Neutron-induced fission cross section of natPb and 209Bi from threshold to 1 GeV: An improved parametrization

PHYSICAL REVIEW C 83, 044620 (2011) Neutron-induced fission cross section of natPb and 209Bi from threshold to 1 GeV: An improved parametrization D. Tarr´ ıo,1,*L. Tassan-Got,2L. Audouin,2B. Berthier,2I. Duran,1L. Ferrant,2S. Isaev,2C. Le Naour,2C. Paradela,1 C. Stephan,2D. Trubert,2U. Abbondanno,3G. Aerts,4F. ´ Alvarez-Velarde,5S. Andriamonje,4J. Andrzejewski,6 P. Assimakopoulos,7G. Badurek,8P. Baumann,9F. Beˇcv´ aˇr,10 F. Belloni,3E. Berthoumieux,4F. Calvi ˜ no,11 M. Calviani,12,13 D. Cano-Ott,5R. Capote,14,15 C. Carrapic¸o,4,16 A. Carrillo de Albornoz,16 P. Cennini,13 V. Chepel,17 E. Chiaveri,13 N. Colonna,18 G. Cortes,19 A. Couture,20 J. Cox,20 M. Dahlfors,13 S. David,2I. Dillmann,21 R. Dolfini,22 C. Domingo-Pardo,23 W. Dridi,4 C. Eleftheriadis,24 M. Embid-Segura,5A. Ferrari,13 R. Ferreira-Marques,17 L. Fitzpatrick,13 H. Frais-Koelbl,14 K. Fujii,3 W. Furman,25 I. Goncalves,17 E. Gonz´ alez-Romero,5A. Goverdovski,26 F. Gramegna,12 E. Griesmayer,14 C. Guerrero,5,13 F. Gunsing,4B. Haas,27 R. Haight,28 M. Heil,29 A. Herrera-Martinez,13 M. Igashira,30 E. Jericha,8Y. Kadi,13 F. K¨ appeler,21 D. Karadimos,7D. Karamanis,7M. Kerveno,9V. Ketlerov,25 P. Koehler,31 V. Konovalov,24 E. Kossionides,32 M. Krtiˇcka,10 C. Lampoudis,4,24 H. Leeb,8C. Lederer,33 A. Lindote,17 I. Lopes,17 R. Losito,13 M. Lozano,15 S. Lukic,9J. Marganiec,6 L. Marques,16 S. Marrone,18 T. Mart´ ınez,5C. Massimi,34 P. Mastinu,12 E. Mendoza,5A. Mengoni,14,13 P. M. Milazzo,3 C. Moreau,3M. Mosconi,21 F. Neves,17 H. Oberhummer,8S. O’Brien,20 M. Oshima,35 J. Pancin,4C. Papachristodoulou,7 C. Papadopoulos,36 N. Patronis,7A. Pavlik,37 P. Pavlopoulos,38 L. Perrot,4M. T. Pigni,8R. Plag,21 A. Plompen,39 A. Plukis,4 A. Poch,19 J. Praena,15 C. Pretel,19 J. Quesada,15 T. Rauscher,40 R. Reifarth,28 M. Rosetti,41 C. Rubbia,22 G. Rudolf,9 P. Rullhusen,39 J. Salgado,16 C. Santos,16 L. Sarchiapone,13 R. Sarmento,16 I. Savvidis,24 G. Tagliente,18 J. L. Tain,23 L. Tavora,16 R. Terlizzi,18 G. Vannini,34 P. Vaz,16 A. Ventura,41 D. Villamarin,5V. Vlachoudis,13 R. Vlastou,36 F. Voss,21 S. Walter,21 H. Wendler,13 M. Wiescher,20 and K. Wisshak21 (n TOF Collaboration) 1Universidade de Santiago de Compostela, Santiago de Compostela, Spain 2Centre National de la Recherche Scientifique/IN2P3, IPN, Orsay, France 3Istituto Nazionale di Fisica Nucleare, Trieste, Italy 4CEA/Saclay, IRFU, Gif-sur-Yvette, France 5Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, Madrid, Spain 6University of Lodz, Lodz, Poland 7University of Ioannina, Ioannina, Greece 8Atominstitut der ¨ Osterreichischen Universit¨ aten, Technische Universit¨ at Wien, Vienna, Austria 9Centre National de la Recherche Scientifique/IN2P3, IReS, Strasbourg, France 10Charles University, Prague, Czech Republic 11Universidad Politecnica de Catalunya, Barcelona, Spain 12Laboratori Nazionali di Legnaro, Istituto Nazionale di Fisica Nucleare, Legnaro, Italy 13CERN, Geneva, Switzerland 14Nuclear Data Section, International Atomic Energy Agency (IAEA), Vienna, Austria 15Universidad de Sevilla, Seville, Spain 16Instituto Tecnol´ ogico e Nuclear (ITN), Lisbon, Portugal 17LIP-Coimbra and Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal 18Istituto Nazionale di Fisica Nucleare, Bari, Italy 19Universitat Politecnica de Catalunya, Barcelona, Spain 20University of Notre Dame, Notre Dame, Indiana 46556, USA 21Karlsruhe Institute of Technology (KIT), Institut f¨ ur Kernphysik, Karlsruhe, Germany 22Universit` a degli Studi Pavia, Pavia, Italy 23Instituto de F´ ısica Corpuscular, CSIC-Universidad de Valencia, Valencia, Spain 24Aristotle University of Thessaloniki, Thessaloniki, Greece 25Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia 26Institute of Physics and Power Engineering, Kaluga Region, Obninsk, Russia 27Centre National de la Recherche Scientifique/IN2P3, CENBG, Bordeaux, France 28Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 29GSI, Darmstadt, Germany 30Tokyo