A liquid parahydrogen target for the measurement of a parity-violating gamma asymmetry in n ⇒ + p → d + γ

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A 16 l liquid parahydrogen target has been developed for a measurement of the parity-violating γ-asymmetryγ-asymmetry in the capture of polarized cold neutrons on protons in the n⇒+p→d+γ reaction by the NPDGamma collaboration. The target system was

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  A liquid parahydrogen target for the measurement of a parity-violatinggamma asymmetry in  ~ n þ p - d þ g S. Santra a,  ,1 , L. Barro´n Palos b,2 , C. Blessinger a,3 , J.D. Bowman c,3 , T.E. Chupp d , S. Covrig e,4 ,C. Crawford g,5 , M. Dabaghyan e,6 , J. Dadras f  , M. Dawkins a,7 , M.T. Gericke a,8 , W. Fox a , R.C. Gillis h,9 ,M.B. Leuschner a,10 , B. Lozowski a , R. Mahurin f  , M. Mason e,7 , J. Mei a , H. Nann a , S.I. Penttila c,3 ,A. Salas-Bacci c , M. Sharma d , W.M. Snow a , W.S. Wilburn c a Indiana University Cyclotron Facility, 2401 Milo B. Sampson Lane, Bloomington, IN 47408, USA b  Arizona State University, Tempe, AZ 85287, USA c Los Alamos National Laboratory, Los Alamos, NM 87545, USA d University of Michigan, Ann Arbor, MI 48104, USA e Department of Physics, University of New Hampshire, Durham, NH 03824, USA f  Department of Physics, University of Tennessee, Knoxville, TN 37996, USA g Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA h Department of Physics, University of Manitoba, Winnipeg, Manitoba, Canada R3T2N2 a r t i c l e i n f o  Article history: Received 22 March 2010Received in revised form16 April 2010Accepted 23 April 2010Available online 7 May 2010 Keywords: Liquid parahydrogenParity-violation g -asymmetryNeutron depolarizationBubble suppressionHydrogen safetyCryorefrigeratorOrtho-to-para converters a b s t r a c t A 16l liquid parahydrogen target has been developed for a measurement of the parity-violating g  asymmetry in the capture of polarized cold neutrons on protons in the  ~ n þ p - d þ g  reaction by theNPDGamma collaboration. The target system was carefully designed to meet the stringentrequirements on systematic effects for the experiment and also to satisfy hydrogen safetyrequirements. The target was designed to preserve the neutron polarization during neutron scatteringon liquid hydrogen (LH 2 ), optimize the statistical sensitivity to the  ~ n þ p - d þ g  reaction, minimizebackgrounds coming from neutron interaction with the beam windows of the target cryostat, minimizeLH 2  density fluctuations which can introduce extra noise in the gamma asymmetry signal, and controlsystematic effects. The target incorporates two mechanical refrigerators, two ortho–para convertors, analuminum cryostat, an aluminum target vessel shielded with  6 Li-rich plastic, a hydrogen fill/vent linewith a passive recirculation loop to establish and maintain the equilibrium ortho–para ratio, a hydrogenrelief system coupled to a vent stack, a gas handling system, and an alarm and interlock system. Low Z,nonmagnetic materials were used for the target vessel and cryostat. Pressure and temperature sensorsmonitored the thermodynamic state of the target. Relative neutron transmission measurements wereused to monitor the parahydrogen fraction of the target. The target was thoroughly tested andsuccessfully operated during the first phase of the NPDGamma experiment conducted at the FP12 beamline at Los Alamos Neutron Science Center (LANSCE). An upgraded version of the target system will beused in the next stage of the experiment, which will be performed at the Fundamental Neutron PhysicsBeam (FnPB) line of the Spallation Neutron Source at Oak Ridge National Laboratory. &  2010 Elsevier B.V. All rights reserved. ARTICLE IN PRESS Contents lists available at ScienceDirectjournal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods inPhysics Research A 0168-9002/$-see front matter  &  2010 Elsevier B.V. All rights reserved.doi:10.1016/j.nima.2010.04.135  Corresponding author. E-mail addresses:  s_satyaranjan@rediffmail.com, ssantra@barc.gov.in (S. Santra). 1 Present address: Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India. 2 Present address: Universidad Nacional Auto´noma de Me´xico, Me´xico, D.F. 04510, Mexico. 3 Present address: Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 4 Present address: Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA. 5 Present address: Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA. 6 Present address: Mass. General Hospital Boston, MA, USA. 7 Present address: Texas A&M University, College Station, TX 77843, USA. 8 Present address: Department of Physics, University of Manitoba, Winnipeg, Manitoba, Canada R3T2N2. 