Integral measurement of the 12C(n, p)12B reaction up to 10 GeV

EPJ manuscript No. (will be inserted by the editor) Integral measurement of the 12C(n,p)12B reaction up to 10 GeV P. ˇ Zugec1,a, N. Colonna2, D. Bosnar1, A. Ventura3, A. Mengoni4, S. Altstadt5, J. Andrzejewski6, L. Audouin7, M. Barbagallo2, V. B´ecares8, F. Beˇcv´aˇr9, F. Belloni10, E. Berthoumieux11, J. Billowes12, V. Boccone13, M. Brugger13, M. Calviani13, F. Calvi˜no14, D. Cano-Ott8, C. Carrapi¸co15, F. Cerutti13, E. Chiaveri13, M. Chin13, G. Cort´es14, M.A. Cort´es-Giraldo16, L. Cosentino17, M. Diakaki18, C. Domingo-Pardo19, R. Dressler20, I. Duran21, C. Eleftheriadis22, A. Ferrari13, P. Finocchiaro17, K. Fraval11, S. Ganesan23, A.R. Garc´ıa8, G. Giubrone19, M.B.G´omez-Hornillos14, I.F. Gon¸calves15, E. Gonz´alez-Romero8, E. Griesmayer24, C. Guerrero13, F. Gunsing11, P. Gurusamy23, S. Heinitz20, D.G. Jenkins25, E. Jericha24, F. K¨appeler26, D. Karadimos18, N. Kivel20, M. Kokkoris18, M. Krtiˇcka9, J. Kroll9, C. Langer5, C. Lederer5, H. Leeb24, L.S. Leong7, S. Lo Meo3,4, R. Losito13, A. Manousos22, J. Marganiec6, T. Mart´ınez8, C. Massimi27, P. Mastinu28, M. Mastromarco2, E. Mendoza8, P.M. Milazzo29, F. Mingrone27, M. Mirea30, W. Mondalaers10, A. Musumarra31, C. Paradela10,21, A. Pavlik32, J. Perkowski6, A. Plompen10, J. Praena16, J. Quesada16, T. Rauscher33,34, R. Reifarth5, A. Riego14, F. Roman13, C. Rubbia13, R. Sarmento15, A. Saxena23, P. Schillebeeckx10, S. Schmidt5, D. Schumann20, G. Tagliente2, J.L. Tain19, D. Tarr´ıo21, L. Tassan-Got7, A. Tsinganis13, S. Valenta9, G. Vannini27, V. Variale2, P. Vaz15, R. Versaci13, M.J. Vermeulen25, V. Vlachoudis13, R. Vlastou18, A. Wallner32,35, T. Ware12, M. Weigand5, C. Weiß13, and T. Wright12 1Department of Physics, Faculty of Science, University of Zagreb, Croatia 2Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Italy 3Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Italy 4ENEA, Bologna, Italy 5Johann-Wolfgang-Goethe Universit¨at, Frankfurt, Germany 6Uniwersytet L´odzki, Lodz, Poland 7Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France 8Centro de Investigaciones Energeticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain 9Charles University, Prague, Czech Republic 10 European Commission JRC, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium 11 CEA/Saclay - IRFU, Gif-sur-Yvette, France 12 University of Manchester, Oxford Road, Manchester, UK 13 CERN, Geneva, Switzerland 14 Universitat Politecnica de Catalunya, Barcelona, Spain 15 C2TN-Instituto Superior Tecn´ıco, Universidade de Lisboa, Portugal 16 Universidad de Sevilla, Spain 17 INFN - Laboratori Nazionali del Sud, Catania, Italy 18 National Technical University of Athens (NTUA), Greece 19 Instituto de F´ısica Corpuscular, CSIC-Universidad de Valencia, Spain 20 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 21 Universidade de Santiago de Compostela, Spain 22 Aristotle University of Thessaloniki, Thessaloniki, Greece 23 Bhabha Atomic Research Centre (BARC), Mumbai, India 24 Atominstitut der ¨ Osterreichischen Universit¨aten, Technische Universit¨at Wien, Austria 25 University of York, Heslington, York, UK 26 Karlsruhe Institute of Technology (KIT), Institut f¨ur Kernphysik, Karlsruhe, Germany 27 Dipartimento di Fisica, Universit`a di Bologna, and Sezione INFN di Bologna, Italy 28 Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Italy 29 Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy 30 Horia Hulubei National Institute of Physics and Nuclear Engineering - IFIN HH, Bucharest - Magurele, Romania 31 Dipartimento di Fisica e Astronomia DFA, Universit`a di Catania and INFN-Laboratori Nazionali del Sud, Catania, Italy 32 University of Vienna, Faculty of Physics, Austria 33 Centre for Astrophysics Research, School of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, United Kingdom 34 Department of Physics, University of Basel, Basel, Switzerland ae-mail: [email protected] arXiv:1604.05749v1 [nucl-ex] 19 Apr 2016 2 35 Research School of Physics and Engineering, Australian National University, ACT 0200, Australia Received: date / Revised version: date Abstract. The integral measurement of the 12C(n,p)12B reaction was performed at the neutron time of flight facility n TOF at CERN. The total number of 12B nuclei produced per neutron pulse of the n TOF beam was determined using the activation technique in combination with a time of flight technique. The cross section is integrated over the n TOF neutron energy spectrum from reaction threshold at 13.6 MeV to 10 GeV. Having been measured up to 1 GeV on basis of the 235U(n,f) reaction, the neutron energy spectrum above 200 MeV has been reevaluated due to the recent extension of the cross section reference for this particular reaction, which is otherwise considered a standard up to 200 MeV. The results from the dedicated GEANT4 simulations have been used to evaluate the neutron flux from 1 GeV up to 10 GeV. The experimental results related to the 12C(n,p)12B reaction are compared with the evaluated cross sections from major libraries and with the predictions of different GEANT4 models, which mostly underestimate the 12B production. On the contrary, a good reproduction of the integral cross section derived from measurements is obtained with TALYS-1.6 calculations, with optimized parameters. 