Measurement of resolved resonances of 232Th(n, γ) at the n_TOF facility at CERN

PHYSICAL REVIEW C 85, 064601 (2012) Measurement of resolved resonances of 232Th(n,γ) at the n_TOF facility at CERN F. Gunsing,1,*E. Berthoumieux,1G. Aerts,1U. Abbondanno,2H. ´ Alvarez,3F. Alvarez-Velarde,4S. Andriamonje,1 J. Andrzejewski,5P. Assimakopoulos,6L. Audouin,7G. Badurek,8P. Baumann,9F. Beˇ cv´ aˇ r,10 F. Calvi ˜ no,11 D. Cano-Ott,4 R. Capote,12,13 A. Carrillo de Albornoz,14 P. Cennini,15 V. Chepel,16 E. Chiaveri,15 N. Colonna,17 G. Cortes,11 A. Couture,18 J. Cox,18 M. Dahlfors,15 S. David,9I. Dillman,19 R. Dolfini,20 C. Domingo-Pardo,21 W. Dridi,1I. Duran,3C. Eleftheriadis,22 M. Embid-Segura,4L. Ferrant,7A. Ferrari,15 R. Ferreira-Marques,16 L. Fitzpatrick,15 H. Frais-Koelbl,23 K. Fujii,2W. Furman,24 I. Goncalves,16 E. Gonzalez-Romero,4A. Goverdovski,25 F. Gramegna,26 E. Griesmayer,23 C. Guerrero,4B. Haas,27 R. Haight,28 M. Heil,19 A. Herrera-Martinez,15 M. Igashira,29 S. Isaev,7E. Jericha,8F. K¨ appeler,19 Y. Kadi,15 D. Karadimos,6 D. Karamanis,6M. Kerveno,9V. Ketlerov,15,25 P. Koehler,30 V. Konovalov,15,24 E. Kossionides,31 M. Krtiˇ cka,10 C. Lampoudis,22 H. Leeb,8A. Lindote,16 I. Lopes,16 M. Lozano,13 S. Lukic,9J. Marganiec,5L. Marques,14 S. Marrone,17 P. Mastinu,26 A. Mengoni,15,23 P. M. Milazzo,2C. Moreau,2M. Mosconi,19 F. Neves,16 H. Oberhummer,8S. O’Brien,18 M. Oshima,32 J. Pancin,1C. Papachristodoulou,6C. Papadopoulos,33 C. Paradela,3N. Patronis,6A. Pavlik,34 P. Pavlopoulos,35 L. Perrot,1M. T. Pigni,8R. Plag,19 A. Plompen,36 A. Plukis,1A. Poch,11 C. Pretel,11 J. Quesada,13 T. Rauscher,37 R. Reifarth,28 M. Rosetti,38 C. Rubbia,20 G. Rudolf,9P. Rullhusen,36 J. Salgado,14 L. Sarchiapone,15 I. Savvidis,22 C. Stephan,7G. Tagliente,17 J. L. Tain,21 L. Tassan-Got,7L. Tavora,14 R. Terlizzi,17 G. Vannini,39 P. Vaz,14 A. Ventura,38 D. Villamarin,4M. C. Vincente,4V. Vlachoudis,15 R. Vlastou,33 F. Voss,19 S. Walter,19 H. Wendler,15 M. Wiescher,18 and K. Wisshak19 (n_TOF Collaboration†) 1CEA/Saclay—DSM/Irfu/SPhN, F-91191 Gif-sur-Yvette, France 2Istituto Nazionale di Fisica Nucleare, Trieste, Italy 3Universidade de Santiago de Compostela, Spain 4Centro de Investigaciones Energeticas Medioambientales y Technologicas, Madrid, Spain 5University of Lodz, Lodz, Poland 6University of Ioannina, Ioannina, Greece 7Centre National de la Recherche Scientifique/IN2P3—IPN, Orsay, France 8Atominstitut der ¨ Osterreichischen Universit¨ aten, Technische Universit¨ at Wien, Wien, Austria 9Centre National de la Recherche Scientifique/IN2P3—IReS, Strasbourg, France 10Charles University, Prague, Czech Republic 11Universitat Politecnica de Catalunya, Barcelona, Spain 12International Atomic Energy Agency, NAPC/Nuclear Data Section, Vienna, Austria 13Universidad de Sevilla, Sevilla, Spain 14Instituto Tecnol´ ogico e Nuclear (ITN), Lisbon, Portugal 15CERN, Geneva, Switzerland 16LIP—Coimbra & Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal 17Istituto Nazionale di Fisica Nucleare, Bari, Italy 18University of Notre Dame, Notre Dame, Indiana, USA 19Karlsruhe Institute for Technology (KIT), Campus North, P.O. Box 3640, 76021 Karlsruhe, Germany 20Universit` a degli Studi Pavia, Pavia, Italy 21Instituto de F´ ısica Corpuscular, CSIC—Universidad de Valencia, Valencia, Spain 22Aristotle University of Thessaloniki, Thessaloniki, Greece 23International Atomic Energy Agency (IAEA), Nuclear Data Section, Vienna, Austria 24Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia 25Institute of Physics and Power Engineering, Kaluga region, Obninsk, Russia 26Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Legnaro, Legnaro, Italy 27Centre National de la Recherche Scientifique/IN2P3—CENBG, Bordeaux, France 28Los Alamos National Laboratory, Los Alamos, New Mexico, USA 29Tokyo Institute of Technology, Tokyo, Japan 30Oak Ridge National Laboratory, Physics Division, Oak Ridge, Tennessee, USA 31NCSR, Athens, Greece 32Japan Atomic Energy Research Institute, Tokai-mura, Japan 33National Technical University of Athens, Athens, Greece 34Institut f¨ ur Isotopenforschung und Kernphysik, Universit¨ at Wien, Wien, Austria 35Pˆ ole Universitaire L´ eonard de Vinci, Paris La D´ efense, France 36CEC-JRC-IRMM, Geel, Belgium 37Department of Physics and Astronomy, University of Basel, Basel, Switzerland 064601-1 0556-2813/2012/85(6)/064601(17) ©2012 American Physical Society F. GUNSING et al. PHYSICAL REVIEW C 85, 064601 (2012) 38ENEA, Bologna, Italy 39Dipartimento di Fisica, Universit` a di Bologna, and Sezione INFN di Bologna, Bologna, Italy (Received 13 February 2012; published 1 June 2012; publisher error corrected 20 June 2012) The yield of the neutron capture reaction 232Th(n, γ ) has been measured at the neutron time-of-flight facility n_TOF at CERN in the energy range from 1 eV to 1 MeV. The reduction of the acquired data to the capture yield for resolved resonances from 1 eV to 4 keV is described and compared to a recent evaluated data set. The resonance parameters were used to assign an orbital momentum to each resonance. A missing level estimator wasusedtoextractthes-wave level spacing of D0=17.2±0.9eV. DOI: 10.1103/PhysRevC.85.064601 PACS number(s): 25.40.Lw, 25.40.Ny, 28.20.Fc, 27.90.+b I. INTRODUCTION The nucleus 232Th plays an important role in the thoriumuranium nuclear fuel cycle [1–4] based on the fissile 233U bred from 232Th. The potential use of this fuel cycle is under study mainly because of its lower build-up of high-mass actinides, therefore reducing the production of radiotoxic nuclear waste, as compared to the widely used conventional uranium-plutonium fuel cycle. Accurate knowledge of cross sections of the 232Th neutron-induced reactions is crucial input for the efficiently optimized design of a thorium-fuel-based nuclear system combining safe operation with the necessary power and criticality level. Another field of interest for neutron-induced resonance reactions concerns the large parity-nonconservation effects which have been observed in neutron p-wave resonances of several isotopes including 232Th [5,6]. These effects, on the order of 10−7in nucleon-nucleon interactions, were found to be up to 10% in polarized neutron transmission experiments on several nuclei including 232Th [7]. The