PHYSICAL REVIEW C 81,025807(2010)
Production of radioactive isotopes through cosmic muon spallation in KamLAND
S. Abe,1 S. Enomoto,1,2 K. Furuno,1 Y. Gando, 1 H. Ikeda,1 K. Inoue,1,2 Y. Kibe, 1 Y. Kishimoto, 1 M. Koga,1,2 Y. Minekawa, 1 T. Mitsui,1 K. Nakajima,1,* K. Nakajima,1 K. Nakamura,1,2 M. Nakamura,1 I. Shimizu,1 Y. Shimizu, 1 J. Shirai,1 F. Suekane,1 A. Suzuki,1 Y. Takemot o, 1 K. Tamae,1 A. Terashima,1 H. Watanabe,1 E. Yonezawa,1 S. Yoshida,1 A. Kozlov,2 H. Murayama,2,3 4 4, 4 4 4, 4, 2,4 3 3 J. Busenitz, T. Classen, † C. Grant, G. Keefer, D. S. Leonard, ‡ D. McKee, § A. Piepke, T. I. Banks, T. Bloxham, 3 2,3 2,3 3, 3 3, 3 3 J. A. Detwiler, S. J. Freedman, B. K. Fujikawa, F. Gray, ! E. Guardincerri, L. Hsu, ¶ K. Ichimura, R. Kadel, 3 3 3 3 3,** 5 5, 5, C. Lendvai, K.-B. Luk, T. O’Donnell, H. M. Steiner, L. A. Winslow, D. A. Dwyer, C. Jillings, †† C. Mauger, ‡‡ R. D. McKeown,5 P. Vogel, 5 C. Zhang,5 B. E. Berger,6 C. E. Lane,7 J. Maricic,7 T. Miletic,7 M. Batygov,8 J. G. Learned,8 8 8 9 2,9 9 10, 11 11 S. Matsuno, S. Pakvasa, J. Foster, G. A. Horton-Smith, A. Tang, S. Dazeley, §§ K. E. Downum, G. Gratta, 11, 12 2,12 12 12 13 13 K. Tolich, !! W. Bugg, Y. Efremenko, Y. Kamyshkov, O. Perevozchikov, H. J. Karwowski, D. M. Markoff, W. Tornow, 13 K. M. Heeger,2,14 F. Piquemal,15 J.-S. Ricol,15 and M. P. Decowski2,16 (KamLAND Collaboration) 1Research Center for Neutrino Science, Tohoku University, Sendai 980-8578, Japan 2Institute for the Physics and Mathematics of the Universe, Tokyo University, Kashiwa 277-8568, Japan 3Physics Department, University of California, Berkeley and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 4Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA 5W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA 6Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA 7Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA 8Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA 9Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA 10Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA 11Physics Department, Stanford University, Stanford, California 94305, USA 12Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA 13Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA and Physics Departments at Duke University, North Carolina Central University, and the University of North Carolina at Chapel Hill 14Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA 15CEN Bordeaux-Gradignan, IN2P3-CNRS, and University Bordeaux I, F-33175 Gradignan Cedex, France 16Nikhef, Science Park 105, NL-1098 XG Amsterdam, The Netherlands (Received 1 July 2009; published 23 February 2010)
Radioactive isotopes produced through cosmic muon spallation are a background for rare-event detection in ν detectors, double-β-decay experiments, and dark-matter searches. Understanding the nature of cosmogenic backgrounds is particularly important for future experiments aiming to determine the pep and CNO solar neutrino fluxes, for which the background is dominated by the spallation production of 11C. Data from the Kamioka liquid-scintillator antineutrino detector (KamLAND) provides valuable information for better understanding these backgrounds, especially in liquid scintillators, and for checking estimates from current simulations based upon MUSIC, FLUKA,andGEANT4.Usingthetimecorrelationbetweendetectedmuonsandneutroncaptures,theneutron 4 1 1 2 production yield in the KamLAND liquid scintillator is measured to be Y (2.8 0.3) 10− µ− g− cm . n = ± × For other isotopes, the production yield is determined from the observed time correlation related to known isotope lifetimes. We find some yields are inconsistent with extrapolations based on an accelerator muon beam experiment.
DOI: 10.1103/PhysRevC.81.025807 PACS number(s): 96.50.S ,96.60. j, 24.10.Lx, 25.30.Mr − −
*Present address: Center of Quantum Universe, Okayama University, Okayama 700-8530, Japan. ** †Present address: Department of Physics, University of California, Present address: Department of Physics, Massachusetts Institute Davis, California 95616, USA. of Technology, Cambridge, Massachusetts 02139, USA. ‡Present address: Department of Physics, University of Maryland, ††Present address: SNOLAB, Lively, ON P3Y 1M3, College Park, Maryland 20742, USA. Canada. §Present address: Department of Physics, Kansas State University, ‡‡Present address: Subatomic Physics Group, Los Alamos National Manhattan, Kansas 66506, USA. Laboratory, Los Alamos, New Mexico 87545, USA. !Present address: Department of Physics and Computational §§Present address: Lawrence Livermore National Laboratory, Science, Regis University, Denver, Colorado 80221, USA. Livermore, California 94550, USA. ¶Present address: Fermi National Accelerator Laboratory, Batavia, !! Present address: CENPA, University of Washington, Seattle, Illinois 60510, USA. Washington 98195, USA.
0556-2813/2010/81(2)/025807(14) 025807-1 ©2010 The American Physical Society S. ABE et al. PHYSICAL REVIEW C 81,025807(2010)
I. INTRODUCTION Cosmic-ray muons and their spallation products are potential sources of background for neutrino detectors, double-β-decay experiments, and dark-matter searches, even when the detectors are deployed underground. Characterizing cosmic-ray-muon-induced backgrounds, particularly the sec- ondary neutrons and radioactive isotopes produced by muon- initiated spallation processes, is essential for interpreting these experiments. Liquid-scintillator detectors such as the KamLAND (Kamioka liquid-scintillator antineutrino detector), Borexino [1–3], CANDLES IV (calcium fluoride for studies of neutrino and dark matters by low-energy spectrometer) [4,5], SNO (Sudbury Neutrino Observatory) [6,7], LENS (low-energy+ neutrino spectroscopy) [8], and LENA (low-energy neutrino astronomy) [9]aredesignedtodetectlow-energyphenomena. FIG. 1. Schematic diagram of the KamLAND detector at the In an organic liquid scintillator (LS), energetic muons and Kamioka underground laboratory. subsequent showers interact mostly with 12C, the most abun- dant nucleus heavier than 1HintheLS,generatingneutrons protects the LS against the diffusion of ambient radon from and isotopes by electromagnetic or hadronic processes. The the surrounding components. The total volume of LS in the muon-initiated spallation of carbon targets is a matter of balloon is 1171 25 m3 as determined with flow meters ± primary interest. during the initial filling. The LS consists of 80% dodecane Isotope production by muon-initiated spallation has been and 20% pseudocumene (1,2,4-trimethylbenzene) by volume, studied by an earlier experiment [10]usingtheCERN and 1.36 0.03 g/liter of the fluor PPO (2,5-diphenyloxazole). ± 3 Super Proton Synchrotron (SPS) muon beam. The energy The density of the LS is 0.780 g/cm at 11.5◦C. The calculated dependence was studied with 100 and 190 GeV incident elemental composition of the LS is given in Table I. muons. The production yield at other energies is estimated Abuffercomprising57%isoparaffinand43%dodecane from these data by extrapolation, assuming a power-law oils by volume fills the region between the balloon and dependence on the muon energy. Direct measurements of the surrounding 18-m-diameter spherical stainless-steel outer the production yield by underground detectors such as the vessel to shield the LS from external radiation. The specific Mont Blanc liquid scintillation detector (LSD) [11], the INFN gravity of the buffer oil (BO) is adjusted to be 0.04% large-volume detector (LVD) [12], and Borexino [13]were lower than that of the LS. An array of photomultiplier tubes compared with calculations exploiting simulations based on (PMTs)—1325 specially developed fast PMTs masked to MUSIC [14], FLUKA [15,16], and GEANT4 [17,18]. Particular 17 in. diameter and 554 older 20-in.