9 Present address: Physics Department, Indiana University, Bloomington, IN 47408, USA. 10 Present address: Procure, Bloomington, IN 47408, USA.Nuclear Instruments and Methods in Physics Research A 620 (2010) 421–436  ARTICLE IN PRESS 1. Introduction A nonzero photon asymmetry A g  with respect to the neutronspin in the radiative capture of polarized neutrons by protons ð ~ n þ p - d þ g Þ  is a manifestation of parity violation [1]. Quark-quark weak interactions in the standard electroweak model canproduce parity-odd effects in nucleon–nucleon (NN) interactions.Quantitative calculations will not be possible until the stronginteraction QCD effects can be successfully attacked using latticegauge theory techniques [2]. In the Standard Model there are twogeneral statements one can make about the weak NN interaction:(i) the current–current weak interactions involving quarks (andtherefore the weak NN interaction) can change isospin by D I  ¼ 0 , 1 , 2, and (ii) at low energies where only  L ¼ 0 and 1 partialwaves are important. There are five parity violating s–p transi-tions possible in NN elastic scattering. A g  in the  ~ n þ p - d þ g reaction is dominated by a  D I  ¼ 1 transition [3], and in the loosely bound deuteron this transition is expected to be mainly carried bylong range pion interaction. In the model by Desplangues,Donoghue and Holstein (DDH) [4] the weak  p  interaction isrepresented by the weak pion coupling constant f  1 p . The n–psystem is the simplest nuclear system and therefore theuncertainties due to the nuclear structure are negligible, andhence a measurement of A g  will be interpretable in any lowenergy treatment of the weak NN interaction, such as the recenteffective field theory (EFT) approaches under development [5–7].The predicted value of A g  by DDH model and hybrid EFT approachis equal to   5.0  10  8 [1,3].Fig. 1 shows a conceptual diagram of the FP12 and theNPDGamma experiment at LANSCE [8–10]. Spallation neutronsare produced by the incident 800MeV, pulsed (20Hz) protonbeam from the LANSCE accelerator complex on a split tungstentarget. The neutrons are cooled by a cold H 2  moderator [11] andthen guided by 9.5cm   9.5cm cross-sectional area and 21mlong  m ¼ 3 supermirror, neutron guide to the FP12 experimentalcave [12]. A frame-definition chopper located between themoderator and the experiment is used to absorb the neutronswith energy less than 1meV to prevent frame overlap of theneutrons from different pulses. The neutrons are transverselypolarized by transmitting the unpolarized beam through a glasscell of optically polarized  3 He gas [13]. A resonant radio frequencyspin rotator [14] is used to reverse the neutron spin direction on apulse-by-pulse basis before the neutrons are captured in a 16lliquid parahydrogen target operated at 17K. The 2.2MeV  g -raysfrom the n–p capture reaction are detected by an array of 48CsI(Tl) scintillators arranged to four rings around the target. Thescintillators are viewed by vacuum photodiodes and operated incurrent mode [15]. The entire apparatus is in a verticalhomogeneous 10G magnetic field which is needed to operatethe  3 He polarizer, to preserve the neutron polarization betweenthe polarizer and the target, and to suppress Stern–Gerlachsteering of the neutrons upon spin flip, which could produce afalse asymmetry in the detector signal. Three parallel plate  3 Heionization chambers, filled with an admixture of   3 He,  4 He and N 2 to a total pressure of one atmosphere, are used to monitor beamintensity, measure beam polarization and transmission, andmonitor the parahydrogen fraction in the target. These ionchambers are also operated in current mode.A central component of the experiment is a large volume (16l),thermally stable, and operationally reliable and safe liquidparahydrogen (LH 2 ) target. An additional requirement is thatthe target cannot introduce any systematic effect that couldproduce any false asymmetry for the experiment which does notcome from the radiative n–p capture. Our goal was to suppressthe systematic effects below the 10  8 level for the phase 1experiment at LANSCE and the 10  9 level for the phase 2experiment at Spallation Neutron Source (SNS) at Oak Ridge.Based on these criteria, a liquid parahydrogen target wasdesigned, built, tested and then successfully operated in theNPDGamma experiment at FP12.LH 2  targets have been used in many different forms overseveral decades for experiments and facilities in nuclear, particle,and condensed matter physics [16–23]. Nevertheless, the specialfeatures required for the NPDGamma experiment make our targetunique. The design criteria for our target share some similaritieswith targets constructed for parity violation measurements inelectron scattering [17,18]. In both cases, the experiments searchfor a very small parity-odd observable and must controlsystematic effects. The target should not introduce extra noisethrough target density fluctuations to the current-mode detectorsignal. In the targets for electron scattering, the electron beamtypically deposits several hundred watts (up to 2kW) of power to Fig. 1.  