asymmetries are explained as the admixing of nearby large s-wave resonances in small p-wave resonances with the same channel spin. Resonance parameters are used in the analysis of the measured asymmetries. In general, neutron resonance data are an important calibration point for any level density model [8–10]. A careful interpretation of measured resonance data with a correction of missing levels [11,12] allows the extraction of the level density at the neutron separation energy. The 232Th(n, γ ) cross sections in most of the evaluated data libraries [13] or data compilations [14,15] are based on a rather limited set of experiments [16–26] for which discrepancies have been pointed out to exist. A recent evaluation by Sirakov et al. [27] for neutron-induced reactions of 232Th in the unresolved resonance region included in addition several recent capture measurements [28–31]. The recent release of the ENDF/B-VII.0 evaluated library [32] includes a new evaluation of 232Th [33] based on a new simultaneous analysis of several resolved resonance data sets, including preliminary capture yield data from this experiment. Neutron capture data of 232Th measured with the time-offlight technique in the resolved resonance region have often been hindered by the large radioactivity background from the *Corresponding author:[email protected] †www.cern.ch/ntof high-energy γrays of up to 2.6 MeV originating from the β decay of the daughter product 208Tl. We have measured the capture cross section of 232Th at the n_TOF facility at CERN where the high neutron flux per burst allowed us to strongly reduce the background due to radioactivity. The results of this measurement have been given previously for the unresolved resonance region [31]. In this paper we report the results for the resolved resonances. Since the measurement setup and data reduction procedure are the same, we only briefly describe the setup and we emphasize only the parts of the data reduction that are essential for the resolved resonances. II. EXPERIMENTAL SETUP The neutron-capture experiment has been performed at the n_TOF facility at CERN during phase I, before the upgrade of the spallation target [34]. A detailed description of its performances can be found elsewhere [35] and the setup used for this particular experiment has also been described previously [31]. The spallation neutrons produced with a pulsed, 6-ns wide, 20 GeV/c proton beam with up to 7 ×1012 protons per pulse ina80×80 ×60 cm3lead target are moderated by a 5.8-cm water slab surrounding the lead target. The neutron beam was obtained by means of two collimators, consisting of layers of iron and borated polyethylene. The first collimator has an inner diameter of 11 cm and an outer diameter of 50 cm and is placed 135 m from the lead target. The second collimator is located near the experimental area at a distance of 175 m and has an outer diameter of 40 cm and a variable inner diameter. For this capture experiment we used an inner diameter of 1.8 cm while for most fission experiments [36–39] a diameter of 8 cm has been used. The collimation resulted in a nearly symmetric Gaussian-shaped beam profile at the sample position of 185.2 m with a standard deviation of about 0.77 cm at low neutron energies. The spatial distribution has been accurately measured, confirming previous simulations [40], and modeled as a function of neutron energy [41]. A 1.5-T sweeping magnet placed at a distance of 145 m from the spallation target removed residual charged particles traveling along the neutron beam line. A 3-m-thick iron shielding was placed just after the magnet to remove negative muons. The neutron beam line is extended for an additional 12 m beyond the experimental area to minimize the background from back-scattered neutrons. A multifilter changer has been installed in the beam line upstream of the first collimator. 064601-2 MEASUREMENT OF RESOLVED RESONANCES OF ... PHYSICAL REVIEW C 85, 064601 (2012) FIG. 1. (Color online) The broadened simulated spectra (in black) and part of the measured response of one detector for each of the three γ-ray sources mentioned in the text (in red, blue, and green). The simultaneously adjusted channel-energy calibration using the three response functions is shown in the inset. The repetition period of the proton pulses was a multiple of 2.4 s, which is long enough to cover the energy range down to subthermal energies in the experimental area at 185.2 m and to prevent overlapping of slow neutrons in subsequent cycles. Two in-house-developed deuterated benzene C6D6γ-ray detectors contained in a low-mass carbon fiber housing [42] have been used for neutron capture measurements. The samples, placed in air, were kept in position by a remotely controlled carbon fiber sample changer [43]. For the energy calibration of each C6D6γ-ray detector we measured the response to radioactive sources of 137Cs (0.662 MeV), 60Co (1.173 and 1.332 MeV), and a composite source of 238Pu with 13C, giving a 6.13-MeV γray through the 13C(α, n)16O∗reaction. With the code MCNP [44] we simulated the energy deposition in the C6D6liquid scintillator volume for each of these sources. Then both the energy calibration and the Gaussian broadening of the detector response were fitted simultaneously to the regions around the Compton edge of the measured response functions, as shown in Fig. 1. This method allows us to obtain a reliable energy calibration over a large energy range. Two disk-shaped thorium samples of 99.5% purity with a total mass of 2.8046 g and a diameter of 15 mm were placed in the beam at a flight path of 185.2 m. In addition to these samples, we used a natural lead sample to estimate the scattered photon background and a gold sample to verify the analysis procedure. All samples were fixed on thin kapton foils and mounted on the sample changer. The distance of the detectors from the center of the beam was 2.9 cm and the detectors were shifted 9.2 cm upstream from the center of the sample in order to reduce the scattered photon background. The data-acquisition system [45] was based on Acqiris flash ADCs with 8-bit amplitude resolution and down to 1 ns sampling interval with 8 Mbytes of memory, recording for each detector its full output signal