-diameter PMTs reused attention was paid to neutron production, since isotope pro- from the Kamiokande experiment [21]—are mounted on the duction measurements are difficult with the small scintillator inner surface of the outer containment vessel, providing 34% masses used in these detectors. KamLAND, owing to its larger photocathode coverage. During the period from 5 March 2002 mass— 1kilotonofLS—doesnotsufferfromthisdifficulty to 27 February 2003, the photocathode coverage was only 22%, and is well∼ placed to study a variety of isotopes of interest. This paper presents the neutron and isotope production rates TABLE I. Elemental composition of the KamLAND liquid in KamLAND from muon-initiated spallation based upon data scintillator. The hydrogen-to-carbon ratio was verified by ele- mental analysis ( 2%). The liquid scintillator contains traces collected from 5 March 2002 to 12 May 2007. The results ± are compared with simulations and other experiments. These of nitrogen and oxygen from its fluor, PPO (C15H11NO), and comparisons provide important information for validating dissolved gases. Measurements in similar liquid hydrocarbons Monte Carlo simulations. [19,20] indicate that the amount of dissolved nitrogen saturates at about 200–500 parts per million (ppm). The range of nitrogen composition values given in this table reflects the extreme cases of zero dissolved nitrogen gas to full saturation. The dissolved II. DETECTOR DESCRIPTION AND PERFORMANCE oxygen content of liquid scintillator taken from the center of KamLAND is located under the peak of Ikenoyama KamLAND was measured to be less than 3 ppm, which is (Ike Mountain, 36.42◦N, 137.31◦E), and the vertical rock insignificant compared to the oxygen contribution from PPO. overburden is approximately 2700 meters water equivalent (mwe). A schematic diagram of KamLAND is shown in Element Stoichiometry Number of targets Fig. 1.KamLANDconsistsofanactivedetectorregionof (per kiloton) approximately 1 kiloton (kton) of ultrapure LS contained in Hydrogen 1.97 8.47 1031 a13-m-diametersphericalballoonmadeof135-µm-thick Carbon 14.30 × 1031 transparent nylon-EVOH (ethylene vinyl alcohol copolymer) 4≡ 4 27 × 28 Nitrogen 1 10− to 6 10− 5 10 to 3 10 × ×4 × 27× composite film and supported by a network of Kevlar ropes. Oxygen 1 10− 5 10 In addition to providing containment for the LS, the balloon × ×
025807-2 PRODUCTION OF RADIOACTIVE ISOTOPES THROUGH ... PHYSICAL REVIEW C 81,025807(2010) since the 20-in. PMTs were not operated. A 3-mm-thick acrylic scintillation [25,26]andCherenkovradiation.Thescaleis barrier at 16.6 m in diameter helps prevent radon emanating adjusted so that Evis is equal to Edep for the 2.225-MeV γ ray from the PMT glass from entering the BO. The inner detector from neutron capture on 1H. The observed energy resolution is (ID), consisting of the LS and BO regions, is surrounded by 7.4%/√Evis(MeV) for the period without the 20-in. PMTs, ∼ a3.2-ktonwater-Cherenkovdetectorinstrumentedwith225 and 6.5%/√Evis(MeV) for the rest of the data. 20-in. PMTs. This outer detector (OD) absorbs γ rays and The∼ calibration sources are also used to determine system- neutrons from the surrounding rock and enables tagging of atic deviations in position reconstruction by comparison with cosmic-ray muons. the source’s known position. This comparison gives an average The KamLAND front-end electronics (FEE) system is position reconstruction uncertainty of less than 3 cm for events based on the analog transient waveform digitizer (ATWD) [22] with energies in the range 0.28 to 6.1 MeV. which captures PMT signals in 128 10-bit digital samples at intervals of 1.5 ns. Each ATWD captures three gain levels of aPMTsignaltoobtainadynamicrangefrom1photoelectron III. COSMIC-RAY MUONS (p.e.) to 1000 p.e. Each ATWD takes 27 µstoreadout, Adigitalmap[27]ofthetopologicalprofileofIkenoyama so two are attached to each PMT channel to reduce dead is shown in Fig. 2.TheverticaloverburdenatKamLANDis time. The FEE system contains discriminators set at 0.15 p.e. approximately 1000 m of rock, and the minimum overburden ( 0.3mV)thresholdwhichsenda125-ns-longlogicsignal corresponding to a nearby valley is approximately 900 m. to∼ the trigger electronics. The trigger electronics counts the Cosmic-ray muons are identified either by the large amount number of ID and OD PMTs above the discriminator threshold of scintillation and Cherenkov light detected by the ID PMTs, with a sampling rate of 40 MHz and initiates readout when the or by the Cherenkov light detected by the OD PMTs. Muons number of 17-in. ID PMTs above the discriminator threshold crossing the ID (ID muons)areselectedbyrequiringthatone (N )exceedsthenumbercorrespondingto 0.8MeV 17 of the following conditions was satisfied: deposited energy. The trigger system also issues independent∼ readout commands when the number of OD PMTs above (i) ID 10000 p.e. ( 30 MeV), L ! ∼ threshold exceeds a preset number. (ii) ID ! 500 p.e., and NOD ! 5, The energy can be estimated from the N parameter, L max where is the total light yield measured by the ID defined as the maximum value of N in a 200-ns period ID 17 17-in. PMTs,L and N is the number of OD PMTs with following the trigger command. However, the offline analysis OD signals above threshold. Approximately 93% of the ID muons takes full advantage of the information stored in the digitized PMT signals by identifying individual PMT pulses in the waveform information that is read out. The time and integrated 36.5 1600 area (called “charge”) are computed from the individual pulses. For each PMT, the average charge corresponding to a single p.e. is determined from single-pulse waveforms observed 1400 in low-occupancy events. The ID PMT timing is calibrated with light pulses from a dye laser ( 1.2-ns pulse width), injected at the center of the detector through∼ an optical fiber. 1200 The vertices of spatially localized low-energy (<30 MeV) 36.45 events are estimated by comparing calculated time-of-flights 1000 of optical photons from the hypothetical vertex to the measured arrival times at the PMTs in KamLAND. The reconstructed energies of events are calibrated with γ 800 sources: 203Hg, 68Ge, 65Zn, and 60Co; and with n γ sources: 241 9 210 13 +
Am Be and Po C[23]. These are deployed at (m) Altitude + + Latitude (deg) various positions along the vertical axis of the detector and 36.4 600 occasionally off the vertical axis within 5.5 m from the detector center [24]. Such calibrations cover energies between 0.28 and 6.1 MeV. The energy calibration is aided with studies 400 of background contaminants 40Kand208Tl, 212Bi 212Po, and 214Bi 214Po sequential decays, 12Band12Nspallation− products,− and γ ’s from thermal neutron captures on 1H 200 and 12C. 36.35 The visible energy Evis of an event is computed from the measured light yield. Specifically, Evis is the number of de- 0 tected p.e. after corrections for PMT variation, dark noise, solid 137.25 137.3 137.35 angle, shadowing by suspension ropes, optical transparencies, Longitude (deg) and scattering properties in the LS. The relationship between Evis and the deposited energy Edep of γ ’s, e±’s, protons, and α’s FIG. 2. (Color) Ikenoyama topological profile [27]. The black is nonlinear and modeled as a combination of Birks-quenched point near the center is the location of KamLAND.
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107 × 106 1 (a) 106 0.5 105 Light Yield (p.e.)
Light Yield (p.e.) 0 0 200 400 600 800 1000 1200 1400 104 Track Length in LS (cm) × 104 0 200 400 600 800 6 Impact Parameter (cm) (b) FIG. 3. (Color) Correlation between the light yield in the inner 4 detector and the shortest distance from the muon track to the KamLAND detector center (impact parameter). The vertical dashed 2 red line represents the boundary between the LS and BO at 650 cm.