2 1 Introduction Neutron induced reactions are important for a variety of research fields, from fundamental Nuclear Physics and Nuclear Astrophysics to applications of nuclear technologies to energy production, nuclear medicine, material characterization, cultural heritage, etc. Neutron induced reactions on light nuclei – such as Carbon, Oxygen and Nitrogen – are of particular interest in nuclear medicine due to their high abundance in the human body. Particularly significant in this respect are the reactions leading to the emission of charged particles. Among them, the 12C(n,p)12B reaction – occurring at neutron energies above the threshold of 13.6 MeV – may affect the dose distribution in hadrontherapy or conventional radiotherapy if high energy secondary neutrons are produced during the treatment delivery, since the 12C(n,p)12B reaction leads both to the emission of protons and energetic electrons (6.35 MeV average energy) from the decay of 12B. This reaction is also important for calculations in radiological protection, as well as for the design of shields and collimators at accelerator facilities, spallation neutron sources and fusion material irradiation facilities – such as MTS and IFMIF – whose neutron spectrum shows an important tail extending above the threshold of this reaction [1]. Finally, the cross section of the 12C(n,p)12B reaction is important for accurately simulating the response of diamond detector to fast neutrons [2,3]. Despite their importance, cross section data for this reaction are scarce and largely discrepant. Figure 1 shows the current status of experimental results. Below 20 MeV four old measurements are present in literature [4,5,6, 7], all obtained with the activation technique, with short pulses of monoenergetic neutrons inducing the reaction, followed by long beam-off intervals for counting the 12Bβ- decay. Recently, Pillon et al. measured a series of neutroninduced reactions on carbon for neutron energies from 5 MeV to 20.5 MeV, by using a single crystal diamond detector [3]. The measurements were performed at the Van de Graaff neutron generator of the EC-JRC-IRMM, Geel, Belgium. Thanks to the high energy resolution of the device, structures related to various neutron-induced reactions on carbon could be distinguished in the detected energy spectrum. The cross section was extracted from the structures identified as due to the (n,p) reaction. The results, shown in fig. 1, are consistent with those of ref. [6]. However, according to the authors, not all possible excited states of the residual nucleus could be identified, thus resulting in an underestimate of the cross section. Above 20 MeV only one data point from Kellogg [8] is present in EXFOR, centered at 90 MeV, but with a poor resolution in energy and a large uncertainty in cross section. The discrepancy between existing data below 20 MeV, combined with the scarcity of reliable data above 20 MeV, is reflected in the differences between evaluated cross sections in various libraries, as well as in highly uncertain theoretical predictions at all neutron energies. The cross sections reported in the major libraries are shown in fig. 1. Up to 20 MeV the latest versions of all libraries contain the same cross section, based purely on the dataset from Rimmer and Fisher [6]. Among older versions, TENDL- 2009 predicts a cross section a factor of three higher than all other evaluations. For the reaction considered herein, this library was based on TALYS calculations [9]. On the other hand, a drastically lower evaluation is adopted by TENDL-2010 and subsequent versions. Above 20 MeV [MeV] n E 20 30 40 50 60 100 Cross section [mb] 0 10 20 30 40 50 60 70 ENDF/B-VII.1 TENDL-2009 TENDL-2010 JENDL/HE-2007 M. Pillon+, 2011 V.E. Ablesimov+, 1972 V.V. Bobyr+, 1972 E.M. Rimmer+, 1964 W.E. Kreger+, 1959 D.A. Kellogg, 1953 bla Fig. 1. Compilation of the available experimental and evaluated data on the 12C(n,p)12B reaction. 3 evaluations are based on theoretical estimates. In particular, ENDF/B-VII.1 has adopted calculations performed with the Feshbach-Kerman-Koonin (FKK)-GNASH code described in ref. [10], up to 150 MeV [11]. A completely different cross section, based on calculations by Watanabe et al., [12] is contained in the special high energy file of the Japanese evaluated nuclear data library, JENDL/HE-2007 [13,14]. Models can be used in the main Monte Carlo codes for neutron transport to estimate the cross section of this reaction. In particular, the GEANT4 package [15] offers various options for calculating the cross section of this reaction, from threshold to several GeV. However, the trends and values of the cross section largely vary, depending on the selected