from the start time given by the incident protons. The digitizers were operated at 500 Msamples/s, allowing storage of the detector signal neutron energy (eV) 110 2 10 3 10 4 10 5 10 6 10 counts 1 10 2 10 FIG. 2. (Color online) The unweighted spectrum of the thorium sample showing the resonance structure. The constant radioactive background, well below the time-of-flight spectrum, is shown in blue. In this and the following figures, counts Care expressed as counts per unit of lethargy, i.e., as dC/d lnE=EdC/dE. during a 16-ms-long time-of-flight interval, corresponding to a minimum neutron energy of 0.7 eV. After zero suppression, the data were transferred to CERN’s data storage facility CASTOR for off-line analysis with dedicated pulse-shape analysis routines for each detector. III. DETERMINATION OF THE CAPTURE YIELD From the stored digitized detector signals, events consisting of the time of flight and the pulse height, related to the deposited energy, were extracted for each detected γray. These raw event data were processed to obtain the pulse-heightweighted spectra used to derive the capture yield. Only signals above the electronic threshold corresponding to 160-keV pulse height were processed further. Runs without beam served to determine the background due to the thorium activity. In order to appreciate the signal-to-background ratio we show in Fig. 2the counting spectrum for one detector together with the background constant in time. The spectra are given as the number of counts per logarithmic bin width per nominal pulse of 7 ×1012 protons. In this way the constant background in time is visible as a decreasing line when represented as a function of the equivalent neutron energy En, i.e., the converted time of flight tusing the relativistic time-energy relation En=mc2(γ−1),(1) with γ=(1 −v2/c2)−1/2and v=L/t and where mis the neutron mass and cthe speed of light. The flight time twas calibrated for each pulse using the so-called γflash. The flight path length Lwas calibrated using a measurement of the first resonance of gold. We used a measurement with gold to fit the flight path L=185.2 m in combination with the resolution function. The energy of the first resonance is listed as 4.89 eV, the value which we adopted here, in ENDF/B-VII.0 and JENDL-4.0, but as 4.906 eV in JEFF-3.1 and ENDF/B-VI.8. This difference in energy scale is clearly visible at the 185.2-m flight path. 064601-3 F. GUNSING et al. PHYSICAL REVIEW C 85, 064601 (2012) A. Weighting function We applied the total energy method using the so-called pulsed-height-weighting technique (PHWT) to determine the number of capture reactions from the measured complex γ-ray cascade spectrum following neutron capture. This method, which is explained in considerably more detail in Ref. [46,47] and references therein, consists of using a detector withalowγ-ray efficiency so that at most one γray from the capture cascade is detected. Then a weight W(Ed) is applied to each event with a deposited energy Edin the detector for each detected capture event. The weights W(Ed)havetobe chosen in such a way that the detection efficiency γbecomes proportional to the incident γ-ray energy Eγ, γ=W(Ed)Rγ(Ed)dEd=k×Eγ,(2) where Rγ(Ed) is the detector’s response to Eγ. Then the efficiency cof the γ-ray cascade is proportional to the cascade energy Ecas c=k×Ec. The neutron time-of-flight spectrum CW(En) from the weighted counts obtained in this way becomes then CW(En)=Y(En)(En)kEc,(3) where Y(En) is the capture yield and (En) is the number of incident neutrons. The proportionality constant kis usually taken as 1 per unit of energy. The weighting function W(Ed) is determined from simulated detector response functions to a series of monoenergetic γrays. We have adjusted the parameters of a fourth-order polynomial for W(Ed). In order to account for the finite threshold of 160 keV applied in this experiment, in principle two methods can be used. One can try to estimate the missing part of the response by calculating realistic γ-ray cascades and deduce the corresponding missing detector response and correct for it [46]. The other approach (see, for example, [47] and references therein), which we have followed here, is to assume that the applied threshold is part of the detector response in the fit procedure of the weighting function. B. Weighting function correction for the spatial distribution of γemission In the determination of the weighting function we simulated the detector response to monoenergetic γrays using a homogeneous distribution of the γrays throughout the volume of the sample. In reality, when the cross section of incident neutrons is high, as in the peaks of strong resonances, all capture reactions occur in a first thin layer of the sample. In general, the distribution of γrays in the sample is not homogeneous but dependent on the cross section. To account for this effect, we have calculated the capture yield in the two limiting conditions, once with a weighting function derived from a homogeneous γ-ray distribution and once with a weighting function from a γ-ray distribution concentrated in a thin layer on the neutron incident side of the sample. The maximum effect of the two extreme weighting functions for the flat part of the saturated resonances, where the layer approximation for the γdistribution holds, was a factor aγ=0.964 for a 160-keV threshold. Assuming a γ-ray distribution which changes across the sample axis in relation to the transmission of the neutrons through the sample, related to the total cross section σTand the sample thickness n, we applied the empirical correction factor already used in Ref. [47], fγ(En)=aγ+(1 −aγ)exp[−nσT(En)],(4) to the neutron capture yield derived with the weighting function with the homogeneous γ-ray distribution in order to take this effect into account. This factor reflects the limiting case fγ≈1 outside the the resonances where nσT1 and the other limit fγ≈aγin the peaks of the saturated resonances where nσT1. In between these limits the correction factor follows the transmission exp(−nσT), which is a measure for the opacity to neutrons. C. Dead-time correction The use of flash ADCs for the data acquisition nearly eliminates dead time. Nevertheless, a small effective