Events located to the left of this boundary and above the horizontal Light Yield (p.e.) blue dashed line ( 4 104 p.e.) are designated as LS muons. 0 LID = × 0 200 400 600 800 1000 1200 1400 Track Length in BO (cm) satisfy the first selection criterion. The ID muon track is reconstructed from arrival times of the first-arriving Cherenkov FIG. 4. (Color) Correlation between the total light yield measured or scintillation photons at the PMTs. Since for relativistic by the ID 17-in. PMTs ( ID)andthemuontracklengthfor(a)muons L muons the wavefront of the scintillation light proceeds at the that pass through both the LS and BO regions and (b) muons that Cherenkov angle, and since muons generate enough light to pass through only the BO region. The red lines shows the fitted light yield per unit length of d S /dX 629 47 p.e./cm and generate photoelectrons in every PMT, by restricting the fit ( L )= ± d ˇ /dX 31 2p.e./cm. to the first-arriving photons both Cherenkov and scintillation ( LC )= ± photons can be treated identically. The observed muon track is then established by minimizing time-of-flight deviations We define an excess light yield parameter % , L from hypothetical muon tracks. The fit converges for 97% of d Cˇ d S all ID muon events. The majority of the events that are not % ID LBO L LLS L , (2) L = L − dX − dX reconstructed are believed to be multiple muons or muons ! " ! " accompanied by large electromagnetic or hadronic showers for the purpose of describing showering muons associated with for which the tracking model is not valid. secondary particles. Muons passing only through the BO produce mostly The LS muon rate is estimated by selecting muons with Cherenkov light, whereas muons passing through the LS > 4 104 p.e. and impact parameter <650 cm. The light generate both Cherenkov and scintillation light. Figure 3 ID Lyield cut× has a negligible inefficiency for LS muons, while the shows the correlation between the light yield ( )andthe ID impact parameter cut eliminates LS muons that reconstruct shortest distance between the reconstructed muonL track and outside the balloon because of the resolution of the fitter the center of KamLAND (impact parameter). The boundary algorithm. This provides the lower limit on the LS muon at 650 cm between the BO and LS regions is evident. The rate. An upper limit is established by removing the impact correlations between and the reconstructed muon track ID parameter cut and increasing the cut to >105 p.e. to length in the BO and LSL regions (L and L ,respectively) ID BO LS eliminate muons that pass through theL BO without transversing are plotted in Figs. 4(a) and 4(b).Alineartrend,corresponding the LS. This cut again has a small inefficiency for LS muons but to minimum ionizing muons, is apparent in both distributions. does not eliminate muons which shower in the BO. Averaging The slope of each line is the light yield per unit length in the the two measurements yields R 0.198 0.014 Hz, where respective material. In BO, where the light is predominantly µ the error estimate is dominated= by systematic± uncertainties Cherenkov, the light yield per unit length is found to be due to temporal variations, the difference between the two d /dX 31 2p.e./cm; the fit was restricted to path Cˇ measurements, and the presence of muon bundles, in which (lengthsL above)= 700± cm, since fits at shorter path lengths are multiple simultaneous muons may be tagged as single-muon complicated by the presence of PMTs which may obstruct events. Using the parametrization of Ref. [28], the effect some of the emitted light. In the LS, we obtain of muon bundles was estimated to be <5%. The muon rate corresponds to an integrated muon intensity of J d S ID LBO d Cˇ /dX µ L L − ( L ) 629 47 p.e./cm, (1) 5.37 0.41 m2 h 1,wheretheerrorincludesuncertaintiesin= dX = L = ± − LS the shape± of the LS volume but is dominated by the uncertainty 6 where d S /dX includes the Cherenkov light created in the in the muon rate. Using a cut of % > 10 p.e., which is LS. TheL muons in Fig. 4 generating light yields above the equivalent to a 3GeVthreshold,therateofshoweringmuonsL baseline linear trend are likely to involve secondary particles. in the LS is ∼0.03 Hz. It is possible that some atmospheric ∼ 025807-4 PRODUCTION OF RADIOACTIVE ISOTOPES THROUGH ... PHYSICAL REVIEW C 81,025807(2010)
350 TABLE II. Calculated Jµ and Eµ values for various rock types 300 using the simulation method from Ref. [33]. The range in values for Jµ and Eµ corresponds to varying the specific gravity of the rock from 250 2.65 to 2.75 g/cm3.Thegenericskarnisdefinedtobe70%graniteand 200 30% calcite (by weight) with the following properties: Z 10.22, A 20.55 a.u., and radiation length X 25.411 g/cm( )2.= 150 ( )= 0 =
Events/10 cm 100 2 1 Ikenoyama rock model Jµ (m h− ) Eµ (GeV) 50 0 Inishi rock 5.66–6.71 262–268 0 500 1000 Standard rock 4.95–5.83 256–262 Track Length in LS (cm) Generic skarn 4.90–5.82 254–260
FIG. 5. (Color) Distribution of muon track lengths in the This measurement 5.37 0.41 – KamLAND LS. The dashed blue line shows the expected linear ± distribution for a sphere of nominal volume, and the average track length in this case is 867 cm. The average muon track length measured IV. SPALLATION NEUTRON YIELD in the detector is 878 cm, in agreement with the value 874 13 cm calculated using the proper LS shape and muon angular distributions.± Most of the neutrons produced in the KamLAND LS are captured on hydrogen or carbon atoms. The capture cross neutrino interactions leak into the LS muon sample. However, section varies inversely with respect to velocity, and the mean an estimate with the neutrino flux from Ref. [29]andcross neutron capture time τn is constant with respect to energy. The t/τn 5 capture time (t) distribution is exponential, P (t) e− .A sections from Ref. [30]giveslessthan4 10− Hz from ∝ atmospheric neutrinos. The muon track length× distribution calculation using the elemental composition of the KamLAND is shown in Fig. 5.Themeasuredaveragetracklengthis LS given in Table I and the thermal neutron capture cross sections from Ref. [38]givesτn 206 µs. This calculation Lµ 878 cm, in agreement with the calculated value of = indicates that 99.5% of the neutrons= are captured on 1H, while Lµ 874 13 cm, where the nonspherical corrections to the 12 balloon= shape± and the muon angular distributions were taken the remainder are captured mostly on C. The probability for capture on the other isotopes in the LS, such as 13C, is 2 10 4 into account. × − The production yield of radioactive isotopes from muon- or less. initiated spallation is energy dependent. KamLAND does not Neutrons produced by muon-initiated spallation in the LS measure the muon energy, so it is estimated from simulation. can be identified by the characteristic capture γ rays. Figure 6 shows the Evis distributions in signal (150 %T < 1000 µs) There are previous estimates of the mean energy Eµ ranging " from 198 GeV [31]to285GeV[10,32]attheKamiokande, and background (4150 " %T < 5000 µs) coincidence win- dows following some muons, where %T (t tµ)isthetime KamLAND, and SuperKamiokande detectors. The authors of ≡ − elapsed since the muon’s passage. The Evis distribution clearly Ref. [33]madeadetaileddeterminationofJµ and Eµ using 1 MUSIC shows peaks from neutron captures on H(2.225MeV)and the muon simulation code ( )[14]totransportmuons, 12 generated according to the modified Gaisser parameterization C(4.9MeV),whicharenotevidentinthebackground. [34]sea-levelmuonfluxdistribution,throughadigitalprofile Figure 7 shows the %T distribution for events within the of Ikenoyama. Although this calculation reproduces the zenith and azimuthal angular distributions observed by KamLAND, n 1H 105 as shown in Fig. 10 of Ref. [33], it overestimates Jµ by 14% relative to this work. The calculation assumed a homogeneous 104 rock entirely of the Inishi type (see Table II of Ref. [33]forthe 3 chemical composition), but other rock types, such as granite, 10 n 12C limestone, and several types of metamorphic rock, are common 2 in Ikenoyama in unknown quantities [35]. Table II shows the 10 result of calculations of Jµ and Eµ using the same simulation Events/50 keV 10 method of Ref. [33]butforstandardrock[36,37]andgeneric skarn,agenericmixtureofrocktypesfoundinaskarn-type 1 mine like that of Ikenoyama. Here, generic skarn is defined to 12345678 be 70% granite and 30% calcite by weight. The Jµ values range 2 1 3 Visible Energy (MeV) from 4.90 m h− ,for2.75 g/cm specific gravity generic 2 1 3 skarn, to 6.71 m h− ,for2.65 g/cm specific gravity Inishi FIG. 6. Visible energy spectra of the events following muons rock, while Eµ varies from 254 to 268 GeV. The value of Jµ in the signal time window 150 %T < 1000 µs(crosses)com- 3 2 1 " for 2.70 g/cm specific gravity standard rock is 5.38 m h− , pared with background in the time window 4150 " %T < 5000 µs in excellent agreement with our measured value. The value (dashes). The low-energy tails in the n1Handn12Cpeaksarecaused of Eµ for this rock is 259 GeV. We take Eµ 260 8GeV, by the electronics effect discussed in the text. In the time window = ± 1 where the uncertainty is chosen to cover the full range for the 1300 " %T < 2150 µs (solid), there is a small n Hpeakwithoutthe various rock types. low-energy tail.