model (as shown in later fig. 4). While, in principle, these predictions can be checked against experimental data below 20 MeV, with the current status of data discrepancy it is practically impossible to decide which of the various options is more reliable in simulating this particular reaction in GEANT4 or in any other Monte Carlo code for neutron transport. Furthermore, due to the lack of experimental data, nothing can be said about the validity of the calculations at higher neutron energies. Considering the present status of experimental data, evaluated libraries and model predictions, new accurate data are highly desirable, covering a wide energy range extending from the reaction threshold to the GeV region. Time-of-flight facilities based on the spallation neutron sources could, in principle, be used to this purpose, with an experimental setup able to detect the emitted proton. In practice, however, such a measurement is complicated by the presence of other competing reaction channels, in particular elastic and inelastic scattering, (n,d) and (n,α) reactions [2]. A somewhat simpler, yet useful approach, would be to perform an integral measurement of the cross section by means of the activation technique with a pulsed neutron beam of a low repetition rate and with an energy spectrum extending much above the reaction threshold. Both requirements are met by the n TOF facility at CERN [16], characterized by a white neutron spectrum extending up to ∼10 GeV, and a low repetition rate (≤0.8 Hz). A new technique was applied at n TOF to extract an energy-integrated cross section. The measurement relied on the detection of the 12Bβ-decay within the same neutron bunch in which the reaction takes place. The main features of the measurement and its results have been reported in ref. [17]. The main aim of the measurement was to provide an information that could be used as a benchmark for validating the evaluated cross sections and the predictions of the model calculations. In this paper the technique and the analysis procedure are described in greater detail, with the result and its physical implications being discussed at length. The experimental result is compared with various models available in GEANT4, from which the information on the reliability of these models is obtained. Furthermore, it will be shown that the measured observable can be closely reproduced by calculations based on the TALYS code, with optimized parameters. The paper is organized as follows: the experimental setup is presented in Section 2, while the on-line activation technique and data analysis are discussed in Section 3. Section 4 describes the method used to estimate this cross section from GEANT4 simulations. Section 5 is dedicated to the comparison between the experimental result and the predictions of various models and evaluations. A comparison between the various experimental results and the optimized TALYS-1.6 calculations is shown in Section 6. Finally, Section 7 summarizes the main conclusions of this work. 2 Experimental setup The neutron beam at n TOF is produced by the protoninduced spallation in the massive Pb target. The pulsed beam of 20 GeV protons is provided by the CERN Proton Synchrotron, delivering an average of 7 ×1012 protons per pulse, with 7 ns spread, a repetition rate in multiples of 1.2 s and a typical average frequency of 0.4 Hz. On average, 300 neutrons are produced per incident proton. Spallation neutrons are moderated passing through the Pb block itself, through 1 cm of demineralized water and 4 cm of borated water surrounding the block. The borated water significantly suppresses the production of 2.2 MeV γ-rays from neutron capture on hydrogen, thanks to the 10B(n,α)7Li reaction. The outgoing neutron flux spans 12 orders of magnitude in energy – from thermal (∼10 meV) up to ∼10 GeV. An evacuated beam line leads to the Experimental Area 1, at a distance of approximately 185 m from the spallation target. The charged particles are removed from the beam by a 1.5 T sweeping magnet at 145 m from a spallation target, while the neutron beam itself is shaped by a set of two collimators at 137 m and 178 m. Outside the beam line, the flux of particles and radiation from the spallation target is attenuated by massive concrete walls, together with a 3.5 m thick iron shielding. A description of the general features of the n TOF facility may be found in ref. [16]. The neutron flux at n TOF is measured by multiple detector systems, in order to reliably cover the whole energy range from thermal up to 1 GeV. In particular, the flux between 10 MeV and 1 GeV, which is the energy range of interest to this work, has been measured by the Parallel Plate Avalanche Counters (PPAC [18,19]) relying on the 235U(n,f) reaction. The cross section of this reaction – as the reference for the absolute normalization of the data – is not considered a standard above 200 MeV. However, the cross section reference for this reaction has recently been extended up to 1 GeV [20], and the neutron flux at these energies has been reevaluated accordingly (Section 5.2). Dedicated GEANT4 simulation of a spallation process were used to extend the flux evaluation up to 10 GeV, with the simulation results normalized to the experimental data around the transition point at 1 GeV. A detailed description of the neutron flux measurements at n TOF may be found in ref. [21]. 