Conceptual diagram of FP12 and the NPDGamma experiment at LANSCE. S. Santra et al. / Nuclear Instruments and Methods in Physics Research A 620 (2010) 421–436  422  ARTICLE IN PRESS the LH 2 , and therefore the LH 2  must be cooled by recycling itrapidly with pumps through powerful heat exchangers cooled byliquid helium. By contrast, the low energy neutron beam used forNPDGamma deposits several orders of magnitude less power intothe LH 2 , and therefore there is no need for fast hydrogenrecirculation. Because of the large neutron beam size, and therather large liquid volume, a quasi-static operating mode, and theneed to maintain the liquid in the parahydrogen state, ourtarget also possesses some similarities with the operatingparameters for LH 2  and deuterium moderators at slow neutronsources. Unlike the application for neutron moderators, werequire a very low concentration of orthohydrogen in the target.For the purposes of this paper we will define the ‘‘target’’broadly to include (1) the target cryostat and vacuum systeminside the experimental cave, (2) the gas handling and targetcontrol system external to the cave, and (3) the safety system,including the relief system and vent line.The details of the target design are described in Section 2. Thetest results, target performance and conclusions are given inSections 3–5, respectively. 2. Liquid parahydrogen target for the NPDGamma experiment The design goals and the details of the target subsystems aredescribed in the following subsections.  2.1. Design goals The physics goals of the experiment coupled with the knownproperties of cold neutron interactions in hydrogen, MeV gammainteractions with materials, and the need for the target system tobe consistent with the other subsystems of the experiment,implicitly define the following design goals for the target.(a)  Parahydrogen : To achieve the required ultimate statisticalsensitivity of 10ppb for the gamma asymmetry, the target mustcapture as much of the polarized cold neutron beam flux aspossible without depolarizing the neutron beam before capture.The need to prevent neutron depolarization requires the target toconsist mainly of parahydrogen. The ground state of the hydrogenmolecule, parahydrogen, has  J  ¼ L ¼ S  ¼ 0, and the first excited stateof the molecule, orthohydrogen ( S  ¼ 1), is 15meV above theground state. For neutrons with kinetic energies less than 15meV,the para-hydrogen molecule cannot be excited, and so only elasticscattering is allowed. Furthermore, since the cold neutronwavelength is very large compared to the range of the strongneutron–proton interaction, only s-wave scattering is importantin the partial wave expansion. Under these conditions neutronspin-flip scattering is forbidden by the conservation of angularmomentum. Since a very large fraction of the neutrons from thesource has energy below 15meV, the neutron polarization cansurvive the 1–2 scattering events that occur on average before thecapture in the target. It is important to emphasize that thiscircumstance is quite special to the dynamics of the hydrogenmolecule. Other hydrogen-rich materials are essentially impos-sible to use for this experiment because the energy differencesbetween different spin states of the hydrogen are always muchsmaller than 15meV and can therefore be excited by the incomingneutrons, leading to beam depolarization. At any finite tempera-ture the orthohydrogen fraction is nonzero in thermal equili-brium. To keep the orthohydrogen fraction low enough inequilibrium that the neutron spin flip scattering is negligible,the liquid temperature must be no higher than 17K as discussedbelow.To set the target dimensions, we modeled the transport of theneutrons in liquid parahydrogen using both the Monte CarloN-Particle (MCNP) general purpose transport code [24] developedby Los Alamos National Laboratory (LANL) and our own MonteCarlo code. The scattering kernel used in the calculationsreproduces the measured dynamic structure factor  d 2 s = d O dE   of liquid parahydrogen where it has been measured [25]. Thesecalculations were performed (a) to determine the optimumdimensions of the target and (b) to study the neutron depolariza-tion in the target at incident neutron energies ð Z 15meV Þ for thesmall fraction of the incident neutron energy spectrum which canexcite the parahydrogen molecule.As can be seen in Fig. 