in Fig. 14a, were candidates forthe muon measurements. Two such directions were chosenand will be referred to as directions 1 and 2. Direction 1was selected at ( θ, φ ) = (90 ◦ , . ◦ ) , and direction 2 wasat ( θ, φ ) = (90 ◦ , . ◦ ) . Each measurement was taken for20 days, producing approximately 2300 muon events in eachmeasurement.An assumption has been made that any anisotropy thatwould exist in the light output and pulse shape producedby muon interactions would follow the same crystal axes asthe anisotropy from proton recoil events. Although these twointeraction directions are not those of greatest difference inlight output and pulse shape from the neutron measurements,there was still a significant difference in the light output andpulse shape at these two angles from 14 MeV and 2.5 MeVproton recoils, as listed in Table IV. EEE TRANSACTIONS ON NUCLEAR SCIENCE 10 (a) Cartoon of experimental setup(not to scale) (b) Photo of experimental setupFig. 14. Experimental setup used in cosmic muon measurements. Light Output (keVee) N u m be r o f c oun t s Light output spectrum for min measurement (1A) (a) Light output spectrum formuon events through anthraceneat angle 1. N u m be r o f c oun t s Light Output at Peak for Muon Measurements Path 1Path 2 (b) Comparison of peak in lightoutput spectra for muons travel-ing at directions 1 and 2. Thevertical line indicates ˆ L values ascalculated by Gaussian fits.Fig. 15. Analysis of light output spectra in muon measurements. D. Data Analysis and Results
In order to evaluate whether there is a significant differencein the light output and pulse shapes produced by muon eventsat directions 1 and 2, the expected light output ˆ L and pulseshape value ˆ S for events at the peak feature in the light outputspectrum were calculated by following these three steps:1) Light output spectrum fit: A light output spectrum of allevents was produced, as shown for the measurement atdirection 1 in Fig. 15a. A Gaussian fit with centroid ˆ L and standard deviation σ was applied to the peak feature,as shown for both directions in Fig. 15b.2) Peak event selection: Events in the peak feature areidentified by selecting events with light output in therange ˆ L ± σ .3) Pulse shape distribution fit: A distribution of the S valuefor peak events is produced. A Gaussian fit is appliedto this distribution to estimate the expected pulse shapevalue ˆ S produced by a muon, as shown in Fig. 16. Pulse shape value ˆ S N u m be r o f c oun t s Path 1Path 2
Fig. 16. Distribution of S values for events with light output in the range ˆ L ± σ produced by cosmic muons in anthracene. The overlying curves are theGaussian fits applied, and the vertical lines are the location of the expectedpulse shape values ˆ S . The magnitudes of change in the ˆ L and ˆ S between mea-surements were calculated as the ratio of the maximum tominimum of each measurement. The magnitude of change inthe ˆ L value was . ± . , and the magnitude of change inthe ˆ S value was . ± . . Neither showed a statisticallysignificant change for muons between paths 1 and 2.It is still possible that there is a very small anisotropypresent that is not measurable by this system. These results canserve to set an upper boundary on the magnitude of anisotropyin anthracene at these muon paths. To 1- σ , these results areinconsistent with a magnitude of change in light output greaterthan 1.013 and a magnitude of change in the pulse shape valuegreater than 1.030 for muons traveling at directions 1 and 2. E. Discussion
Table IV compares the magnitude of change measured in thelight output and pulse shape value for protons, electrons, andmuons traveling at directions 1 and 2 in the anthracene crystal.The table shows two major differences in the interactions ofthese particles. First, protons and muons travel in a straightpath as they deposit their energy, while the electron does not.Second, the electron and muon produce comparable dE/dx ,while the proton recoil produces much higher dE/dx in thematerial. Of these particles, an anisotropy was only observedin proton recoil interactions.The lack of anisotropy observed in muon interactionsprovides new insights on the mechanism that produces thedirectional dependence in heavy charged particle interactions.Since the muon, which travels in a straight path, does notexperience a directional dependence, it can be concluded thatthe meandering recoil electron is not solely responsible for thelack of directional dependence in gamma-ray interactions. Thislends support to the theory that a high dE/dx is necessary forproducing a directional dependence.This result agrees with the hypothesis presented in Sec. III-Ethat says the anisotropy is partly due to preferred directionsof excitation transport. This transport changes the excitationdensity over time. Depending on the initial distribution ofexcitations compared to the directions of rapid transport, theexcitations may move towards one another or away fromone another, changing the rates of interactive processes suchas triplet-triplet annihilation and singlet quenching and, inturn, affecting the amount of light produced and the time