4 The natural carbon sample used for the measurement was 7.13 g in mass, 2 cm in diameter and 1 cm in thickness. A high chemical purity of 99.95% was confirmed by the chemical analysis performed at Paul Scherrer Institute, excluding the possibility of contamination by neutron poisons. For the detection of β-rays from a decay of 12B produced by the 12C(n,p)12B reaction, two C6D6(deuterated benzene) liquid scintillation detectors were employed, which are commonly used at n TOF for neutron capture measurements. The two detectors are referred to as Bicron and FZK. The former is a modified version of the commercially available Bicron detector, while the latter was custom built at Forschungszentrum Karls-ruhe, Germany. These detectors have been specifically optimized so as to exhibit a very low neutron sensitivity [22]. They were mounted 8.2 cm upstream of the sample and 6.8 cm from the beam line axis. The backward position significantly reduces the background of neutrons and in-beam γ-rays scattered off the sample. The scintillation liquid volumes amount to 618 ml and 1027 ml for Bicron and FZK, respectively. Their energy calibration was performed using standard 137Cs, 88Y and Am/Be γ-ray sources. A high-performance digital data acquisition system – based on 8-bit flash analog-to-digital converter units (FADC) – was used for recording the electronic signals from the measurements. The sampling rate of 500 MHz in combination with a 48 MB memory buffer allows uninterrupted waveforms of 96 ms duration. Further details on the digital data acquisition used at n TOF may be found in ref. [23]. 3 Experimental data analysis The integral measurement of the cross section of 12C(n,p)12B reaction has been performed using the activation technique in combination with the time of flight technique [17]. During the neutron irradiation of the natC sample, the high energy section of the neutron beam (above the reaction threshold of 13.6 MeV) causes the production of 12B nuclei in the sample, which undergo a β−-decay with a half-life of 20.2 ms and a Q-value of 13.37 MeV. The highly energetic β-rays – with a mean kinetic energy of 6.35 MeV – are then detected by two C6D6detectors. Though the data have been measured within the time window of 96 ms, due to the reduced statistics after the background subtraction at higher decay times, they have been analyzed only up to 80 ms, which corresponds to four half-lives of 12B. The intense γ-flash caused by the proton beam hitting the spallation target was used as a reference point for the time calibration. Due to the low repetition rate of the n TOF beam, the decay of 12B is detected within the same neutron bunch in which it is produced, without any possibility of wrap-around background. The measurements are affected by several sources of background. One component is caused by the scattering of in-beam γ-rays off the sample itself. This component was measured with a Pb sample and was found to be negligible. The second component is caused by the neutron beam crossing the experimental area. It was measured by recording data with the beam in the experimental area, but without any sample in place. The third component is the ambient background, caused by the natural radioactivity and the neutron activation. It was measured by turning off the neutron beam. All these components were properly normalized and subtracted from the measured counts with the natC sample. These background components have already been discussed in ref. [24]. The fourth and final component is referred to as the neutron background, caused by the neutrons scattering off the sample itself. To precisely identify this component, one must rely on dedicated simulations, taking into account the detailed geometric description of the detectors and experimental surroundings, the full framework of the neutron induced reactions and their complete temporal evolution. These simulations have been developed in GEANT4 [15] and described in detail in ref. [25]. A major portion of the neutron background is caused by the detection of γ-rays – mainly from the neutron captures inside the experimental area – with only a minor contribution from β-rays coming from activation of the experimental setup. A potential problem in the simulations of this background component is the lack of correlations between the capture γ-rays from simulated γ-ray cascades, which alters their energy distribution (relative to the real one), thus affecting an average γ-ray detection efficiency. However, the use of the Pulse Height Weighting Technique (PHWT) [26] compensates for the lack of correlations, making the detection