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The fit shown in Fig. 7 in the region %T ! 1300 µsresultsin 5 6 2 10 Nn (4.2 0.3) 10 and χ /d.o.f. 98/118. = ± × = The actual number of neutrons n produced by muon- N s initiated spallation is related to the fit result Nn by an µ efficiency )n, 104 Nn n , (4)
Events/10 N = )n which accounts for other neutron-eliminating nuclear reactions 12 103 such as C(n, p)andanetneutronlossattheLS-BO boundary. This efficiency is calculated using the MUSIC-based 500 1000 1500 2000 2500 muon simulation described in Sec. III and the GEANT4-based ∆T (µs) Monte Carlo of KamLAND described in Sec. VI A.Themuon simulation generates muons with a three-momentum distri- FIG. 7. (Color) Time difference between a muon and the neutron bution appropriate to the KamLAND site inside Ikenoyama. capture event, with the cuts 1.8 LS volume and with 1.8 V. SPALLATION ISOTOPE YIELD 5000 The method for determining the yields of spallation- 3 generated isotopes is similar to the neutron analysis described 4000 10 2 in Sec. IV.Spallation-generatedisotopesareidentifiedby Events/ms 3000 10 their decay time relative to their creation and by their 200 400 decay energy. The decay time, %T t t ,iscalculatedfor ∆T (ms) µ 2000 each event relative to all previous≡ muons.− Usually, several Total 12B different isotopes decay in a given time window. The number Events/0.5 MeV 1000 12N of each isotope produced, i ,isobtainedfromabinned N 9Li, 8He, 9C maximum likelihood fit [39]tothe%T distribution, using the 0 function 4 6 8 10 12 14 16 18 20 N i (t tµ)/τi Visible Energy (MeV) r(t) e− − rB , (6) = τ + i i # FIG. 8. (Color) Background-subtracted Evis spectrum where Ni is related to i by an event selection efficiency above 4 MeV. Signal and background events are taken from N ( i Ni /)i ), τi is the mean lifetime, and rB is a constant 2 " %T < 60 ms and 502 " %T < 560 ms, respectively. The rateN = of uncorrelated background events that are in accidental production rate of 12B(τ 29.1ms,Q 13.4MeV)isestimatedto 1 =1 = coincidence with muons. be 54.8 1.5 kton− day− , from fitting Eq. (6) to the %T distribution shown in± the inset. This fit has a χ 2/d.o.f. 509/495. The production In terms of i ,thespallationproductionyieldforisotopei 12 = is equal to N rate N(τ 15.9ms,Q 17.3MeV)isestimatedtobe2.2 1 = 1 = ± 0.5 kton− day− , from a similar fit to the %T distribution for i events with 14 " Evis < 20 MeV, where the higher Evis threshold is Yi N , (7) 12 = RµTLρLµ imposed to exclude B. where Rµ, TL, ρ,andLµ are defined as in Eq. (5). The 12 7 yields are calculated to be Y ( B) (42.9 3.3) 10− and spallation production rate for isotope i is equal to 12 7 1 = 1 2± × Y ( N) (1.8 0.4) 10− µ− g− cm .Theproduction = 12 ± × 12 1 i rates are R( B) 54.8 1.5andR( N) 2.2 0.5kton− Ri N , (8) 1 = ± = ± = ρVT TL day− . 3 where VT 1171 25 m is the target volume. = ± B. 8Li and 8B A. 12Band12N 8Li (τ 1.21 s, Q 16.0MeV)[41] β decay and 8B = = − 12 (τ 1.11 s, Q 18.0MeV)[41] β+ decay candidate events B(τ 29.1ms,Q 13.4MeV)[40] β−-decay and = = 12 = = are selected according to Evis and %T .TheinsetinFig.9 shows N(τ 15.9ms,Q 17.3MeV)[40] β+-decay candidate events are= selected via= cuts on E and %T .TheinsetinFig.8 the distribution of %T for all preceding muons for events with vis 4 E < 20 MeV and 0.6 %T < 10 s, where the lower shows the distribution of %T for events with 4 E < " vis " " vis limit on %T is chosen to exclude 9C, 8He, 9Li, and other 20 MeV and 2 %T < 500 ms. A binned maximum like- " isotopes with shorter lifetimes. Isotopes with longer lifetimes lihood fit to the %T distribution using Eq. (6), and including are roughly constant over the selected range of %T .Toavoid the long-lived isotopes 8He, 9Li, 9C, and 12Nascontaminants, alargeaccidentalcoincidencebackgroundfromuncorrelated yields N(12B) (5.94 0.10) 104 events with χ 2/d.o.f. = ± × = muons, all showering muons and a portion of nonshowering 509/495. Longer lived isotopes give roughly constant decay muons whose track is within 3 m of a 8Li or 8Bcandidate rates on this time scale and fit out as a component of rB . 8 are selected. Figure 9 shows the Evis distribution of Li and Asimilarfittothe%T distribution for events with 14 8 " Bcandidateeventswith0.6 " %T < 4.0saftersubtracting Evis < 20 MeV, where the higher Evis threshold is imposed background estimated from the range 10.6 %T < 14.0s. 12 12 2 " to exclude B, gives N( N) (2.8 0.3) 10 events. A 8 8 = ± × N( Li) and N( B) are determined from a simultaneous binned comparison with the predicted Evis spectrum is shown in maximum likelihood fit to the %T distribution and a chi-square Fig. 8.TheE spectra are predicted from the allowed 12B vis fit to the Evis distribution. The expected Evis spectra for and 12N β -decay spectra, taking into account the KamLAND ± KamLAND are calculated by convolving the β± spectra from 12 detector response, normalized to the observed N( B) and Refs. [42,43]withKamLAND’sdetectorresponse.Forthe 12 N( N). The detector response model includes the energy fit to the Evis distribution, the energy scale parameters are nonlinearities and boundary effects described in Sec. II. constrained to an allowed region determined by a prior fit to 12 12 12 The inefficiency in identifying Band Ncandidates γ -ray calibration data (described in Sec. II)andthe BEvis is dominated by the Evis cut. The efficiencies calculated by distribution in Fig. 8. integrating the predicted Evis spectra over the selection win- The efficiency is given by the product of )E for the dow give )(12B) (82.9 0.7)% and )(12N) (9.3 1.6)%, E selection and ) for the muon-8Li or muon-8Bspatial = ± = ± vis S where the errors come from the uncertainty in the detector correlation. By integrating the expected spectra over 4 " 8 8 response. Using Eq. (7), the resultant isotope production Evis < 20 MeV, )E( Li) and )E( B) are estimated to be 025807-7 S. ABE et al. PHYSICAL REVIEW C 81,025807(2010) 3500 × 103 -1 10 (a) -1 (b) 3000 15 15 9 day day -1 2500 -1 8 10 10 Events/0.1 s 2000 2 4 6 8 10 ∆T (s) B kton 5 B kton 5 8 1500 8 Total 1000 8Li Events/1.0 MeV 0 0 8 0 5 10 15 0 5 10 15 500 B 8Li kton-1day-1 8Li kton-1day-1 0 468101214161208 FIG. 11. (Color) Allowed regions for the production rates of 8Li Visible Energy (MeV) and 8B from the combined fits of the energy spectra and the %T distributions at 1σ ,2σ ,and3σ C.L. for (a) showering muons (% > 6 6 L FIG. 9. (Color) Background-subtracted Evis spectrum above 10 p.e.) and (b) nonshowering muons (% < 10 p.e.) with %L < L 4 MeV, where signal and background events are taken from 0.6 " 3 m track cut. The black points indicate the best-fit parameters. %T < 4.0sand10.6 " %T < 14.0 s, respectively. The production rates of 8Li (τ 1.21 s, Q 16.0MeV)and8B(τ 1.11 s, = = = 