Institute of Technology, Tokyo, Japan 31Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 32NCSR, Athens, Greece 33Faculty of Physics, University of Vienna, Vienna, Austria 34Dipartimento di Fisica, Universit` a di Bologna, and Sezione INFN di Bologna, Bologna, Italy 35Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki, Japan 36National Technical University of Athens, Athens, Greece 37Institut f¨ ur Isotopenforschung und Kernphysik, Universit¨ at Wien, Vienna, Austria 044620-1 0556-2813/2011/83(4)/044620(9) ©2011 American Physical Society D. TARRIO et al. PHYSICAL REVIEW C 83, 044620 (2011) 38Pˆ ole Universitaire L´ eonard de Vinci, Paris La D´ efense, France 39CEC-JRC-IRMM, Geel, Belgium 40Department of Physics, University of Basel, Basel, Switzerland 41ENEA, Bologna, Italy (Received 10 February 2011; published 28 April 2011) Neutron-induced fission cross sections for natPb and 209Bi were measured with a white-spectrum neutron source at the CERN Neutron Time-of-Flight (n TOF) facility. The experiment, using neutrons from threshold up to 1 GeV, provides the first results for these nuclei above 200 MeV. The cross sections were measured relative to 235U and 238U in a dedicated fission chamber with parallel plate avalanche counter detectors. Results are compared with previous experimental data. Upgraded parametrizations of the cross sections are presented, from threshold energy up to 1 GeV. The proposed new sets of fitting parameters improve former results along the whole energy range. DOI: 10.1103/PhysRevC.83.044620 PACS number(s): 25.85.Ec, 28.65.+a, 29.25.Dz, 28.41.−i I. INTRODUCTION Data on neutron-induced fission cross sections at intermediate energies are crucial for the development of acceleratordriven systems. natPb and 209Bi play a key role, because liquid lead-bismuth eutectic is the reference spallation target material [1]. The fission induced by high-energy neutrons in these structural materials determines the neutron spectrum shape, the extent of the target heating, and the remaining radioactivity of the target. These data are also important in fundamental nuclear physics. The fission of subactinide nuclei, for example, is instrumental in studying the effect of the transient time, where saddle configurations are more elongated. 209Bi(n,f ) was recommended as a cross section reference nucleus for neutron energies above 50 MeV, but new measurements are requested [2]. Because of its high threshold (about 20 MeV), it can be used as a fluence monitor for high-energy neutrons, even when a low-energy neutron background is present. In addition, 209Bi is a monoisotopic, nonradioactive material that shows a smooth dependence of the fission cross section on neutron energy, making it very well suited for this purpose. The present work provides a new set of high-precision measurements for the 209Bi(n,f ) and natPb(n,f ) cross sections, covering the entire energy range from threshold up to 1 GeV. The high-intensity neutron beam of the CERN Neutron Time-of-Flight (n TOF) facility compensates for the low cross section values. The results presented here are part of an experimental campaign on fission cross sections performed with the same detection setup [3,4]. II. EXPERIMENTAL METHOD The experiment was performed at the CERN n TOF facility [5]. A very intense neutron flux was produced by spallation reactions on a lead target using a 20 GeV/c proton beam from the Proton Synchrotron at CERN. The cooling water surrounding the spallation target acted as a moderator to produce a neutron flux covering a wide energy range. The long, 185-m flight path between the spallation target and the *[email protected] experimental area makes it possible to obtain high-resolution time-of-flight (TOF) measurements. Presently, n TOF is the only neutron facility that can cover the whole energy range from thermal energy to 1 GeV. More detailed descriptions can be found in the literature [6,7]. The fission fragments were detected in a reaction chamber with parallel plate avalanche counters (PPACs) that