efficiency independent of the actual cascade paths, as long as the energy is conserved in simulating the capture γ-rays. In this case simulations become highly reliable, as demonstrated in ref. [25] by the very good agreement between the simulated and measured yield of natC in an energy region where the neutron background dominates. The details on the PWHT applied at n TOF may be found in ref. [27]. After subtracting the experimentally determined background components, the weighted spectrum CW(t) of counts per neutron bunch – as a function of decay time t– may be expressed as: CW(t) = W(E)⊗Cγ(t) + hWi × Cβ(t) (1) Here W(E) is the weighting function from PHWT, dependent on the energy Edeposited in the detectors and determined for each detector separately. Cγ(t) is the neutron background – mostly composed of capture γ-rays – while ⊗symbolically denotes the operation of applying the weighting function to the neutron background counts. Cβ(t) are the β-ray counts, pertaining only to the β-rays from the decay of 12B produced in natC sample. The βrays coming from other sources and reactions – including the 12C(n,p)12B reaction outside the sample (e.g. from the detector housing made of carbon fiber) – are all part of the neutron background Cγ(t). In the case of β-rays – always emitted with unit multiplicity – the application of the PWHT is equivalent to multiplying the overall spectrum by the average weighting factor hWi, which may be 5 expressed as: hWi=REmax Emin Sβ(E)W(E)dE REmax Emin Sβ(E)dE(2) where Sβ(E) is the deposited energy spectrum of β-rays from the 12B decay. In order to determine the average weighting factor hWifrom eq. (2), the spectrum Sβ(E) extracted from simulations of the 12B-decay in the natC sample was used (contrary to γ-ray cascades, there is no difference between the simulated and measured spectrum of the energy deposited by β-rays in the C6D6). The average value hWidepends on the lower and upper thresholds Emin and Emax set during the data analysis. In particular, the lower threshold needs to be the same as the threshold used for calculating the weighting functions from PHWT, i.e. Emin = 200 keV. The upper threshold is set to Emax = 13.37 MeV, which is the Q-value of the 12B decay. The weighted simulated neutron background Cγ(t) and the average weighting factor hWi– calculated from the simulated spectrum Sβ(E) – are then used to invert eq. (1) and determine the background-subtracted, unweighted β-rays spectrum: Cβ(t) = CW(t)−W(E)⊗Cγ(t) hWi(3) The remaining spectrum corresponds to the time distribution of 12B decays: Cβ(t) = εβN12B τe−t/τ (4) with τ= 29.14 ms as the lifetime of 12B and N12 Bas the total number of 12B nuclei produced per single neutron bunch. A final factor to be considered is the total β-ray detection efficiency εβ. It was extracted from simulations, as the ratio between the number of detected β-rays within the energy thresholds used in the analysis (Emin = 200 keV and Emax = 13.37 MeV) and the total number of 12B nuclei generated in the natC sample. For the Bicron detector it was determined as εβ;Bicron = 4.3%, while for the FZK as εβ;FZK = 6.8%. A fit to the exponential form of eq. (4) – with N12 B as the only free parameter – yields the total number of 12B nuclei produced per neutron bunch. For the Bicron detector the fit yields N(Bicron) 12B= 68.03 ±0.66, while the data from FZK detector yield N(FZK) 12B= 68.74 ±0.44. Figure 2 shows the experimental data for both detectors, before and after subtracting the neutron background. The top panel (a) shows the spectra uncorrected for the β-ray detection efficiency εβ, in order to facilitate the visual separation of exponential fits. The bottom panel (b) shows the data corrected for the β-ray detection efficiency, emphasizing the consistency of results from two detectors. It is evident from fig. 2 that after the background subtraction the time distribution of the detected counts follows the expected exponential trend (with the expected lifetime), proving that no additional background components are present in the results. ToF [ms] 0 10 20 30 40 50 60 70 80 ) -1 bunches -1 Detection rate (counts ms -2 10 -1 10 1 10 Total counts (FZK) Total counts (Bicron) -rays (FZK)β -rays (Bicron)β (a) bla ToF [ms] 0 10 20 30 40 50 60 70 80 ) -1 bunches -1 Decay rate (counts ms -1 10 1 10 2 10 Total counts (FZK) Total counts (Bicron) -rays (FZK)β -rays (Bicron)β (b) bla Fig. 2. Time distribution of the β-decay of 12B nuclei produced by the 12C(n,p)12B reaction, measured by two C6D6detectors (Bicron and FZK). Total counts show the data after subtracting all experimentally identified background components, with the neutron background still remaining. After subtracting the simulated neutron background, the purely exponential spectra reveal the contribution from a β-decay of 12B. Top panel (a) shows the detection rate (before correcting for the β-ray detection efficiency), while bottom panel (b) shows the decay rate (after correcting for the β-ray detection efficiency). According