1 Q 18.0MeV)areestimatedtobe15.6 3.2and10.7 2.9 kton− does not include the uncertainties in the muon track and the =1 ± ± day− , respectively, from simultaneously fitting the Evis spectrum and isotope decay vertex reconstruction; it is only used to study the %T distribution shown in the inset. The fit to the %T distribution the isotope dependance of )S .Therangeofvaluesof)S from has a χ 2/d.o.f. 95/91. FLUKA for different spallation isotopes is used to estimate the = 12 systematic error that should be added to )S( B) in order to obtain a common )S for all spallation isotopes. The resulting 8 (77.6 0.9)% and (88.4 0.7)%, respectively. For showering value, )S (91.6 8.4)%, is used for estimating the Li and ± ± 8 = 9± 8 9 muons, )S is 100% because no correlation requirement is B(and,laterthe C, He, and Li) yields. imposed. For nonshowering muons, )S is estimated from the Combining the above analyses, we obtain Y (8Li (12.2 12 12 7 8 7 1 = 1 ±2 Band Nanalysis(Sec.VA), and the systematic error 2.6) 10− and Y ( B (8.4 2.4) 10− µ− g− cm . arising from variations between isotopes is estimated with The× isotope production= rates are± R(8×Li) 15.6 3.2and 8 1 1 = ± a FLUKA simulation. Figure 10 shows the impact parameter R( B) 10.7 2.9kton− day− .Thecontourplotsin (%L) distribution for the 12Band12Ncandidateeventsfor Fig. 11=show the± correlation between 8Li and 8B. Due to their nonshowering muons (% < 106 p.e.). We find that (91.6 similar lifetimes, 8Li and 8Bareidentifiedprimarilybytheir L ± 4.3)% of the candidates are within 3 m of the muon track. This energy spectra. 12 fraction is the value of )S ( B) for %L < 3m. 8 8 To obtain )S ( Li) and )S( B), an additional correction for the difference between the muon-8Li or -8Bandthemuon-12B C. 8He and 9Li spatial correlations is applied. This correction is derived from 8 9 the FLUKA simulation described in Sec. VI B.Thesimulation He (τ 171.7ms,Q 10.7MeV)[41]and Li (τ 257.2ms,Q= 13.6MeV)[=41] β -decay candidate events are= = − selected according to the cuts 1 " Evis < 13 MeV and %T < 10 s, and by the detection of a neutron following the β−-decay 103 event. 8He decays to neutron-unstable excited states of 8Li with a(16 1)% branching ratio [41], and 9Li decays to neutron- ± 9 102 unstable excited states of Be with a (50.8 0.9)% branching ratio [41]. The neutron is identified by the± 2.225-MeV γ ray from radiative capture on 1H(1.8 E < 2.6MeV).Theγ 10 " vis ray is required to be within 200 cm and 1.0 ms of the 8He Events/10 cm 9 8 9 or Li β−-decay candidate. Finally, the He- Li analysis is 1 performed using a 5.5-m-radius spherical fiducial volume to reduce the number of accidental coincidences between the -1 10 0 200 400 600 800 1000 1200 1400 β−-decay candidate and external γ -ray backgrounds near the balloon. Distance from Muon Track (cm) The inset in Fig. 12 shows the %T distribution for the FIG. 10. (Color) Impact parameter distribution for events identi- events that satisfy the criteria outlined above. Figure 12 also fied as 12B (blue points) and neutrons (black histogram) produced shows the residual Evis distribution corresponding to the sub- by muon-induced spallation. Only nonshowering muons (% < traction of a background spectrum in the 5.002 " %T < 6s 106 p.e.) were used to make this plot. The efficiencies forL the window from a signal in the 0.002 " %T < 1swindow.The 8 9 %L < 3 m track cut (represented by the vertical dashed line) are expected Evis distributions for He and Li are calculated by evaluated to be (91.6 4.3)% from 12Bevents,and(95.9 0.7)% incorporating the KamLAND response and adjusting for the from neutron events. ± ± energy deposited by the thermalizing neutron from 8He or 9Li 025807-8 PRODUCTION OF RADIOACTIVE ISOTOPES THROUGH ... PHYSICAL REVIEW C 81,025807(2010) 300 2.5 2.5 3 -1 10 -1 (a) (b) 250 2 2 day day -1 200 102 -1 1.5 1.5 Events/0.1 s 0 2 4 6 8 10 1 1 150 ∆T (s) He kton He He kton He 8 Total 8 0.5 0.5 100 9Li Events/1.0 MeV Events/1.0 0 0 50 8He 0123 0123 9Li kton-1day-1 9Li kton-1day-1 0 246810121416 FIG. 13. (Color) Allowed regions for the production rates of 9Li Visible Energy (MeV) and 8He from the combined fits of the energy spectra and the %T distributions at 1σ ,2σ ,and3σ C.L. for (a) showering muons (% > 6 6 L FIG. 12. (Color) Background-subtracted Evis spectrum above 10 p.e.) and (b) nonshowering muons (% < 10 p.e.) with %L < L 1 MeV, where signal and background events are taken from 0.002 " 3 m track cut. The black points indicate the best-fit parameters. %T < 1sand5.002 " %T < 6s,respectively.Detectionofa neutron capture following a β decay is required to select events previously described analyses. This constraint includes the 9 from the β− n decay mode. The branching ratios for Li and 8 8 + correlation between Li and BshowninFig.11.Byintegrat- 8He are (50.8 0.9)% and (16 1)%, respectively. The production 9 ing the theoretical C Evis spectrum, we obtain the efficiency 8 ± ± 9 rates of He (τ 171.7ms,Q 10.7MeV)and Li (τ 257.2ms, for the 12 E < 20 MeV cut of )(9C) (7.2 1.0)%. = = = 1 " vis Q 13.6MeV)areestimatedtobe1.0 0.5and2.8 0.2kton− Combining this with the above results gives=Y (9C) ± (3.0 =1 ± ± day− , respectively, from simultaneously fitting the Evis spectrum and 7 1 1 2 9 = ±1 1.2) 10− µ− g− cm and R( C) 3.8 1.5kton− the %T distribution shown in the inset. The fit to the %T distribution day ×1. = ± has a χ 2/d.o.f. 95/97. − = decay. N(8He) and N(9Li) are determined from a simultaneous E. 11C binned maximum likelihood fit to the %T distribution and a 11 chi-square fit to the E distribution. For the fit to the E The production of C(β+ decay, τ 29.4min,Q vis vis = = distribution, the uncertainty in the energy scale parameters are 1.98 MeV) [40]throughmuon-initiatedspallationisusually treated in the same manner as the 8Li-8Banalysisdescribedin accompanied by a neutron, allowing identification by the triple Sec. VB. coincidence of the primary muon, the spallation neutron, and 8 9 11 The procedure for calculating the He and Li selection the subsequent β+ [13,45]. The C β+ decays are selected 8 8 efficiency is the same as for the Li and Befficiency in the range 1.4 " Evis < 2.0MeVandareprecededbya analysis (Sec. VB), except for the correction for the neutron detected muon that is accompanied by at least one neutron detection requirement, which is calculated with the GEANT4- capture, identified by the 2.225-MeV γ ray from capture based Monte Carlo simulation described in Sec. VI A.The on 1H. The γ ray is required to be in the time window resultant efficiencies )(8He) (14.9 1.0)% and )(9Li) 10 " %T < 2500 µsrelativetothemuon.Toreducethe (46.1 1.1)% include the appropriate= ± β-n branching frac-= ± tions. Since a reduced volume is used in this analysis, the 1.6% 200 × 102 fiducial volume uncertainty from Ref. [44]isincludedinthe 8 above efficiencies. The resulting yields are Y (8He) (0.7 7 7 9 7 1 = 1 ±2 150 0.4) 10− and Y ( Li) (2.2 0.2) 10− µ− g− cm . 