2, the neutron scattering cross-section, atenergies  E  n o 15meV, is much larger for orthohydrogen thanparahydrogen. So, in order to minimize the beam depolarizationin the target we need to suppress the orthohydrogen fraction. Atfinite temperatures there is a nonzero ortho-fraction producing asmall amount of depolarization. We calculate that one retains inthe NPDGamma target 98% of the incident neutron polarizationupon capture in the presence of a 0.2% orthohydrogenconcentration. Higher energy neutrons  ð E  n 4 15meV Þ  willundergo spin-flip scattering and will depolarize. We thereforeexpect the neutron polarization before capture to be high below15meV and to fall sharply above 15meV as spin-flip scatteringbecomes possible.Fig. 3(a) and (b) show a typical neutron spectrum as a functionof time of flight and energy, respectively, measured by the beammonitor (M2) located upstream near the LH 2  target.The cross-sections for spin-flip and non-spin-flip scatteringfrom a single isolated proton are [27]:  s noflip ¼ s c  þ 13 s i  and s  flip ¼ 23 s i , where  s c   and  s i  are the coherent and incoherentneutron scattering cross-sections. When coherent scattering isdominant, the depolarization is small. When incoherent scatter-ing is dominant, as it is for neutrons with  E  n 4 15meV onhydrogen, the beam is quickly depolarized. Although in theNPDGamma experiment almost all of the incoming neutrons arebelow the 15meV threshold, we performed Monte Carlo calcula-tions of the neutron polarization upon capture as a function of incident neutron energy for the higher energy neutrons toinvestigate what takes place in the high energy tail of the neutronspectrum in the target. The results are shown in Figs. 4 and 5. Theneutrons with energy greater than 15meV, which are susceptibleto depolarization quickly (within 1–2 collisions) lose enoughenergy in elastic scatterings that their kinetic energy falls below15meV, where they are safe from further depolarization beforecapture. In the incident energy range from 15 to 50meV, the E n  (meV)10 0 10 1 10 2    σ    (   b   ) 10 -1 10 0 10 1 10 2 Fig. 2.  Measured total scattering cross-sections for neutrons on liquid parahydrogen(circles) and neutrons on normal (75% ortho–25% para) hydrogen (stars) as a functionof neutron energy in meV. The solid line is the n–p capture cross-section. The cross-sectionshavebeentakenfromMCNPlibraries[24]whicharesameasinRef.[26].Since thecapturecross-section is small comparedto thescatteringcross-section,thepossibleeffect of neutron depolarization upon scattering must be carefully considered. The verylarge difference between the ortho- and parahydrogen cross-sections is exploited tomonitor the parahydrogen fraction in the target. S. Santra et al. / Nuclear Instruments and Methods in Physics Research A 620 (2010) 421–436   423  ARTICLE IN PRESS neutrons undergo on average one scattering event with a largeenergy loss that brings their final energy below 15meV, and sothe final polarization upon capture for this class of neutrons isclose to the theoretical extreme of    13 , that is the polarizationdecreases and is reversed. At yet higher energies where onescatters twice on average before falling below 15meV, thepolarization is positive again and down by another factor  13 . Thisis an approximate estimate of the spin flip dynamics as it treatsthe atoms in the molecule independently and so is expected to beaccurate only for scattering events from higher energy neutronswith large enough momentum transfer that the scatteringapproaches the impulse approximation limit and can thereforebe described accurately by neutron–atom collisions. It will fail tosome degree in the intermediate energy region where we haveapplied it, and more sophisticated calculations are necessaryusing the free rotor approximation for molecules in LH 2  (theYoung–Koppel model [28]). We did not pursue a more detailedtreatment of the depolarization process for purposes of our targetdesign for two reasons. As mentioned above and seen from thespectrum in Fig. 3, the fraction of the neutrons which have kineticenergy above 15meV is very small. In addition, the great majorityof the  g -rays from this small fraction of higher energy down-converted neutrons arrive before the neutron time-of-flight (TOF)window set by the data acquisition system, which starts at TOFvalue corresponding to 15meV neutrons.