Measurements of the Neutron-Proton and Neutron-Carbon Total Cross Section from 150 to 800 keV B. H. Daub,1,∗ V. Henzl,1,† M. A. Kovash,2 J. L. Matthews,1 Z. W. Miller,2 K. Shoniyozov,2 and H. Yang2 1Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 2Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506 (Dated: January 29, 2013) There have been very few measurements of the total cross section for np scattering below 500 keV.InordertodifferentiateamongNN potentialmodels, improvedcrosssection databetween20 3 and600keVarerequired. WemeasuredthenpandnCtotalcrosssectionsinthisenergyregion by 1 transmission; a collimated neutron beam was passed through CH2 and C samples and transmitted 0 neutrons were detected by a BC-501A liquid scintillator. Cross sections were obtained with a 2 precision of 1.1-2.0% between 150 and 800 keV using ratios of normalized neutron yields measured with and without the scattering samples in the beam. In energy regions where they overlap, the n present results are consistent with existing precision measurements, and fill in a significant gap in a J thedata between En=150 and 500 keV. 8 2 I. INTRODUCTION However, the relevant data [3–6], plotted with the ENDf/B-VII.1 tabulation [2] in fig- ] x Nucleon-nucleon interactions and NN po- ure 1, reveal a lack of precise measurements e tentialmodelsareanimportantrepresentation between 150 and 500 keV. Previous measure- - l of the strong interaction and a component of ments all employed the method of neutron c u thetheoryofnuclei. Measurementsofthetwo- transmission to determine the total cross sec- n body interaction in pp and np reactions have tion,usingpolyethyleneandcarbonsamplesto [ been applied to studies of the structure and accountforthecarboncontributionandobtain dynamics of light nuclei as well as testing the the np crosssection. We focused on the range 2 v charge, spin, and isospin dependence of the between 150 and 800 keV, covering the region 3 strong nuclear force [1]. below 500 keV where there are very limited 0 Additionally, np scattering data are appli- data. 2 cable to the detection of neutrons in organic 2 scintillators below 2 MeV, where the primary . 1 mechanismfordepositingenergyinthescintil- II. EXPERIMENTAL PROCEDURE 1 latorisnpelasticscattering. Therefore,deter- 2 mining the efficiencyofa neutrondetectorus- 1 Wemeasuredthetotalcrosssectionforneu- ing either Monte Carlo or analytical methods : tron scattering from polyethylene and pure v requires accurate knowledge of the np elastic i cross section. Since the np → dγ cross sec- carbon samples using the method of neutron X transmission. The neutron beam were pro- tion is typically 5 ordersofmagnitude smaller r duced via the 7Li(p,n)7Be reaction, with a a than the elastic cross section in this energy 1.875 MHz pulsed proton beam produced by range [2], measurement of the total np cross the Van de Graaff accelerator located at the section effectively yields the elastic cross sec- University of Kentucky. The Q-value for this tion. reaction is -1.644 MeV [7]. The neutron pro- duction target was composed of 20 k˚A thick ∗ Electronic address: [email protected]; Currently LiF ona tantalumbacking;this thickness was atUniversityofCalifornia,Berkeley,Berkeley,CA chosensuchthat2.25MeVprotonswouldlose † Currently at Los Alamos National Laboratory, Los approximately 50 keV before exiting the tar- Alamos,NM get. Using a thin target limited the spread 2 FIG.1. Existingnptotalcrosssectionmeasurementsforneutronenergiesfrom150to800keV,measured by(squares)Frisch[3],(circles)Baileyet. al.[4],(triangles)Bretscheret. al.[5],and(diamonds)Clement et. al. [6] plotted with the ENDf/B-VII.1tabulation (solid line) from Hale et. al. [2]. where a sample was shifted by several cen- timeters off its centered position in the beam. These shifts did not produce any changes in theneutronyields,indicatingthattheneutron beam is confined to the central region of the samples. Previousexperiments[3,4],inwhich the beam profile was largerthan the detector, required an additional correction due to neu- trons produced at angles outside the detector acceptance which scattered into the detector. In our geometry, this correction was not re- quired. FIG. 2. Detectorand shielding configuration. The bombarding proton energies ranged from 2.00 to 2.55 MeV in 50 keV increments, yielding neutrons from 150 to 800 keV. This of neutron energies and reduced the back- spacing produced minimal overlap of neutron grounds. energies, especially above a proton energy of The neutrons were collimated by a copper 2.25 MeV. This resulted in an increase in the shield, with a 6.35 cm opening and 50.8 cm statistical uncertainty near neutron energies thickness. The beam was additionally defined of 650, 700, and 750 keV. For