to the simulations, the contribution of βrays from 12B produced outside the sample by the scattered neutrons is below 1%. Though their contribution has been removed from the data through the neutron background subtraction, this source of uncertainty has been assigned a systematic value of 2%. In addition, 13C content in natural carbon (with 1.1% natural abundance) also contributes to the production of 12B and 13B (with decay properties very similar to those of 12B) through the (n,p), (n,d) and (n,np) reactions, whose cross sections are highly uncertain. No attempt was made to decouple their contribution from the measurements, except for the portion already included in the neutron background. Therefore, a 3% systematic uncertainty related to the contribution of 13C has been assigned to the number of produced 12B nuclei. Finally, a 6% systematic uncertainty was adopted in order to account for the uncertainty in both the simulated β-ray detection efficiency and the simulated neutron 6 background. Combining the results from both detectors, the final value is N12B= 68.5±0.4stat ±4.8syst. 4 GEANT4 cross sections It was already shown in Section 3 that GEANT4 simulations play a central role in the experimental data analysis, in determining the weighting functions required by the PHWT, of identifying the neutron background and of determining the β-ray detection efficiency of the two C6D6detectors. As will be shown in Section 5, simulations are also indispensable in bringing the number of produced 12B nuclei into relation with the cross section of the 12C(n,p)12B reaction and in exerting control over the same procedure. In that, the (effective) cross sections for 12C(n,p)12B reaction will play an important role. (By effective we mean the cross sections which are not directly sampled from the preexisting data, but arise as an end-product of the model calculations.) Five different models from GEANT4 were considered in this work: HP (High Precision) package, Binary cascade, Bertini cascade, INCL++/ABLA model (INCL intranuclear cascade coupled to the ABLA deexcitation model) and QGS (Quark- Gluon-String) model [28]. GEANT4 version 9.6.p01 was used for all models except for INCL++/ABLA, which was run in GEANT4 version 10.0 (the only reason being that the INCL++/ABLA model is not available in version 9.6.p01). It should be remarked that the reliability of the total and elastic scattering cross sections adopted by GEANT4 is of crucial importance for the quality of subsequent analysis, directly affecting both the self-shielding and the multiple scattering factor discussed in Section 5. The cross sections for all reactions of interest were extracted from GEANT4 by the following procedure. The natC sample was irradiated in the simulation with neutrons following the exact energy dependence of the n TOF flux. The occurrence Nr(En) of a given reaction rwas counted only if rwas the first reaction to take place. In [MeV] n E 10 2 10 3 10 4 10 Cross section [b] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 C(n,tot) nat Geant4 C(n,tot) nat ENDF/B-VII.1 C(n,tot) 12 ENDF/HE-VI C(n,el) nat Geant4 C(n,el) nat ENDF/B-VII.1 C(n,el) 12 ENDF/HE-VI bla Fig. 3. Total cross section for the neutron induced reactions on natC and the elastic scattering cross section extracted from GEANT4 simulations, compared to ENDF/B-VII.1 [11] and ENDF/HE-VI [29] libraries (data from ENDF/HE-VI are given for 12C). [MeV] n E 10 2 10 3 10 4 10 Cross section [mb] 1− 10 1 10 2 10 Binary cascade Bertini cascade INCL++ / ABLA QGS model HP package bla Fig. 4. Cross sections for natC(n,p)12B reaction from 5 different GEANT4 models (see text for details). parallel, the occurrence Ntot(En) of any reaction in the sample was also counted. The probability for reaction r without multiple scattering effects, i.e. the first-chance yield Yr(En) at neutron energy Enmay be expressed as: Yr(En) = (1 −e−nσtot(En))σr(En) σtot(En)=Nr(En) N0(En)(5) The first expression is given in terms of the reaction cross section σr(En), total cross section σtot(En) and an areal density nof the sample (in number of atoms per unit surface, which for the used natC sample is equal to n= 0.114 atoms/barn). The second part of eq. (5) expresses the probability as the ratio between the number Nr(En) of times the reaction has occurred and the total number N0(En) of incident neutrons with energy En. In order to be able to evaluate the particular cross section σr(En), the total cross section σtot(En) must first be determined by inverting eq. (5), considering all neutron interactions in the sample: σtot(En) = −1 nln 1−Ntot(En) N0(En)(6) Ultimately, adopting σtot(En) from simulations (as opposed to any particular database) allows for the self-consistent calculation of σr(En) of interest: σr(En) = Nr(En) Ntot(En)σtot(En) (7) Figure 3 compares the total and elastic cross section extracted from GEANT4 – by eq. (6) and eq. (7), respectively – with those from ENDF/B-VII.1 [11] and ENDF/HEVI [29] library. It should be noted that the