6 8 9 × = ± × Events/0.1 s The production rates are R( He) 1.0 0.5andR( Li) 5 1 1 = ± = 100 2 4 6 8 10 2.8 0.2kton− day− .ThecontourplotsinFig.13 show the ∆T (s) correlation± between 9Li and 8He. Total 9C 50 8 9 Events/0.5 MeV Li, Li 8B D. 9C 0 The inset in Fig. 14 shows the %T distribution for all events 12 13 14 15 16 17 18 19 20 with visible energy 12 " Evis < 20 MeV. The analysis region 9 Visible Energy (MeV) (0.2 " %T < 0.6s)containseventsfrom C(τ 182.5ms, Q 16.5MeV)[41] β decay. N(9C) is determined= from + FIG. 14. (Color) Background-subtracted Evis spectrum above asimultaneousbinnedmaximumlikelihoodfittothe= %T 12 MeV, where signal and background events are taken from 0.2 " distribution and a chi-square fit to the Evis distribution. The %T < 0.6sand10.2 " %T < 10.6s,respectively.Theproduction uncertainty in the energy scale parameters are treated in the rate of 9C(τ 182.5ms,Q 16.5MeV)isestimatedtobe3.8 1.5 8 8 1 1= = ± same manner as the Li- BanalysisdescribedinSec.VB. kton− day− from a simultaneous fit to the Evis spectrum and the %T In this fit, 8Li, 8B, and 9Li are treated as possible contaminants, distribution shown in the inset. The fit to the %T distribution has a the amounts are constrained to the values obtained in the χ 2/d.o.f. 97/96. = 025807-9 S. ABE et al. PHYSICAL REVIEW C 81,025807(2010) 6000 200 × 103 5 5000 2 4 10 3 150 4000 10 Events/5 s Events/5 min 100 200 300 100 200 300 3000 ∆T (min) 100 ∆T (s) 11 C 10 2000 C Events/0.05 MeV Events/0.05 Events/0.1 MeV 50 1000 0 0 1.4 1.5 1.6 1.7 1.8 1.9 2 2 2.5 3 3.5 4 Visible Energy (MeV) Visible Energy (MeV) FIG. 15. (Color) Background-subtracted Evis spectrum above FIG. 16. (Color) Background-subtracted Evis spectrum above 1.4 MeV, where signal and background are selected from 5 %T < " 2MeV,wheresignalandbackgroundareselectedusing10" %T < 90 min and 185 " %T < 270 min, respectively. The production rate 90 s and 190 %T < 270 s, respectively. The production rate of 11 " of C(τ 29.4min,Q 1.98 MeV) is estimated to be 1106 178 10C(τ 27.8s,Q 3.65 MeV) is 21.1 1.8kton 1 day 1,as 1 = 1 = ± − − kton− day− by fitting Eq. (6) to the %T distribution shown in the determined= by fitting= Eq. (6) to the %T distribution± shown in the 2 inset. The fit to the %T distribution has a χ /d.o.f. 76/57. inset. The fit to the %T distribution has a χ 2/d.o.f. 80/56. = = background, a 7-m-diameter fiducial volume is used. To avoid inefficiencies from run boundaries and the long lifetime of usually accompanied by a neutron, so the selection criterion 11 C, the first 5 h of the typically 24-h-long run are not used in requiring a triple coincidence of the primary muon, the 11 11 the selection of the Ccandidates.Thenumberofmuon- C neutron, and the 10Ccandidateisused.Theneutronisidentified coincidences is extracted from the %T distribution for all by the 2.225-MeV n 1Hcaptureγ ray. The number of events that meet the criteria, shown in the inset of Fig. 15. 10CcandidatesisdeterminedfromfittingEq.(+ 6)tothe%T The efficiency determination takes into account the visible distribution for all events identified as 10C, shown in the inset energy range for 11C β decay, (22.7 3.6)%, and the 11 10 + ± in Fig. 16. Be is a potential background for this Canalysis, previously discussed neutron detection efficiency (Sec. IV). but the correction to the 10C yield is estimated to be less than 11 The efficiency also takes into account a correction for C 1% because of the low 11Be production rate and the neutron production modes, designated invisible modes,whichdonot coincidence requirement. The efficiency for the visible energy produce neutrons [13,45]. To measure this correction, muon- cut 2.0 E < 4.0MeVis(73.5 3.2)%. The visible 11 " vis Ceventpairswereselectedwithandwithouttheneutron mode efficiency is ) (90.7 5.5)%± after correcting for 11 vis requirement for a subset of the data where the Ccandidateis the electronics effects following= ± muons. The final efficiency required to be within 50 cm of the muon track; restricting the is (89.6 5.5)%. The resulting isotope yield is Y (10C) study to a subset of the data mitigated the reduced signal- ± 7 1 1 2 = (16.5 1.9) 10− µ− g− cm ,andtheproductionrate to-background ratio associated with relaxing the neutron 10± × 1 1 is R( C) 21.1 1.8kton− day− . requirement. The number of muon-11Ccoincidencesineach = ± case was extracted from a fit of Eq. (6)tothecorresponding %T distribution. The visible mode efficiency )vis,takenas the ratio of the number of muon-11Cpairswithoneormore G. 11Be 11 11 neutrons to the number of muon- Cpairswithouttheneutron The Be β−-decay (τ 19.9s,Q 11.5MeV)[40] requirement, is (88.4 2.4)%. Applying the correction for events are selected according= to 5.5 E =< 16.0MeV.The ± " vis post-muon electronics effects, the visible mode fraction is Evis cut efficiency is 63.4%. The inset in Fig. 17 shows the (96.3 2.0)%, consistent with Ref. [45], which obtains )vis %T distributions for the events only after showering muons. ± = 95.6% for 285-GeV muons. For nonshowering muons, a tighter muon track cut %L < 1m Due to the relatively long 11Clifetime,wealsoconsidered is applied in order to reduce the background rate. The track the effect of diffusion. An analysis of 222Rn that was acci- cut efficiency is estimated from the 12Bcandidatesusingan dentally introduced into the center of KamLAND during the analysis similar to that in Sec. VB.Theresultingisotopeyield 11 7 1 1 2 deployment of a calibration device shows that the diffusion is Y ( Be) (1.1 0.2) 10− µ− g− cm ,andproduction 11= ± × 1 1 speed is approximately 1 mm/h. From this study, the effect rate is R( Be) 1.4 0.3kton− day− . of 11Cdiffusionontheefficiencyisestimatedtobelessthan = ± 0.5%. Combining this with the above results gives Y (11C) 7 1 1 2 11 = (866 153) 10− µ− g− cm and R( C) 1106 ± 1 × 1 = ± VI. MONTE CARLO SIMULATIONS 178 kton− day− . The GEANT4andFLUKA simulations are used to reproduce F. 10C the measurements from KamLAND. While GEANT4isused 11 10 As with C, the production of C(β+ decay, τ 27.8s, only to simulate neutron production, both neutron and light Q 3.65 MeV) [41]throughmuon-initiatedspallationis= isotope production are tested with FLUKA. = 025807-10 PRODUCTION OF RADIOACTIVE ISOTOPES THROUGH ... PHYSICAL REVIEW C 81,025807(2010) 50 e+ is the prompt signal, and the γ ray from neutron capture is 70 the delayed signal and therefore a potential background. These 60 40 50 neutrons are also a background for dark-matter experiments 40 that employ nuclear recoils as a detection method. 