proton ener- by a wax collimator with an opening matched gies above 2.25 MeV (neutron energies above to that ofthe copper shieldandtapereddown 450 keV), a total of four hours of data were toa2.2cmopening. Thesamplewasplacedin taken at eachproton energy. For protonener- the beamline past this collimation. The neu- gies below 2.25 MeV (neutron energies below tronsweredetectedbya13.7cmdiameterBC- 450 keV) a total of eight hours of data were 501Aliquidscintillator,whichwashousedina takenateachprotonenergy. Theseadditional lead and wax shield, with a 4.4 cm lead lining statistics were collectedto compensate for the in the internal aperture and a 7 cm wax lin- decreasing 7Li(p,n)7Be cross section and the ing around the lead. The experimental setup increasing np total cross section. is shown in figure 2. The geometry of the col- Fourpolyethyleneandthreecarbonsamples limation resulted in a beam size smaller than were used, in addition to the empty position both the samples and the neutron detector. used to determine the yield with no sample in This was tested by performing several runs thebeam. Acaliperwasusedtomeasureeach 3 Material Nominal Thickness (cm) τ (g/cm2) CH2 0.5 0.479±0.003 CH2 1.0 0.959±0.006 CH2 2.0 1.93±0.01 CH2 3.0 2.91±0.02 C 3.1 4.89±0.02 C 4.6 7.24±0.03 C 6.1 9.42±0.04 FIG. 3. Neutron energy spectrum with a sulfur sample for Ep = 2.00 MeV. This corresponds to TABLE I. CH2 and C sample thicknesses. amaximumneutronenergyof230keV,andthere is a visible decrease in counts associated with the sulfur resonance at En =203 keV. target dimension with an uncertainty of 0.25 mm. The mass was determined with a scale to an accuracy of 10 mg. The polyethylene The neutron energy spectrum with a sulfur samples were rectangular prisms, with nomi- sample for Ep = 2.00 MeV is shown in fig- nal length and width of 7.6 and 5.1 cm, with ure 3. a thickness varying from 0.5 to 3.0 cm. The The data were recorded event by event, us- carbontargetswere cylindrical,with a diame- ing NIM and CAMAC electronics. The dead ter of 4.8 cm and a thickness varying from 3.1 time ranged from 5-40%, depending on the to 6.1 cm. The nominal thickness and areal event rate. density of each sample are given in table I. Approximately 30% of the transverse area of III. ANALYSIS eachsamplewasexposedtotheneutronbeam. The samples were mounted on a remotely- controlled wheel which could position up to We used pulse shape discrimination in the twelve samples in the neutron beam. Dur- neutron detector to separate neutrons and ing each two hour run, the wheel would au- γ-rays, thus significantly reducing the back- tomatically switch which target was in the ground. Thepulsesfromtheliquidscintillator beam at pre-programmed intervals, resulting weresplitandwererecordedinseparateADCs in a series of irradiations between one and usingalonggate(500ns)andashortgate(100 seven minutes long. Feedback signals from ns). The short-gated pulse height versus the the wheel indicated when samples were being long-gated pulse height is shown in figure 4. moved, and which sample was in the beam The upper and lower broad bands correspond at a given moment. By using these short to γ-rays and neutrons, respectively. They intervals, the yields from each irradiation of mergeatsmallpulse heights,where the differ- the samples could be compared under similar enceinthelongandshortportionsofthepulse beam conditions, eliminating potential varia- is too small to separate,but using a conserva- tions due to beam current fluctuations or the tivecutallowstheeliminationofallhigheren- condition of the LiF target. At each of the ergy γ-rays. Figure 5 shows the neutron time twelve positions, the samples were mounted of flight spectrum for E = 450 to 500 keV n ontoasmallerwheel. Wheninthe beamposi- withnoconditions(solid)andthe pulse shape tion,asecondmotorrotatedthissmallerwheel discrimination condition (dashed). The back- soastoaverageoverpossiblenon-uniformities ground outside the neutron peak (270-300ns) in thickness. is reduced by 75% while the neutron yield is Additionally, a sulfur sample was used to unaffected. Neutron yields were determined calibrate the neutron energy. With its multi- in 10 keV bins from 150 to 800 keV, and the pleresonancesinourenergyrange,wecanuse integrated live current was recorded for each the observed decreases in yield and the max- sample irradiation in order to normalize the imum neutron energy for each proton beam neutron yields. energy to calibrate the absolute time of flight. To extract a cross section from the yields 4 of the neutron detector efficiency nor the ab- solute beam flux. The proton beam current was integrated for each irradiation, and the dead time of the data acquisition system was precisely measured as a function of the event