EEE TRANSACTIONS ON NUCLEAR SCIENCE 11
TABLE IVS
UMMARY OF M EASUREMENTS M ADE ON A NTHRACENE S AMPLE FOR I NTERACTIONS AT D IRECTIONS AND Source Particle Neutron Neutron Gamma ray MuonRecoil Particle Proton Proton Electron –Path Straight Straight Non-straight StraightEnergy (MeV) 14 2.5 0.478 4000dE/dx (MeV/cm) 42.9 166.7 2.5 2.4 ˆ L mag. change 1.060 ± ± ± ± ˆ S mag. change 1.062 ± ± ± ± distribution. For heavy charged particle that interact with high dE/dx , the change in the excitation density is significantcompared to the overall density. For gamma-ray and muoninteractions, the overall excitation density is low enough due totheir low dE/dx that these changes are not significant enoughto change the scintillation output on an observable level.VI. C ONCLUSION
The anisotropic scintillation response of crystalline an-thracene to heavy charged particles has been investigatedthrough a series of measurements using incident neutrons,gamma rays, and muons. The directional dependence of thescintillation amplitude and pulse shape for proton recoils at 14MeV and 2.5 MeV is consistent with previous measurementsat similar energies. These measurements are used to evaluatethe contribution of the anisotropy to the energy resolution ofanthracene for typical neutron detection scenarios in whichthe proton recoil direction is not known event by event. Thiscontribution is 3.7% for 14 MeV proton energy deposited and8.3% for 2.5 MeV proton energy deposited.In identical measurements using incident 662 keV gammarays, an anisotropic response was not observed. Variationsamong the datasets at different electron recoil angles do notfollow a clear directional pattern, and are consistent withunrelated systematic variability. But under the conservativeassumption that observed variability is due to an anisotropy,we limit the relative magnitude of the directional variability toless than a tenth of that observed in the neutron measurements.This is the first quantitative estimate of or limit on theanisotropic response of a crystal organic scintillator to electronrecoils.Finally, in order to aid in distinguishing among differenthypotheses for the physical origin of the anisotropy, cosmicmuons were measured at two directions through the sameanthracene crystal. These measurements are statistically lim-ited and only one pair of directions was measured, but theabsence of a significant difference in light output or pulseshape between the two directions indicates that the anisotropyis weak or not present for low- dE/dx particles, even whenthe particle track is straight.Beyond preferred directions of excitation transport, it is un-clear what physical mechanisms contribute to the anisotropicscintillation response in neutron interactions, and what physi-cal or chemical properties dictate its magnitude and behaviorin a given material. This work raises the question whetherthe effect may be corrected for in order to improve energy resolution, and whether the effect may be exploited to usethese materials as compact directional neutron detectors. Bothof these applications would benefit from a deeper understand-ing of the physical mechanism that is responsible for theanisotropy. A
CKNOWLEDGEMENTS
The authors wish to thank John Steele for his assistance inbuilding the motor driven rotational stage, and Andrew Glennof Lawrence Livermore National Laboratory for his suggestionto measure cosmic muon events.This material is based upon work supported by the NationalScience Foundation Graduate Research Fellowship Programunder Grant No. DGE 1106400. This material is basedupon work supported by the Department of Energy NationalNuclear Security Administration under Award Number. DE-NA0000979 through the Nuclear Science and Security Con-sortium. Sandia National Laboratories is a multi-programlaboratory managed and operated by Sandia Corporation, awholly owned subsidiary of Lockheed Martin Corporation, forthe U.S. Department of Energy’s National Nuclear SecurityAdministration under contract DE-AC04-94AL85000.R
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