30 Events/4 s 30 The primary purpose of this Monte Carlo simulation is 50 100 150 20 ∆T (s) to estimate the rate of untaggedfastneutrons,i.e.,neutrons 11Be produced by muons where the muon is undetected by the 10 KamLAND ID. A few of these muons are detected by the OD, Events/0.5 MeV 0 either from the Cherenkov radiation produced by the muon itself (tracked muons), or by accompanying electromagnetic -10 and hadronic showers that enter the OD (untracked muons). A 6 8 10 12 14 prompt signal in coincidence with these tracked and untracked Visible Energy (MeV) muons followed by a delayed capture γ signal identifies candidates for untagged fast neutrons. FIG. 17. (Color) Background-subtracted Evis spectrum above 5.5 Fast neutrons generated by untracked muons are produced MeV for showering muons (% > 106 p.e.), where signal and primarily in the rock surrounding the OD, whereas fast L background are selected by 8 " %T < 60 s and 408 " %T < 460 neutrons from tracked muons are primarily produced in the s, respectively. The production rate of 11Be (τ 19.9s,Q water of the OD. It is shown in the Monte Carlo that the = =1 11.5MeV)forshoweringmuonsisestimatedtobe1.0 0.2kton− tracked and untracked muons give distinguishable OD visible 1 ± day− by fitting Eq. (6) to the %T distribution shown in the inset energy distributions. A comparison between Monte Carlo and (χ 2/d.o.f. 37/41). measurement of the distribution of the number of OD PMTs = with signals above threshold for tracked and untracked muons reveals a deficiency of fast neutrons from untracked muons, A. GEANT4 consistent with the underproduction of neutrons by GEANT4in GEANT4isawidelyusedtoolkitforperformingparticle concrete reported in Ref. [47]. tracking simulations on an event-by-event basis. A description Figure 18 shows the Evis distribution of the prompt events of the available physics processes included is given in from the Monte Carlo simulation of tracked and untracked Refs. [17,18]. Here we compare the GEANT4(version9.1) muons compared with the measured data. The measured data prediction for neutron yield by spallation with the results and the Monte Carlo simulation correspond to an equal live obtained in Sec. IV. We use the physics list QGS BIC, time exposure of 1368 days. Figure 19 shows the radial developed by the GEANT4grouptosupportthebinarycascade distribution of the prompt events relative to the KamLAND (BIC) model at lower energies (below 10 GeV for p and n,and center. Both the measured data and the GEANT4simulation below 1.2 GeV for π). This treatment is also appropriate for exhibit an exponential attenuation of the neutrons as they the simulation of interactions of nucleons and ions. At higher penetrate farther into the detector, with the simulation yielding energies, a quark-gluon string (QGS) model is applied for the an attenuation length of 69 2g/cm2,consistentwiththe hadronic interactions. Neutron elastic and inelastic interactions measurement 70 2g/cm2. ± below 20 MeV are described by a high-precision data-driven ± model (NEUTRONHP). The G4EMEXTRAPHYSICS physics list B. FLUKA is also used to model the photonuclear and muon-nuclear interaction processes, which dominate the neutron production FLUKA is a mature code that models nuclear and parti- by muons in the simulation. cle physics processes from thermal neutrons to heavy-ion To estimate the neutron production yield as a function of muon energy in GEANT4, monoenergetic muons of several energies are injected at the center of a generic hydrocarbon 90 Measurement block of thickness 40 m. The region more than 10 m away from 80 MC (tracked muon) the edges of the block is analyzed to avoid boundary effects. As 70 MC (untracked muon) shown later in Fig. 20,theneutronproductionyieldspredicted 60 by GEANT4aresystematicallylowerthanexperiment,withthe 50 exception of point (F) from the LVD [12]. These results are 40 consistent with previous work [46]. 30 AMonteCarlosimulationbaseduponGEANT4andMUSIC Events/7 MeV (described in Sec. III)isusedtostudyneutronsproduced 20 by muon-induced spallation in the material outside of the 10 KamLAND ID. Some of these neutrons have sufficient energy 0 0 100 200 300 400 500 600 700 to enter the ID, where they thermalize and capture. They can be Visible Energy (MeV) identified by the coincidence of a prompt signal (for example, from n p elastic scattering) and a delayed signal from the FIG. 18. (Color) Evis distribution of the prompt events from can- capture+γ ray. This is the same inverse β-decay reaction didates identified as neutrons produced by muon-induced spallation signature used for νe detection, νe p e n,wherethe in the material outside of the KamLAND ID. + → + + 025807-11 S. ABE et al. PHYSICAL REVIEW C 81,025807(2010) 10-3 Measurement (G) 2.5 ) MC (tracked muon) 2 MC (untracked muon) cm 2 -1 this meas. g 3 -1 (E) µ 1.5 (D) Events/m 1 -4 10 (F) 0.5 (B) 0 (C) 300 350 400 450 500 550 600 650 700 (A) Prompt Event Radius (cm) Neutron Production Yield ( Yield Production Neutron FIG. 19. (Color) Radial distribution (from the center of -5 KamLAND) of the prompt event from candidates identified as 10 0 100 200 300 400 500 neutrons produced by muon-induced spallation in the material outside Muon Energy (GeV) of the KamLAND ID. Assuming an exponential distribution, a fit to the measured data (red dashed lines) yields an attenuation length of FIG. 20. (Color) Neutron production yield in liquid scintillator as 70 2g/cm2. A similar fit to the Monte Carlo (black dotted lines) a function of muon energy. The red star point shows the KamLAND ± yields 69 2g/cm2. result, Y (2.8 0.3) 10 4 µ 1 g 1 cm2,for260 8GeV.Other ± n − − − points show= the results± from× experiments at (A) 20 mwe± [48], (B) 25 mwe [49], (C) 32 mwe [50], (D) 316 mwe [49], (E) 570 mwe [51], collisions [15,16]. It has been used previously to model (F) 3000 mwe [12], and (G) 5200 mwe [11]. The blue square and muon-initiated spallation in liquid scintillator [31,46,52,53]. green triangle show the GEANT4andFLUKA Monte Carlo predictions, We use FLUKA version 2006.3b to model neutron and light respectively, from monochromatic muon beams. isotope production from muon-initiated spallation in Kam- LAND. A 40-m-radius by 40-m-high cylinder of KamLAND liquid scintillator is used in the simulation; the concentric since µ− may capture, creating spallation products, while µ+ inner cylinder of 20-m radius and 20-m length is used for may not. This ratio, combined with the µ+ to µ− ratio at analysis. KamLAND, leads to a correction to the flux of 0.98 0.06 To estimate neutron production yield as a function of muon for light isotopes and 0.981 0.005 for neutrons. The reduced± ± energy in FLUKA,monoenergeticbeamsofµ− ranging from production yield due to averaging over the muon spectrum is 10 GeV to 350 GeV were simulated as in Refs. [31,46,52,53]. on average 