dead time on the order of a few tens of nanoseconds is present and is related to the software pulse extraction. Its effect is often negligible, except at large local count rates, like in large resonances. To estimate this effect and to correct for it, we calculated the distribution of the time differences between two consecutive events in the same time-of-flight burst, for each of the two γ-ray detectors separately. The distribution showed a nearly total suppression of the events following a previous event by less than approximately 25 ns. The same distribution but now for two consecutive events in either of the two detectors showed a pronounced peak well below 25 ns, revealing the coincidences of two γrays of the same capture event. In the processing of the events, we discarded all events from both detectors within a fixed time τ=30 ns after the detection of an event. In this way we counted only one of two coincident γrays and we obtained a sharply defined dead time for which we calculated a nonextendible dead-time correction factor fτ(t) as a function of the time of flight tas fτ(t)=1 1−1 Nbt t−τSobs (t)dt,(5) where Nbis the number of time-of-flight bunches and Sobs(t) is the observed counting spectrum without event selection conditions. The correction factor, shown in Fig. 3, goes up to 1.025 in the peak of resonances in the resolved resonance region and is practically 1.0 in the valleys between them. The factor fτ(t) derived in this way was then applied to the weighted count rate spectrum. D. Neutron sensitivity A recurring problem in neutron-capture measurements is the neutron sensitivity of the experimental setup. Neutrons scattering from the sample and inducing capture reactions in the detector and surrounding materials produce γrays and contribute to the background in the detector. Since the neutron 064601-4 MEASUREMENT OF RESOLVED RESONANCES OF ... PHYSICAL REVIEW C 85, 064601 (2012) neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 dead time correction 1.000 1.002 1.004 1.006 1.008 1.010 1.012 FIG. 3. (Color online) The dead-time correction factor fτ(t) applied to the weighted time-of-flight spectrum as a function of neutron energy. scattering cross section has the same resonance structure as the capture cross section, this special type of background in the capture yield is difficult to distinguish. The detection probability n(En)ofγrays from samplescattered neutrons is usually measured using a sample of carbon, which has a very small and smooth capture cross section but a sizeable scattering cross section. Unfortunately, for the particular setup of this experiment, no data with a carbon sample were available. However, we had at our disposal several data sets with carbon samples which had been measured in capture experiments on other isotopes in similar setups with only slightly different detector-to-sample distances. Therefore we performed simulations of the γ-ray detection efficiency produced by carbon-scattered neutrons, n(En), in all setups and compared the results with the measured carbon data to validate the simulated n(En) for the thorium experiment setup. For this we used again the code MCNP [44], assuming isotropically emitted neutrons throughout the sample volume. In addition, we simulated the detector response to the in-beam photons, also scattered from the carbon sample. The photon spectrum was available from previous simulations [48] and shows peak at time-of-flight values corresponding to the keV region. At this peak position the time-of-flight response is roughly the same for the scattered photons and the sample-scattered neutron-induced γrays. In the comparison of the simulated detector responses, resulting from both sample scattered neutrons and photons, and the measured carbon sample data we found a rather good agreement for neutron energies below about 10 eV, while at higher energies the agreement was within 30%. One reason for this difference may lie in the fact that the necessary detailed information on neutron capture γ-ray spectra for most nuclei is generally not available in the nuclear data libraries. To estimate the effect as shown in Fig. 5,wehave used the spectra of the energy deposit in the detector from neutrons scattered isotropically from the sample position, resulting from simulations with MCNP. From these spectra we calculated the detection efficiency n(En), applying a 160-keV threshold like in the measurement and applying the weighting function we used for the thorium measurements. neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 n ε -4 10 -3 10 -2 10 unweighted weighted FIG. 4. (Color online) The efficiency for detecting γrays from surrounding materials induced by sample scattered neutrons, calculated with the code MCNP [44]. The weighted efficiency includes the weighting function procedure applied to the γrays and is not comparable to unity. In Fig. 4we show this efficiency with and without applying the weighting function. The unweighted response gives the detection efficiency for a single scattered neutron, while the events for weighted response had undergone the same weighting function procedure as the capture events, changing the absolute magnitude and making it therefore not comparable to unity. This weighted neutron efficiency was then multiplied by the calculated scattered neutron yield from the thorium sample and by the incident neutron flux in order to obtain the weighted count rate comparable to the capture count rate. We considered the result, shown in Fig. 5, as the contribution from sample scattered neutrons to the weighted 232Th(n, γ ) spectrum. With this procedure we obtained an off-resonance contribution in the order of 10%, mainly because there the capture cross section drops to very low values while this is not the case for the scattering cross section due to potential scattering. In neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 weighted counts -1 10 1 10 2 10 3 10 4 10 ) spectrumγTh(n, 232 experimental Th 232 experimental radioactivity Th 232 fitted radioactivity background scattered neutrons FIG. 5. (Color online) The weighted count rate spectrum of the 232Th(n, γ ) measurement. The estimation of the background contribution from sample scattered neutrons as obtained by Monte Carlo simulations is shown as well. For comparison also the weighted contribution of the radioactivity is shown in the figure. 