(b)  Target dimensions : The target dimensions can be roughlyestimated from the requirement that we want to stop and captureneutrons from a slow neutron beam of a few meV kinetic energy.The neutron transport in the parahydrogen target can be thoughtof as being composed of two steps: first the neutrons reach theequilibrium temperature with the liquid, and then they diffuse inthe target until they escape or capture. We can perform a crudeestimate of the target size as follows. The mean free path l ¼ 1 = n s s  for 4meV neutrons in parahydrogen is about 9cmwhere  n  is the number density of parahydrogen molecules, andone therefore expects the average number of collisions beforecapture,  N  ¼ s s = s a , to be about 2.5 for 4meV neutrons. Here,  s s and  s a  are the scattering and absorption cross-sections, respec-tively. The mean distance to capture is therefore  l  ffiffiffiffi  N  p  ¼ 14cm.However, this estimate does not include all of the dynamics of theprocess, such as the angular dependence of the scattering and theenergy transfer.The average scattering angle as a function of neutron energy isshown in Fig. 6. Monte Carlo simulations show that above 10meVthe average scattering angle varies from 75 1  to 60 1  as the energyincreases. The Monte Carlo calculations show that at above10meV, the incident neutron loses on average  34  of its initialenergy in the first collision in the target. So, after 1–2 collisionsthe average energy of the neutrons is below 15meV. When thisenergy is reached, the kinetic energy of the neutron is not far fromthat of the molecules in the target, and so one expects thesubsequent neutron motion to become isotropic. Below 15meV,the average number of scattering before capture is similar (seeFig. 2), and it varies slowly as a function of neutron energy for therange of incident neutron energies in the beam. We thereforeexpect that we will need to make the target about twice as long Time of flight (ms) 010203040    S   i  g  n  a   l   (  m   V   ) 0246810 En (meV) 010203040    S   i  g  n  a   l   (  m   V   ) 02468 15 meV Fig. 3.  A typical neutron signal as a function of (a) neutron time of flight and (b)neutron energy, measured by the beam monitor (M2) located upstream near theLH 2  target. The great majority of neutrons in the spectrum have energies belowthe 15meV threshold above which a neutron can excite the ground state of themolecule (parahydrogen) to the first excited state (orthohydrogen). E n  (meV) 050100150200    N  u  m   b  e  r 01234 Fig. 4.  Results of the Monte Carlo calculations for the average number of neutronscatters before capture (solid), scatters with final  E  n 4 15meV (dashed), andscatters that cause neutron spin flip (dotted). E n  (meV) 050100150200    P   n -1.0-0.50.00.51.0 Fig. 5.  Results of a Monte Carlo calculation for the average neutron polarizationupon capture as a function of incident neutron energy, assuming an initialpolarization of 1. The negative polarization region just above 15meV is caused byneutrons which convert parahydrogen molecule to orthohydrogen by flipping thespin of one of the hydrogen nuclei in the molecule and then capture beforescattering again. S. Santra et al. / Nuclear Instruments and Methods in Physics Research A 620 (2010) 421–436  424  ARTICLE IN PRESS along the beam direction as it is wide due to this ‘‘free streaming’’of the beam in the forward direction prior to the first scattering.These estimates are confirmed in simulations using MCNP,which was also used to determine the dependence of the fractionof the slow neutron capture as a function of the targetdimensions. Fig. 7 shows the fraction of incident neutrons thatcapture in a cylindrical target as a function of target length. Weassume a 10cm   10cm incident neutron beam with the energydistribution of the FP12 cold moderator and a beam phase spacedefined by full illumination of a supermirror neutron guide with m ¼ 3, which corresponds to the maximum transverse neutronvelocity on the guide surface of about 21m/s. Given the slow rateof increase of the capture efficiency of the target with theincreasing radius, we settled on a 13.5cm radius and a 30cmlength as the approximate design dimensions for the target. Forthis choice about 60% of the incident neutrons capture in thehydrogen. Of the neutrons that do not capture in the target, about10–15% backscatter or diffuse out the front of the target vessel, 5%are transmitted, and the rest leak out radially. These results forthe fraction of neutrons that capture in the liquid parahydrogentarget are consistent with the estimates described in the previousattempt to measure parity violation in the  ~ n þ p - d þ g  reactionperformed at the ILL  [29]. These approximately optimized designdimensions for a right circular cylinder target vessel were latermodified slightly as we changed the vessel to assume a moreelaborate shape with domed windows to strengthen the vessel forsafety purposes.