were developed at IPN Orsay [8–10], using 235U and 238Uas reference samples for defining the neutron flux. A. Parallel plate avalanche counter The PPACs used in this experiment have a central anode flanked by two cathodes. A low-pressure gas fills the 3-mm gaps between the 1.5-µm aluminized Mylar foil electrodes. The cathodes of each PPAC were segmented in perpendicular directions so that the fission fragment trajectory could be reconstructed. PPAC anode signals are very fast (9 ns width at half maximum), which reduces the pileup probabilities and makes it possible to reach energies as high as 1 GeV. The reaction chamber contained 10 PPACs, with 9 targets in between them, all placed perpendicular to the direction of the neutron beam. The fission events were identified as coincidence signals in the anodes of two consecutive PPACs. A very detailed description of the chamber and the PPACs can be found in Ref. [10]. B. Targets The samples used in this work were produced by different methods. The natPb and 209Bi samples were the result of vacuum evaporation deposition on a 240-µg/cm2extended Mylar foil, while the 235U and 238U samples were produced by electrodeposition on a 2.5-µm-thick aluminum foil. Both U samples were 8 cm in diameter. The mass distributions, the total masses, and the chemical compositions of the samples and backings were determined by Rutherford backscattering spectroscopy. The 235U and 238U masses were also measured independently by αspectroscopy. Isotopic impurities of 238U (6.28% in number of atoms), 234U (0.74%), and 236U (0.27%) were found in the 235U sample [10]. The counting rate for this target was corrected to account for the fission cross sections of these contaminants. 044620-2 NEUTRON-INDUCED FISSION CROSS SECTION OF ... PHYSICAL REVIEW C 83, 044620 (2011) FIG. 1. Schematic view of the PPAC detectors and the samples used in this experiment. Figure 1shows the 10 PPACs and the 9 samples used in the experiment: one 233U target, four 237Np targets, one 209Bi target, one natPb target, and the 235U and 238U samples that were used as reference targets to measure the neutron flux. The fission cross sections of 237Np and 233U are reported in other works [3,4]. Because the PPACs and targets are relatively thin, the neutron beam intensity was reduced in the entire setup by less than 1%, as was indicated by a simulation using the MCNP code [11]. III. DATA ANALYSIS Both fission fragments were emitted in opposite directions and were recorded in the adjacent PPACs within a coincidence window of 10 ns. This coincidence method rejects most of the background produced by αemission of the radioactive targets and by spallation reactions in the materials surrounding the samples. Additionally, the correlation between the time difference and the signal amplitude of the two PPAC anodes improves the identification of the fission events by removing random coincidences. The neutron energy was measured by the TOF technique using γflash signals for calibration. The γflash consists of γrays and ultrarelativistic light-charged particles produced when the proton beam hits the spallation target. It provides a common time reference within 1 ns for all the detectors. The maximum achievable energy in our experiment was limited by the width of the γflash and corresponds to 1 GeV. A. Cross section determination The number of detected fission events (per unit of incident energy) induced by neutrons in a target during the full measuring time is C(E)=(E)Nσ(E)(E),(1) where (E) is the time-integrated neutron fluence (measured in ncm−2MeV−1) for the full measuring time, Nis the total number of atoms in the target, σ(E) is the fission cross section of the isotope, and (E) is the detection efficiency. An additional correction for the counting rate from sample impurities must be included for 235U. The ratio of fission cross sections for two of the samples is σi(E) σj(E)=Ci(E) Cj(E) j(E) i(E) Njj(E) Nii(E).