064601-5 F. GUNSING et al. PHYSICAL REVIEW C 85, 064601 (2012) the resonance region however this value is only on the order of 0.1%, since for 232Th the capture cross section is much higher than the scattering cross section. E. Neutron flux The relative neutron flux as a function of neutron energy is needed over the energy range of interest from approximately 1 eV up to 1 MeV in order to determine the capture yield. In addition to Monte Carlo simulations [35], we have a dedicated measurement of the flux performed with a235U-loaded parallel-plate fission ionization chamber from the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig [49]. Furthermore, during the capture measurements the relative neutron flux was measured with an in-beam neutron monitor SiMon [50], consisting of a 6Li deposit on a Mylar foil and four off-beam silicon detectors for the detection of the 6Li(n, 3H)αreaction products. Up to 1 keV both methods are in good agreement, but at higher energies the 6Li(n, α) reaction suffers the insufficient knowledge of the angular distribution of the αand triton particles. The resonance structure of the materials in the neutron beam, such as the aluminum entrance window near the spallation target, the lead of the target, and the water moderator, do not allow us to determine easily an analytical expression for the neutron flux. For example, the 337-eV resonance from 55Mn present in the aluminum of the entrance window is clearly visible in the SiMon data. The neutron flux we adopted for the capture yield is an analytical fit of the measured flux from the SiMon detectors up to 1 keV and pointwise data from the PTB measurement above this energy, suitably normalized in an overlapping energy region. Note that this flux is intended only for its energy profile and not as an absolute normalization. This adopted flux, shown in fig. 6has been used for most of the capture measurements at n_TOF in the phase-I period [51]. The SiMon detector is still in use for the ongoing phase-II measurements together with other flux monitors. It may be possible that the neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 number of neutrons 4 10 5 10 FIG. 6. (Color online) The adopted neutron flux in the energy range from 1 eV to 1 MeV at 185.2 m with the 20-mm-diameter collimator. The composition of this adopted flux is explained in the text. TABLE I. Numerical values of the parameters of the modeled beam interception factor, Eq. (6). Parameter Numerical value b03.830698 ×10−1 b1−4.134044 ×10−4 b21.060315 ×10−3 b32.292116 ×10−1 angular distribution effects of the SiMon detectors will be known with more precision in the future. At present we assign an uncertainty of 2% to the shape of the flux above 1 keV. Because the beam profile changes with neutron energy, the fraction of the neutron beam hitting the sample varies accordingly. The measured change [41] corresponds well with simulated values [40]. Since the simulations were available with higher statistics we used these to fit an empirical analytical function of the form fbeam(En)=b0Eb1 n+b2Eb3 n,(6) with parameters listed in Table I, and which are valid between 1 eV and 1 MeV, where the neutron beam fraction changes from 0.385 at 1 eV to 0.405 at 1 MeV as shown in Fig. 7.This analytical correction factor has been applied to the neutron flux used to calculate the capture yield. F. Capture yield and normalization The spectrum of the weighted detector counts was corrected for dead time, radioactive background, the spatial distribution of the γemission in the weighting function and for samplescattered neutrons. The corrected spectrum was then divided by the adopted neutron flux to obtain the experimental capture yield. Any remaining background needs to be included in the analysis of the resolved resonances. A normalization factor is needed in order to account for the absolute flux level and for the absolute detector efficiency. neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 beam fraction 0.385 0.390 0.395 0.400 0.405 FIG. 7. (Color online) A histogram of the simulated beam interception factor, i.e., the fraction of neutrons incident on a sample, for a diameter of 1.5 cm, together with the analytical description of Eq. (6). 064601-6 MEASUREMENT OF RESOLVED RESONANCES OF ... PHYSICAL REVIEW C 85, 064601 (2012) The normalization can be obtained if the measured cross section is known well enough in a particular energy region for the investigated nucleus or from a reference sample with a well-known cross section in the same measurement conditions. A related technique can be used with a sample thick enough to have a large macroscopic total cross section (nσT1) in the peak of a resonance. This results in a so-called saturated resonance where in the vicinity of the resonance peak the capture yield is not proportional to the capture cross section nσγbut to the ratio σγ/σT, independent of the sample thickness n. This particular shape of the capture yield allows the extraction of the normalization with an R-matrix fitting code, as explained in more detail for example in Ref. [47]. In this case of the thorium sample with a thickness of 4.1×10−3atoms/b, three saturated resonances of 232Th were present at 21.8, 23.5, and 69.2 eV. While we could obtain a consistent value within 0.5% for the normalization from the two lower resonances depending on the fitting conditions, we could initially not reproduce the shape of the 69.2-eV saturated resonance. The size of the applied corrections due to dead time, neutron sensitivity, and the weighting function was too small to explain the difference in shape in the saturated top of the resonance when comparing the measurement and the calculation with the code SAMMY [52]. We then simulated the expected capture yield with MCNP [44] and with GEANT4 [53], and we calculated the yield with the code REFIT [54], all using the same resonance parameters. For MCNP we have also used several calculated scattering tables [55] for this purpose, taking into account customized Doppler-broadening models, but the differences from the standard free-gas approximation for