(c)  Density fluctuations in LH   2  target  : To ensure that thestatistical sensitivity of the experiment is not compromised byextra noise due to density fluctuations in the target, we require aliquid target in which fluctuations in the pressure and tempera-ture of the LH 2  target are reduced to acceptable levels and bubbleformation is suppressed. Feedback loops can control the refrig-erator and therefore the target temperature to much higherprecision than required, and pressure gauges can easily sense anyunexpected instabilities such as Taconis oscillations from thermalgradients in the fill/vent line. The presence of bubbles on the otherhand are difficult to detect directly without introducing a designelement such as an optical viewport or sensor inside the LH 2 which compromises target safety.Bubbles are a concern both for possible increased systematiceffects due to extra small angle scattering and also for thepossibility of increased statistical noise in the  g -ray asymmetrymeasurement from density fluctuations.It is not easy to predict the density and size distribution of bubbles in a realistic target, which depends in detail on the size of temperature gradients, the nature of surface conditions, and theproperties of the liquid. Bubbles could in principle be measuredusing neutron transmission measurements, and in fact bubbles inboiling liquids have been measured in the past using slow neutrontransmission [30,31]. However, several things are known experi-mentally from the numerous studies that have been performed of bubble formation and dynamics in liquid helium for cryogenicengineering and in LH 2  for bubble chambers used in high energyphysics experiments [32–37]. It is known that the rate of production of bubbles typically increases exponentially for localheat fluxes beyond a certain nonzero critical threshold set bysurface-dependent effects, and so an isothermal target withnegligible heat influx should possess few if any bubbles beyondthose which might be bound to the internal surface upon initialfilling. LH 2  targets have been developed which are capable of absorbing up to 2kW of beam power while still maintainingdensity fluctuations small enough to successfully perform sub-ppm precision parity violation experiments in polarized electronscattering experiments [17,18,38,39] but this requires theelectron beam to be rastered across the target to avoid localboiling. Since the neutron beam itself deposits only about 1 m W of power into the target, the source of possible bubbles in our casehas to be from a critical heat flux sufficient for bubble nucleationon a surface seen by the target vessel, and so we can adoptsimpler methods to suppress bubbles in our target.To suppress external heat loads onto the target surface whichcan produce bubbles we minimize the heat flux into the targetvessel by covering the external surface of the target with highemissivity aluminum tape and surrounding the target vessel by acopper radiation shield that is cooled to 80–100K by twomechanical refrigerators to reduce the radiative heat load to alevel which is well below that needed for bubble formation. Thefill/vent line of the target is bent to avoid a direct line-of-sight forradiative heat from room temperature surfaces. We operate theliquid in a slightly superheated state to render the growth of anybubbles that might be nucleated thermodynamically unfavorable.We also incorporated in our target design the possibility of forcedsuperheating of the LH 2  by using heaters in the fill/vent line of thetarget at the liquid/gas phase boundary but did not need to usethis feature in the experiment since the required temperaturegradient was present without requiring the application of extraheat.Local density gradients near the window may also get induceddue to the microphonic effects as a result of window vibrations.The shape of the LH 2  vessel window makes it stiff and thusreduces the amplitudes of mechanical vibrations and, in addition,the window is in vacuum. Since the target vessel is coupled to the E n  (meV) 050100150200    θ    (   d  e  g   ) 060120180 Fig. 6.  Results of a Monte Carlo calculation for the average scattering angle of neutrons in parahydrogen as a function of neutron energy. L (cm) 30405060    F  r  a  c   t   i  o  n  c  a  p   t  u  r  e   d 0.00.51.0 Fig. 7.  Results of a Monte Carlo calculation for the fraction of neutrons captured inthe parahydrogen target as a function of the target length and radius of thecylindrical target; 10cm (open triangle), 15cm (open square), 20cm (open circle),25cm (filled square), and 30cm (filled circle). The incident beam size is 10cm  10cm. We chose a target radius of 13.5cm and length of 30cm for theexperiment. S. Santra et al. / Nuclear Instruments and Methods in Physics Research A 620 (2010) 421–436   425
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