0.92 0.02 for the light isotopes, which is slightly Care is taken not to double-count the neutrons involved higher than the correction± factor suggested by Ref. [10]. The in reactions like (n, 2n). The results of this simulation are results of the FLUKA simulations for KamLAND presented in included in Fig. 20.TheneutronproductionyieldofthisFLUKA Table V include these two corrections. simulation is 10% lower than previous work [31,46,52,53], but the power-law dependance on muon energy (Eα,where µ VII. DISCUSSION α 0.77) is consistent. Different scintillator compositions were= studied, but they could not explain the deficit. This deficit The isotope production yields from muon-initiated spalla- is insignificant compared to the discrepancy between these tion in a liquid-scintillator target were investigated at CERN by simulations and the data. earlier experiment [10]usingtheSPSmuonbeamwithmuon The production of light isotopes was studied in the same energies of 100 and 190 GeV. Based on those cross-section simulation. The results, including the primary production measurements and the predicted muon energy spectrum at the process and power-law exponent, are summarized in Table IV. KamLAND site, we calculated the isotope production rates For some isotopes, the primary production process is much by extrapolation, assuming a power law of the muon energy 12 α larger than any secondary processes, as in the case of B. For Eµ.ThemeanmuonenergyatKamLANDis260 8GeV,so other isotopes, the primary production process is only slightly KamLAND provides data to test the extrapolation± method at larger than the secondary processes, as is the case for 9Li. The this energy. isotopes produced primarily by γ interactions, 11Cand10C, The production yields for the isotopes from muon-initiated show the weakest dependence on muon energy. In comparison, spallation in KamLAND are provided in Table V.Onaverage, 12Nand13N, where the primary production mechanism is by p the yields from the showering muons ( 15% of all muons), interactions, show the strongest dependence on muon energy. whose excess light yield parameter [%∼,Eq.(2)] is greater 6 L The use of a monoenergetic µ− beam overestimates the than 10 p.e. ( 3 GeV), constitute (70 2)% of the yield from production of neutrons and light isotopes. Simulations using a all muons. The∼ production yield for 11±Cisthelargest,andits monoenergetic µ+ beam and a beam with the energy spectrum measured yield is larger than the FLUKA calculation by a factor from Ref. [33]werealsorun.Thesimulationsshowthat of 2. The Borexino Collaboration also reported a similar ∼ the production yield for µ+ relative to µ− is on average discrepancy [2,3], which is consistent with what is observed 0.96 0.01 for the light isotopes. This reduction is expected, in KamLAND. Some measured production yields, such as 8Li ± 025807-12 PRODUCTION OF RADIOACTIVE ISOTOPES THROUGH ... PHYSICAL REVIEW C 81,025807(2010) TABLE IV. Simulation of neutron and light isotope production in the KamLAND LS by muon-initiated spallation with FLUKA: the isotope production yield by monoenergetic (260 GeV) µ−; the ratio of the production yields by monoenergetic µ+ compared to µ−; the ratio of the production yields by a µ− spectrum that matches Fig. 6 (KamLAND curve) in Ref. [33]comparedwith α monoenergetic µ−; the power-law exponent for the production yield Y (E ) E from a fit to the yields from monoenergetic µ− µ ∝ µ with 10 " Eµ " 350 GeV; and the primary process for producing the isotope. The uncertainties are statistical. Simulated production yield Ratio of simulated production yields Power-law exp. Primary process 7 1 1 2 ( 10− µ− g− cm ) × µ+/µ− Spectrum/monoenergetic 1 12 n 2344 40.969 0.002 0.912 0.003 0.779 0.001 π − H, C 11C460.8 ± 1.70.971 ± 0.005 0.913 ± 0.006 0.703 ± 0.002 12C(+ γ,n) 7Be 116.8 ± 0.90.986 ± 0.011 0.945 ± 0.011 0.684 ± 0.004 12C(γ,nα) 10Be 44.63 ± 0.53 0.960 ± 0.018 0.891 ± 0.019 0.825 ± 0.007 12C(n, 3He) 12B30.85 ± 0.44 0.970 ± 0.021 0.936 ± 0.022 0.828 ± 0.009 12C(n, p) 8Li 23.42 ± 0.39 0.927 ± 0.026 0.936 ± 0.025 0.821 ± 0.010 12C(n, pα) 10 ± ± ± ± 12 C21.13 0.37 0.982 0.025 0.915 0.027 0.810 0.010 C(π +,np) 6He 13.40 ± 0.29 0.916 ± 0.035 0.918 ± 0.035 0.818 ± 0.013 12C(n, 2p3He) 8 ± ± ± ± 12 2 2 B6.40 0.20 0.996 0.045 0.915 0.050 0.804 0.019 C(π +, H H) 9 ± ± ± ± 12 3 Li 3.51 0.15 0.856 0.074 0.842 0.078 0.801 0.026 C(π −, He) 9 ± ± ± ± 12 3 C1.49 0.10 0.850 0.114 0.949 0.102 0.772 0.039 C(π +, H) 12N0.86 ± 0.07 0.963 ± 0.128 1.006 ± 0.120 0.921 ± 0.045 12C(p, n) 11Be 0.94 ± 0.08 0.842 ± 0.145 0.804 ± 0.161 0.753 ± 0.051 12C(n, 2p) 8 ± ± ± ± 12 He 0.35 0.05 0.964 0.200 0.576 0.372 0.926 0.078 C(π −,n3p) 13B0.31 ± 0.04 1.020 ± 0.197 1.062 ± 0.176 0.742 ± 0.075 13C(n, p) 15O0.05 ± 0.02 1.250 ± 0.379 1.635 ± 0.234 0.793 ± 0.244 16O(γ,n) 13N0.06 ± 0.02 1.500 ± 0.272 1.190 ± 0.401 1.120 ± 0.220 13C(p, n) ± ± ± ± and 10C, deviate significantly from estimates based on the muon-initiated spallation in liquid scintillator. The neutron muon beam experiment, indicating that perhaps estimation by production yield is evaluated to be Yn (2.8 0.3) 4 1 1 2 = ± × extrapolation is not sufficient. All isotope yields are consistent 10− µ− g− cm ,whichishigherthantheexpectation within an order of magnitude. from Monte Carlo simulations based on GEANT4 and FLUKA. Some isotope production yields are found to be inconsistent VIII. SUMMARY with extrapolations—based on a power-law dependance We have analyzed KamLAND data to measure production with respect to muon energy—of results from muon beam yields of radioactive isotopes and neutrons through experiments. TABLE V. Summary of the neutron and isotope production yields from muon-initiated spallation in KamLAND. The results of the FLUKA calculation include corrections for the muon spectrum and the µ+/µ− composition of the cosmic-ray muon flux. 7 1 1 2 Lifetime in Radiation energy Yield ( 10− µ− g− cm ) Fraction from showering µ (%) × KamLAND LS (MeV) This measurement Ref. [10] FLUKA calc. This measurement n 207.5 µs2.225 (capt.γ)–209713 2787 311 64 5 12 ± ± ± B29.1ms 13.4(β−)–27.8 1.942.9 3.3682 12 ± ± ± N15.9ms 17.3(β+)–0.77 0.08 1.8 0.47714 8 ± ± ± Li 1.21 s 16.0(β−α)1.9 0.821.1 1.412.2 2.66517 8 ± ± ± ± B1.11 s 18.0(β+α)3.3 1.05.77 0.42 8.4 2.47823 9 ± ± ± ± C182.5ms 16.5(β+)2.3 0.91.35 0.12 3.0 1.29132 8 ± ± ± ± He 171.7ms 10.7(β−γn)0.32 0.05 0.7 0.47645 9 1.0 0.3 ± ± ± Li 257.2ms 13.6(β−γn)3± .16 0.25 2.2 0.2776 11 $ ± ± ± C29.4 min 1.98 (β+)42168 416 27 866 153 62 10 10 ± ± ± ± C27.8s 3.65 (β+γ )5412 19.1 1.316.5 1.9766 11 ± ± ± ± Be 19.9s 11.5(β−) <1.10.84 0.09 1.1 0.27412 6 ± ± ± He 1.16 s 3.51 (β−)7.5 1.512.08 0.83 – – 7Be 76.9day 0.478 (EC γ )107± 21 105.3 ± 6.9– – ± ± 025807-13 S. 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