the Doppler broadening were not significant. All codes gave similar results for the two saturated resonances at 21.8 and 23.5 eV, which we eventually used to determine the normalization. However, the results for the 69.2-eV resonance were inconsistent. The calculated yield from MCNP and SAMMY practically coincided but was different from the GEANT4 simulation result, which we considered closest to reality since no approximations were made in the scattering of the neutrons off the thermally moving atomic nuclei. The results from REFIT, which uses a simplified implementation of the scattering kernel, were closer to those of the GEANT4 simulation. In Fig. 8we have plotted the different results, to which we added for completeness the experimental data. We concluded that both MCNP and SAMMY use approximations in the neutron scattering kernel which are often justified but not in the present case of the 69.2-eV resonance in 232Th with a high capture cross section combined with a high scattering-to-capture ratio. Since then the existence of this effect has been confirmed in the 36.7-eV resonance of 238U measured at Rensselaer Polytechnic Institute (RPI) [56]. Recently, Dagan has described this phenomenon in more detail and provided a workaround [57,58]. We then used the first two saturated resonances to determine the normalization factor for the capture yield. Since we used a detailed description of the geometry for the weighting function, and a neutron flux close to the absolute flux, we expect a normalization value close to unity. The two resonances at 21.8 and 23.5 eV were fitted with the R-matrix code SAMMY [52] together with the normalization. Several combinations of free and fixed resonance parameters were used for each resonance separately and both resonances together. Since the resonances are saturated, the normalization should be independent of the resonance parameters. Indeed, a very low correlation (ρ<0.1) between the normalization and the resonance parameters was found. From the various possibilities of free and fixed parameters we found normalizations consistent within 0.5%. A fit of the two resonances from which the normalization is deduced is shown in Fig. 9. IV. RESOLVED RESONANCES A. Doppler and resolution broadening The shape of the resolved resonances is affected by several broadening effects. Doppler broadening is well understood and the metallic thorium samples can be described satisfactorily with the free-gas model using an effective temperature [59]. The resolution effects due to the target and moderator system are difficult to measure precisely as a function of neutron energy. The most accurate description can be obtained from Monte Carlo simulations, which need to be validated by well-known resonances. For the n_TOF resolution function two independent simulation codes have been used in the past [40,60]. More recently, new simulations have been performed with higher statistics [61], confirming the coinciding results at neutron energies below about 5 keV, but also putting into evidence deviations at higher neutron energies. In the energy interval from 1 eV to 1 MeV we adjusted the numerical results from Ref. [60] with the analytical expression (the “RPI” function) available in the R-matrix code SAMMY [52]. Both the function and its parametrization can be found in the documentation of the code. In the R-matrix fit of resonances, an incorrect modeling of the resolution may lead to wrongly derived resonance parameters. An integral quantity such as the resonance capture integral or a Maxwellian averaged cross section is much less sensitive to incorrect resonance parameters. However, neutron energy (eV) 68.0 68.5 69.0 69.5 70.0 70.5 71.0 capture yield 0.0 0.1 0.2 0.3 0.4 0.5 0.6 n_TOF data GEANT4 REFIT SAMMY MCNP FIG. 8. (Color online) The saturated resonance at 69.2 eV calculated from the same resonance parameters with different codes, together with the experimental data. 064601-7 F. GUNSING et al. PHYSICAL REVIEW C 85, 064601 (2012) 0.0 0.2 0.4 0.6 0.8 1.0 capture yield 20.0 21.0 22.0 23.0 24.0 25.0 neutron energy (eV) -4 -2 0 2 4 residual FIG. 9. (Color online) Fit and residuals for the first two s-wave resonances from which the normalization has been fitted. if the parameters are used to calculate high-resolution cross sections with high accuracy or for example to derive strength functions or level spacings corrected for missing levels, accurate resonance parameters are needed. In addition, the resolution function is in general asymmetric, which results in a shift of the observed peak position of the resonances. In Fig. 10 we show the components (FWHM) contributing to the observed resonance width. The Doppler broadening is the main contribution at lower neutron energies, while the resolution broadening becomes the most important contribution at higher energies. The width of the proton pulse gains importance at even higher energies. The intrinsic resonance width is shown for the resonances given in the evaluated library JEFF-3.1. These widths start to be smaller than both Doppler and resolution broadening above about 60 eV. For comparison also a typical resonance spacing of 20 eV is shown in the figure. At 4 keV, where no more resolved resonances are present in the evaluated library, the resonance spacing is comparable to the combined effect of the broadening components. neutron energy (eV) 1 10 2 10 3 10 4 10 5 10 6 10 E/E (FWHM)δ -5 10 -4 10 -3 10 -2 10 -1 10 Doppler (A=232) target/moderator pulse width (7 ns) resonance spacing, (20 eV) resonance widths FIG. 10. (Color online) The various components contributing to the observed resonance widths. B. Comparison with evaluated data In Fig. 11 we plot the experimental capture yield together with the Dopplerand resolution-broadened capture yield calculated from the recent evaluation of 232Th in ENDF/BVII.0 [33]. The data are represented in 5000 bins per energy decade. ThedatainFig.11 are corrected for the backgrounds from radioactivity, neutron sensitivity, and the time-dependent background component as described in Ref. [31], which is important especially in the unresolved resonance region. A small residual background may still be included in an R-matrix fit of the resonances. The evaluation is