data in ENDF/B- VII.1 are available for natC, while in ENDF/HE-VI for 12C. It is evident that the simulations closely reproduce the tabulated cross sections. Therefore, these results may be used with a high degree of confidence in identifying both the self-shielding and the multiple scattering factor described in the following Section. The (effective) cross sections for the 12C(n,p)12B reaction have also been calculated on the basis of eq. (7). They 7 are shown in fig. 4. In particular, the reconstructed cross section from the HP package builds confidence that the procedure was correctly performed, since the HP package adopts the cross sections from the ENDF/B-VII.1 database [11] (see fig. 1). It should be noted that the cross sections for the 12C(n,p)12B reaction extracted from GEANT4 are not of particular interest to this work, and in some cases are clearly unreliable. For example, this is the case of the one extracted from the quark-gluon- string models, which clearly cannot be applied below several GeV. Nevertheless, all of them extend over the whole energy range from the reaction threshold up to 10 GeV, which makes them useful in determination of the multiple scattering correction discussed in Section 5, and in illustrating the robustness of these results against the wildly varying cross sections. 5 Comparison with models and evaluations The produced number of 12B nuclei per neutron bunch is related to the 12C(n,p)12B reaction cross section through the following expression: N12B=Z10 GeV 13.6 MeV 1−e−nσtot(En) σtot(En)η(En)φ(En)σ(En)dEn (8) where the energy range covered by the integral spans from the reaction threshold at 13.6 MeV up to the highest neutron energy provided by the n TOF beam, i.e. 10 GeV. The product of the first term (consisting of the self-shielding factor divided by the total cross section σtot(En); nbeing the areal density of sample in number of atoms per unit surface) with the cross section σ(En) represents the firstchance reaction yield per incident neutron of energy En, which does not take into account the multiple scattering effect. This is accounted for separately, by the multiple scattering factor η(En) which depends mostly on the elastic cross section. Finally, the sample-incident neutron flux φ(En) also has to be considered. 5.1 Self-shielding factor The self-shielding factor, appearing as the numerator from eq. 8, is central in defining the first-chance yield of the 12C(n,p)12B reaction. It determines the relative portion of the neutron beam that is attenuated after passing through the full length of the sample. Equivalently, it may be considered as a probability for a single neutron to initiate any possible reaction in the sample – as reflected through the adoption of the total cross section σtot(En) – and be removed from the incident neutron beam. On the other hand, the ratio σ(En)/σtot(En) represents the probability that among all possible reactions, the particular one with the cross section σ(En) is to take place. The reliability of the total cross section adopted in GEANT4 has already been confirmed in Section 4 (see fig. 3). 5.2 Neutron flux The neutron flux φ(En) entering the experimental area was measured up to 1 GeV by means of Parallel Plate Avalanche Counters [18,19], relying on the 235U(n,f) reaction. In Refs. [16,21] the n TOF flux was determined on the basis of the standard cross section from the ENDF/B- VII.1 evaluation [11] up to 200 MeV. Above this energy, and up to 1 GeV, the JENDL/HE-2007 database [13] was used. Recently, a new evaluation has been proposed by IAEA as a reference cross section [20], now widely considered to be more reliable. Therefore, it was decided to re-evaluate the experimental flux above 200 MeV using the new IAEA cross section reference. Figure 5 compares the cross sections from JENDL/HE-2007 library, used in the past, with the newly extended reference from IAEA. The ratio between them is also displayed in the figure. Previously evaluated flux simply had to be divided by this ratio in order to obtain the reevaluated flux. Figure 6 compares the new flux (incident on the sample) with the one used in the past. The beam interception factor, required for identifying the portion of the flux incident on the sample, was determined as a function of neutron energy from FLUKA [30] simulations of the neutron transport after the spallation process, and adjusted to the experimental data at low energies using the saturated resonance technique [31] applied to the 4.9 eV neutron capture resonance of 197Au. For clarity, the neutron flux from fig. 6 is shown in units of lethargy, from which the flux per unit energy may be obtained as: φ(En) = dNper bunch dEn =1 En ×dNper bunch dln En (9) [MeV] n E 200 300 400 500 600 700 800 900 1000 Cross section [barns] 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 U(n,f) 235 IAEA 2015 JENDL/HE-2007 bla [MeV] n E 200 300 400 500 600 700 800 900 1000 JENDL σ/ IAEA σ 1.00 1.05 1.10 1.15 1.20 1.25 bla Fig. 5. Top panel: 235U(n,f) cross section from JENDL/HE- 2007 compared with the recently extended reference cross section from IAEA. Bottom panel: ratio between cross sections from the top panel. 