rate in order to determine the total live-time current. Thebackgroundsweredividedintotwocat- egories: the room background, which is inde- pendent of the time of flight, and the sample background, which is due to neutrons which scatter from the sample but are still detected. The room background can be measured from FIG.4. (Coloronline)NeutrondetectorADCout- thedatabyfittingtotheconstantbackground puts: short-gated pulse height versus long-gated outside the neutron time-of-flight peak. The pulseheight. Theupperbroadbandisγ-rays,the samplebackgroundwasdeterminedbyextrap- lower band is neutrons. olating to zero thickness. For each target, the cross sections measured at each energy were combined using a weighted average, in order to produce a single average cross section for the entire energy range. These average cross sectionswerethenplottedversustargetthick- ness and fitted with a linear function. The intercept of this linear function gave the aver- FIG.5. NeutrontimeofflightforEn=450to500 age cross section at zero target thickness. By keV with no conditions (solid line) and the pulse takingtheratioofthe averagecrosssectionat shapediscriminationcondition(dashedline). The zerothicknessandtheaveragecrosssectionfor γ-flash is visible at 10 ns, with the neutron peak each sample, we determine the correction for visible at 270-300 ns. With the pulse shape dis- thebackgroundduetotargetthickness. These crimination condition, the background is reduced corrections ranged from 0.3% for the thinnest by 75% outside theneutron peak. sample to 1.3% for the thickest sample. The corrected cross sections for each energy bin werethencombinedusing aweightedaverage. from each sample, we normalized the neutron yields by the proton beam current, 1 (Y/Q)out IV. RESULTS σ = ln , (1) C τ (Y/Q)C c 1 (Y/Q)out σ Our results are shown in figure 6a for the σp = τpln(Y/Q)CH2 − 2c, (2) np total cross section and in figure 7a for the nC total cross section. Existing np data [3–6] where τ and τ are the sample thicknesses and the ENDf/B-VII.1 [2] tabulation are also p c from table I, Y is the neutron yield, and Q is showninfigure6a,andexistingnCdata[8–10] the integrated live-time current. The carbon and the ENDf/HE-VI [11] tabulation are also contributionofthepolyethylenetargetsissub- shown in figure 7a. Figures 6b and 7b show tracted, and the uncertainty in the nC cross the difference between our experimental cross section is included in the total uncertainty in sections and the tabulations. Error bars are the np cross section. Due to the long lengths suppressed in the previous nC measurements of the CH chains, the variation of the hy- forclarityinthe plot; the uncertaintyinthese 2 drogen to carbon ratio from 2 is insignificant measurements is between 2.7% and 5%. compared to the other systematic uncertain- The total uncertainty in each of our mea- ties. These results do not require knowledge surements is in the range 1.1-2.0%. The sys- 5 FIG.6. (a)Resultsfor(filled circles) thenptotalcross section measurements forneutronenergies from 150 to 800 keV, plotted with ENDf/B-VII.1 tabulation (solid line) from Hale et. al. [2] and previously measured np cross sections from 150 to500 keV,measured by(squares) Frisch [3],(open circles) Bailey et. al.[4],(triangles)Bretscheret. al.[5],and(diamonds)Clementet. al.[6]. (b)Thedifferencebetween ourexperimental cross section and theENDf/B-VII.1 tabulation. Errorbars includethestatistical and systematicerrors addedin quadrature,alongwith thecontributionduetosubtractingtheexperimental nC cross section. tematic uncertainties included the measured V. DISCUSSION masses and dimensions of the samples, listed in table I, contributing 0.35%; the characteri- In order to connect our measurements to zationofthe beamandsystemdeadtime,con- NN potential models, we parameterize the s- tributing 0.5%; and the background determi- wave neutron-proton elastic scattering cross nation, contributing 0.5%. The statistical un- section, certaintywasoftheorderof0.4%. Theuncer- 3 1 tainties due to the target dimensions applied σ = σ + σ , (3) t s uniformlytoalldatapoints,whilethestatisti- 4 4 cal, beam, system dead-time, and background in terms of the triplet and singlet scatter- uncertaintiesweredeterminedforeachsample inglengthsa andenergy-dependenteffective t,s irradiation. ranges ρ (0,T): [12, 13] t,s 4π σ = , (4) d (a−1− 1ρ (0,T)p2)2+p2) d 2 d where the subscript d represents either t or s, ρ (0,T) is the energy-dependent effective d 6 FIG. 7. (filled circles) Results for the nC total cross section measurements for neutron energies from 150to800keV,plottedwiththeENDf/HE-VItabulation[11]andexistingdata,measuredby(squares) Huddleston et. al. [8], (open circles) Wilenzick et. al. [9], and (triangles) Uttley et. al. [10] Error