based on a combined analysis of existing resonance parameters from both transmission measurements [16,22,62] and capture measurements [18,63] but also on experimental transmission data from Olsen et al. [22] measured at the 40-m flight path at the Oak Ridge Electron Linear Accelerator (ORELA) for eight different sample thicknesses and made available in the experimental database EXFOR, as well as a preliminary version of the present capture data, allowing a simultaneous fit of resonance parameters. The agreement is rather good, but starting from 1 keV the agreement between the present data with the evaluated data decreases. The evaluated resonances appear slightly broader than the experimental data. This is probably because in the evaluation [33] a slightly different resolution function was chosen for the n_TOF data which allowed a better match with the ORELA data. Unfortunately, the evaluation also includes many artificial resonances, with small pwaves not contributing significantly to the capture yield but added to make the data set compatible with the statistical model. The evaluated data set can therefore not be used for a statistical level analysis. Therefore we used only the 391 experimentally observed resonances from the 919 resonances presently available in ENDF/B-VII.0. The data set given in Table II reflects only the ENDF/B-VII.0 evaluated parameters without readjustment from resonances experimentally observed in the present measurement. While the only possible spin for s-wave resonances is J=1/2, the two possible spins, 1/2 or 3/2, of the p-wave resonances are usually not known and are randomly assigned in evaluations. In the case of 232Th the situation is different. From the parity nonconservation (PNC) measurements on 232Th [64]ninep-wave resonances investigated up to 300 eV showed statistically significant PNC asymmetries, and these were therefore assigned a spin J=1/2. This was the case for the resonances at 8.4, 38.2, 47.1, 64.6, 98.1, 128.2, 167.1, 196.2, and 232.0 eV. V. DISCUSSION OF UNCERTAINTIES In addition to the uncorrelated uncertainties due to counting statistics, the correlated uncertainties are important. Most of these uncertainties are described in the text. We have neglected the uncertainties due to the mass determination of the sample, dead-time correction, the correction for neutron sensitivity, and the correction from Eq. (4). The fit and subtraction of 064601-8 MEASUREMENT OF RESOLVED RESONANCES OF ... PHYSICAL REVIEW C 85, 064601 (2012) -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 20 40 60 80 100 120 140 capture yield -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 150 200 250 300 350 400 450 500 capture yield -0.05 0 0.05 0.1 0.15 0.2 0.25 500 600 700 800 900 1000 capture yield -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 1000 1200 1400 1600 1800 2000 capture yield -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 2000 2500 3000 3500 4000 capture yield neutron energy (eV) FIG. 11. (Color online) The experimental capture yield (black points) together with the capture yield calculated from evaluated data [33] including Doppler and resolution broadening (red lines). Note that the evaluation has used the present data with a slightly different resolution function than we have applied here. the background due to the radioactivity of the sample did not introduce an uncertainty larger than 0.5%. The normalization was obtained by saturated resonances in the same sample, and therefore the total uncertainty due to the weighting function and normalization was estimated at 0.5%. The most important uncertainty comes from the energy dependence of the neutron flux, including the beam interception factor. At present, we estimate this correlated uncertainty related to the energy dependence of the flux at 2%. These uncertainties have to be taken into account in a future simultaneous R-matrix analysis of all available experimental data sets. VI. STATISTICAL ANALYSIS OF NUCLEAR LEVELS Resolved resonance parameters form an interesting set of closely spaced nuclear levels at a high excitation energy 064601-9 F. GUNSING et al. PHYSICAL REVIEW C 85, 064601 (2012) (eV) 0 n Γg ∑ 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 neutron resonance energy (eV) 0 500 1000 1500 2000 2500 3000 3500 4000 ) -4 10× ( 0 S 0.65 0.70 0.75 0.80 0.85 0.90 0.95 FIG. 16. (Color online) The cumulative reduced neutron width for swaves (upper panel) and the energy-averaged reduced neutron width or neutron strength function S0(lower panel) as a function of neutron resonance energy. of Eq. (14). For the much weaker pwaves with a much larger fraction of missing levels, this method is less applicable. In Fig. 16 the cumulative sum of the reduced neutrons widths is shown in the upper panel. The lower panel shows the estimate of S0as a function of the neutron resonance energy. Up to an energy of 4 keV, an average value of S0= 0.8×10−4is found, which is close to S0=0.87 ×10−4 from Ref. [72] and to S0=(0.84 ±0.08) ×10−4from Refs. [16,65]. If one observes this estimate as a function of the energy interval as shown in the lower panel of Fig. 16,it is however clear that this value is not yet stabilized and that resonance information up to higher energies may be needed. It is therefore more difficult to ascribe a firm value for the uncertainty of S0. VII. CONCLUSION In the present work the measurement of the yield of the 232Th(n, γ ) reaction at the n_TOF facility at CERN is described. This yield, which will be submitted to the EXFOR database, can be used for future evaluations. A combined R-matrix fit with other experimental capture yields and transmission data, as done in Ref. [33], is the preferred way to obtain resonance parameters. Using our data set, we have reduced the number of resonances in the ENDF-B/VII.0 evaluation to only experimentally observed resonances. The resolved resonance data have been analyzed within the statistical model. A separation in sand pwaves, as well as the level spacing D0, and the neutron s-wave strength function S0have been extracted. ACKNOWLEDGMENTS This work has been supported by the European Commission’s 5th Framework Programme under Contract No. FIKW-CT-2000-00107 (n_TOF-ND-ADS Project). The authors would