8 [MeV] n E 10 2 10 3 10 4 10 ) n / d(ln E (incident) per bunch dN 0 5 10 15 20 25 3 10×Incident flux (new) Incident flux (old) GEANT4 bla Fig. 6. Sample-incident neutron flux between 10 MeV and 10 GeV. The total flux up to 1 GeV was measured using PPAC detector and normalized to the 235U(n,f) yield calculated from the associated cross section. The flux above 200 MeV was reevaluated, based on the recently extended 235U(n,f) reference cross section from IAEA. In the energy range above 1 GeV the normalized results from GEANT4 simulations are used. See the main text for the details. where Nper bunch is the number of neutrons per neutron bunch, reaching the experimental area (in case of the evaluated flux) or impinging on the sample (in case of the incident flux). While the flux was measured up to 1 GeV, for the purpose of this work it is necessary to consider the full energy distribution of the n TOF beam, since all neutrons above 13.6 MeV contribute to the 12C(n,p)12B reaction and the production of 12B nuclei. The neutron flux above 1 GeV can be estimated by means of dedicated simulations of the spallation process. It was found that the results from recently developed GEANT4 simulations of the spallation process [32] are in good agreement with the shape of the flux around 1 GeV. For this reason, the GEANT4 simulations have been adopted for extending the evaluated flux up to 10 GeV. In ref. [32] the results from several different physics lists have been compared, namely from FTFP BERT HP, FTFP INCLXX HP, QGSP BERT HP, QGSP BIC HP and QGSP INCLXX HP. The QGSP INCLXX HP list was found to better reproduce the absolute scale of the neutron flux, within the overall energy range from thermal up to 10 GeV. However, the FTFP BERT HP list provides the best reproduction of the shape of the experimental flux at high energies. For this reason, the FTFP BERT HP physics list has been used in this work in order to extend the evaluated flux beyond 1 GeV. These results have been normalized so as to match the experimental flux at 1 GeV. The normalized flux is also shown in fig. 6. It was also multiplied by the energy dependent beam interception factor, in order to translate it into the sample incident flux. 5.3 Multiple scattering factor The multiple scattering factor η(En) was determined from GEANT4 simulations. We remark that in the simulations it is of crucial importance to use a realistic flux, i.e. the one shown in fig. 6, since – after the (in)elastic scattering – the neutrons of initially higher energy are feeding the lower energy portions of the spectrum. In the simulations the primary neutron energy E0was recorded, together with the final energy Enof the neutron giving rise to the natC(n,p)12B reaction. The multiple scattering factor – increasing the 12B production at the neutron energy En– was determined as the ratio between the number N(En) of 12B nuclei produced by all neutrons of energy Enand the number N(En=E0) of those produced by neutrons not previously affected by scattering (i.e. those with the final energy equal to the primary one): η(En) = N(En) N(En=E0)(10) In order to investigate the stability and reliability of results, the simulations were performed using 4 different inelastic scattering models that extend over the full energy range of interest – Binary cascade, Bertini cascade, INCL++/ABLA model and QGS model [28]. Model predictions are compared in fig. 7. It is evident that the models yielding substantially different effective cross sections (see fig. 4) give very consistent multiple scattering corrections up to 11% and 15%, depending in the model used. This is due to the fact that the multiple scattering factor is dominantly affected by the elastic scattering. The reliability of the elastic scattering cross section from GEANT4 has already been confirmed in Section 4 (see fig. 3). Considering the consistency between the multiple scattering factors from Bertini cascade and Binary cascade, their average value was adopted – shown in the inset of fig. 7 – that yields a maximal multiple scattering correction of approximately 11%, peaking around 20 MeV. Additional reason for using the combination of these two cascade models is that their combined result will later be shown to best describe the experimental n TOF data. [MeV] n E 10 2 10 3 10 4 10 Multiple scattering factor 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 bla [MeV] n E 10 2 10 3 10 4 10 Multiple scattering factor 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 bla 10 2 10 3 10 4 10 1 1.02 1.04 1.06 1.08 1.1 1.12 Binary + Bertini Bertini cascade Binary cascade INCL++ / ABLA QGS model h7_MeV Fig. 7. Multiple scattering factor from four different GEANT4 models. Inset shows the final dependence adopted for calculations, obtained by taking the average between the results from Binary cascade and Bertini cascade.