bars are suppressed in the previous nC measurements for clarity in the plot. (b) The difference between our experimental cross section and the ENDf/HE-VI tabulation. Error bars include the statistical and systematic errors added in quadrature. range, and T and p are the center of mass fm and ρ (0,0) = 2.696 ± 0.059 fm. Also, s kinetic energy and momentum, respectively. the zero-energy shape dependence parameter Hackenburg [13] has recently revisited the ∆r =−0.025±0.025 fm. Hackenburg’s anal- t problem of determining the zero-energy cross ysis also concluded that additional total cross section and effective-range theory (ERT) pa- section measurements for np scattering be- rameters from data, including a considera- tween 20 and 600 keV were required in order tionofthecorrelationbetweenthe singletand tousetheparametersofeffectiverangetheory triplet effective range. Measurements of the to differentiate among NN potential models. zero-energy np cross section, σ0 [14, 15], and It was hoped that the present results in the the parahydrogen coherent scattering length, 150-600 keV energy range would reduce the ac [16, 17], given by uncertainties in the parameters determined from the fit to the ERT expression (Eq. 4) σ0 = π(3a2t +a2s), (5) for the cross section. Following Hackenburg’s a = 3a + 1a , method, we included our data in the fit. c 2 t 2 s Theresultingparameterswereconsistentwith were included in the fit due to correlation be- those determined by Hackenburg. The uncer- tween a and a . The ERT parameters result- tainties were not significantly reduced, as our s t ing from the fit were ρ (0,0) = 1.718±0.025 measurements were not precise enough to fur- t 7 ther constrain the parameters. According to data. The previous np data in this range also Hackenberg, a 0.004% precision measurement show a slight increase relative to the theoreti- at 130 keV is required to reduce the uncer- cal curve. tainty in ρ (0,0)and∆r to 0.001fm [13]. By However,whenthe presentdataareusedto t t instead measuring the energy dependence of trytoimprovethefitofeffectiverangetheory, the cross section, we estimate that a precision wefindthatourmeasurementsarenotprecise of 0.5% across the 150 to 800 keV range cur- enoughto increasethe precisiononthe result- rently measured is required to decrease these ing parameters. The effective range parame- uncertainties, and 0.1% measurements across ters ρ are most sensitive to measurements in d thisrangewilldecreasetheuncertaintyto0.01 the 20-600 keV region, but more precise data fm. athigherenergieshavealreadyconstrainedthe parameters more narrowly than the precision of current measurements in this region. The discrepancynotedpreviouslyiscomparableto VI. CONCLUSION thecurrentuncertainty,andsodoesnotsignif- icantly impact the determination of the ERT Our measurement of the np total scattering parameters. To be comparable to the current crosssectionhasfilledinalargegapintheto- uncertainty in ρ (0,0) and ∆r , 0.5% preci- t t tal cross section measurement below neutron sionwouldberequiredacrosstheenergyrange energies of 500 keV. By measuring ratios of measured here, 150 and 800 keV. This preci- transmittedeventswithandwithoutthe sam- sionisattainable withincreasedstatistics and ples in the beam, we were able to determine better characterization of the beam, both of the crosssectionindependently ofthe neutron which are possible with the current configura- detection efficiency. Both the np and nC to- tion. tal cross sections are consistent with previous measurements,andthenCresultsshowsignif- icantly decreased scatter and uncertainty. ACKNOWLEDGMENTS There is a slight systematic discrepancy be- tween our measurements and the ENDf tab- The authors would like to thank J. French ulations, with a −18 mb shift downward in for her work in the setup and running of the the nC crosssection, anda +136mb shift up- experiment. This work was supported by the wardinthenpcrosssection. Thisdiscrepancy United States Department of Energy, the Na- wouldnothavebeenvisibleinthepreviousnC tional Science Foundation, and the SSAA. [1] J.CarlsonandR.Schiavilla,Rev.Mod.Phys. [7] H.Liskien and A.Paulsen, AtomicData and 70, 743 (1998). Nucl.DataTables15,57 (1975),ISSN0092- [2] G. M. Hale and A. S. Johnson, in Proc. 640X. 17th Int. IUPAP Conf. on Few-Body Prob- [8] C.M.Huddleston,R.O.Lane,L.L.Lee,and lems in Physics, 5-10 June 2003, edited by F. P. Mooring, Phys. Rev.117, 1055 (1960). W. Gloeckle and W. Tornow (Elsevier B.V., [9] R. M. Wilenzick, G. E. Mitchell, K. K. Seth, Durham NC, 2004), pp.S120–S122. and H. W. Lewis, Phys. Rev. 121, 1150 [3] D.H. Frisch, Phys.Rev. 70, 589 (1946). (1961). [4] C. L. Bailey, W. E. Bennett, T. Bergstralth, [10] C. A. Uttley, Prog. 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