like to thank R. Dagan from KIT for his help with MCNP in relation to Doppler broadening. [1] S. David et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 443, 510 (2000). [2] A. Bidaud, Ph.D. thesis, University Paris XI, Orsay, 2005. [3] IAEA Technical Report, Thorium Fuel Cycle—Potential Benefits and Challenges, IAEA TECDOC 1450, May 2005 [http:// www-pub.iaea.org/MTCD/Publications/PDF/TE_1450_web. pdf] (unpublished). [4] Thorium Report Committee, Thorium as an Energy Source—Opportunities for Norway, Tech. Rep., January 2008 [http://www.regjeringen.no/upload/OED/Rapporter/ ThoriumReport2008.pdf] (unpublished). [5] G. E. Mitchell, J. D. Bowman, and H. A. Weidenm¨ uller, Rev. Mod. Phys. 71, 445 (1999). [6] E. I. Sharapov et al.,Phys.Rev.C61, 025501 (2000). [7] S. L. Stephenson et al.,Phys.Rev.C58, 1236 (1998). [8] T. von Egidy and D. Bucurescu, Phys. Rev. C 72, 044311 (2005). [9] H. Nakamura and T. Fukahori, Phys. Rev. C 72, 064329 (2005). [10] W. P. Abfalterer, R. W. Finlay, and S. M. Grimes, Phys. Rev. C 62, 064312 (2000). [11] F. Gunsing et al.,Phys.Rev.C61, 054608 (2000). [12] U. Agvaanluvsan et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 498, 459 (2004). [13] See, for example, the International Atomic Energy Agency [www-nds.iaea.org] or the OECD Nuclear Energy Agency [www.nea.fr]. [14] S. I. Sukhoruchkin, Z. N. Soroko, and V. V. Deriglazov, Low Energy Neutron Physics, Volume I/16B, 16C, Tables of Neutron Resonance Parameters (Springer, Landolt-B¨ ornstein, 1998, 2004). [15] S. F. Mughabghab, Atlas of Neutron Resonances (Elsevier, Dordrecht, 2005). [16] F. Rahn et al.,Phys. Rev. C 6, 1854 (1972). [17] M. Lindner, R. J. Nagle, and J. H. Landrum, Nucl. Sci. Eng. 59, 381 (1976). [18] R. L. Macklin and J. Halperin, Nucl. Sci. Eng. 64, 849 (1977). [19] W. P. Poenitz and D. L. Smith, Argonne National Laboratory, Technical Report ANL/NDM-42, 1978 (unpublished). [20] K. Kobayashi, Y. Fujita, and N. Yamamuro, J. Nucl. Sci. Techn. 18, 823 (1981). [21] R. L. Macklin, Nucl. Sci. Eng. 79, 118 (1981). [22] D. K. Olsen, R. W. Ingle, and J. L. Portney, Nucl. Sci. Eng. 82, 289 (1982). [23] R. B. Perez et al., Nucl. Sci. Eng. 80, 189 (1982). [24] K. Kobayashi et al.,Ann. Nucl. Energ. 15, 381 (1988). [25] W. Y. Baek et al.,Nucl. Instrum. Methods Phys. Res., Sect. B 168, 453 (2000). [26] Y. V. Grigoriev et al., J. Nucl. Sci. Technol. Suppl. 2, 350 (2002). [27] I. Sirakov et al.,Ann. Nucl. Energy 35, 1223 (2008). [28] A. Borella et al., Nucl. Sci. Eng. 152, 1 (2006). [29]K.Wisshak,F.Voss,andF.K ¨ appeler, Nucl. Sci. Eng. 137, 183 (2001). [30] D. Karamanis et al., Nucl. Sci. Eng. 139, 282 (2001). [31] G. Aerts et al. (n_TOF Collaboration), Phys. Rev. C 73, 054610 (2006). 064601-16 MEASUREMENT OF RESOLVED RESONANCES OF ... PHYSICAL REVIEW C 85, 064601 (2012) [32] M. B. Chadwick et al.,Evaluated Nuclear Data File ENDF/BVII.0 , Nucl. Data Sheets 107, 2931 (2006). [33] H. Derrien, L. C. Leal, and N. M. Larson, Nucl. Sci. Eng. 160, 149 (2008). [34] E. Chiaveri et al.,J. Korean Phys. Soc. 59, 1620 (2011). [35] U. Abbondanno et al., CERN Technical Report CERN-SL-2002053 ECT, 2003 (unpublished). [36] F. Belloni et al.,Eur.Phys.J.A47 (2011). [37] C. Paradela et al.,Phys.Rev.C82, 034601 (2010). [38] D. Tarrio et al.,Phys. Rev. C 83, 044620 (2011). [39] R. Sarmento et al.,Phys. Rev. C 84, 044618 (2011). [40] V. Vlachoudis. (private communication). [41] J. Pancin et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 524, 102 (2004). [42] R. Plag et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 496, 425 (2003). [43] P. M. Milazzo et al., Nucl. Instrum. Methods Phys. Res., Sect. B213 (2004/1). [44] J. F. Briesmeister, MCNP—A General Monte Carlo N-Particle Transport Code, Version 4C3, 2000. [45] U. Abbondanno et al.,Nucl. Instrum. Methods Phys. Res., Sect. A538, 692 (2005). [46] J. L. Tain et al., J. Nucl. Sci. Technol. Supplement 2, 689 (2002). [47] A. Borella et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 577, 626 (2007). [48] A. Ferrari, C. Rubbia, and V. Vlachoudis, CERN Technical Report CERN-SL-EET-2001-036, 2002 (unpublished). [49] C. Borcea et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 513, 524 (2003). [50] S. Marrone et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 517, 389 (2004). [51] F. Gunsing et al.,Nucl. Instrum. Methods Phys. Res., Sect. B 261, 925 (2007). [52] N. M. Larson, computer code SAMMY version8,OakRidge National Laboratory Report ORNL/TM-9179/R7, 2006. [53] J. Allison et al.,IEEE Trans. Nucl. Sci. 53, 270 (2006). [54] M. C. Moxon and J. Brisland, computer code REFIT, United Kingdom Atomic Energy Authority, Harwell, UK, 1991. [55] R. Dagan (private communication). [56] T.-I. Ro et al.,J. Korean Phys. Soc. 55, 1389 (2009). [57] R. Dagan, Ann. Nucl. Eng. 35, 1109 (2008). [58] R. Dagan et al.,J. Korean Phys. Soc. 59, 983 (2011). [59] W. E. Lamb, Phys. Rev. 55, 190 (1939). [60] C. Coceva et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 489, 346 (2002). [61] C. Carrapico, Nucl. Technology 168, 837 (2009). [62] P. Ribon, Ph.D. thesis, University of Orsay, France, 1969. [63] L. Forman et al.,inProceedings Third Conference on Neutron Cross Sections and Technology, Knoxville, Tennessee,Vol.2 (National Technical Information Service, US Dept. of Commerce, Springfield, Virginia, 1971), p. 735. [64] S. L. Stephenson et al.,Phys. Rev. C 58, 1236 (1998). [65] H. I. Liou, H. S. Camarda, and F. Rahn, Phys.Rev.C5, 1002 (1972). [66] J. E. Lynn, The Theory of Neutron Resonance Reactions (Clarendon, Oxford, 1968). [67] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys.Rev.Lett.52, 1 (1984). [68] M. L. Mehta, Random Matrices (Academic, New York, 1991). [69] H. A. Weidenm¨ uller and G. E. Mitchell, Rev. Mod. Phys. 81, 539 (2009). [70] L. M. Bollinger and G. E. Thomas, Phys. Rev. 171, 1293 (1968). [71] M. Gyulassy, R. J. Howerton, andS. T. Perkins, Lawrence Livermore National Laboratory Technical Report UCRL-50400, 1972 (unpublished). [72] E. S. Soukhovitskii, R. Capote, J. M. Quesada, and S. Chiba, Phys.Rev.C72, 024604 (2005). [73] F. J. Dyson and M. L. Mehta, J. Math. Phys. 4, 701 (1963). [74] G. E. Mitchell and J. F. J. Shriner, International Atomic Energy Agency Technical Report INDC(NDS)-0561, 2009 (unpublished). 064601-17