(2) The mass densities of the targets were accurately measured as explained in Sec. II B. Differences in the neutron flux and the efficiency detection for different samples are explained in the following sections. B. Beam spot correction The samples differed in size and thus received different numbers of neutrons. The 235U and 238U samples were welldefined layers 8 cm in diameter and smaller than the beam size. The natPb and 209Bi samples were spread over the entire Mylar layer, which was larger than the beam size. This is shown in Fig. 2, where the solid circle indicates the position of the 235U reference sample. Using Eq. (1), the ratio of the number of fission events inside this circle with respect to the total number of fissions is given as F=Cin(E) Ctot(E)=φin(E) φtot(E) Sin Stot n n σf(E) σf(E) (E) (E),(3) where φin(E) and φtot(E) are the density of neutrons (ncm−2) that hit the target inside the circle and in the whole beam spot, n is the number of atoms per unit area in the sample, and Sin and Stot are the areas of the circle and of the target region exposed to the beam. Cancellation of equal terms in this equation leads X (mm) -60 -40 -20 0 20 40 60 Y (mm) -60 -40 -20 0 20 40 60 Bi 209 X (mm) -60 -40 -20 0 20 40 60 Y(mm) -60 -40 -20 0 20 40 60 U 235 FIG. 2. (Color online) Position of fission events in 209Bi and 235U samples. The 8-cm circle shows the position of the 235U reference sample. 044620-3 D. TARRIO et al. PHYSICAL REVIEW C 83, 044620 (2011) E (eV) 7 10 8 10 9 10 )-1 o )/W(90 o W(0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 U 238 Bi 209 FIG. 3. (Color online) Parametrization of the anisotropy for 209Bi and 238U reported in Ref. [14] and extended up to 1 GeV assuming a decrease at the highest energies. to a global correction factor for the different target sizes: F=Cin(E) Ctot(E)=φin(E) φtot(E) Sin Stot .(4) By integrating the fission events inside the circle defined by the 235U sample and the events in the whole target, a value of F=0.81 ±0.02 was obtained to correct for the different sizes of the natPb and 209Bi samples with respect to the 235U and 238U samples. C. Detection efficiency correction The detection efficiency is an important issue for the cross section measurements. Although we impose the coincidence detection of both fission fragments, the angular acceptance is reduced because the fragments must pass through material layers before reaching the active part of the detector. The angular acceptance is different for the Pb/Bi and the U samples because of their different backings. For each sample, the maximum acceptance angle was determined by a Monte Carlo simulation and by calculating the fragment energy losses in the samples and backings based on the stopping power values of the respective materials. The thickness and the composition of the samples, backings, and material layers of the PPAC detectors were included. The mass distribution of the fission fragments for natPb and 209Bi is supposedly the same and was taken from a Gaussian fit to the experimental results of Ref. [12] for 30-MeV proton-induced fission of 209Bi. A random generator was used to select the initial fission fragment pair. A unique value of Zwas assigned to each A value, keeping the ratio Z/A constant. The total kinetic energy, calculated using Viola’s systematics [13], was distributed between both fission fragments following the inverse mass relation. For symmetric fission above 30 MeV, a Gaussian mass distribution was also assumed for the 235U and 238U samples. The dependence on the minimum energy thresholds imposed on the particles reaching the active region of the detectors was studied and average maximum acceptance angle values of 60◦ and 66◦were found for the U and Pb/Bi samples, respectively. The limited acceptance angle made it necessary to apply a suitable correction to account for the missing solid angle. The correction depends on the fission angular distributions. TABLE I. Systematic uncertainties in the fission cross sections presented in this work. Uncertainty (%) Contribution E<100 MeV E⩾100 MeV Sample mass 1.2 1.2 Thickness and threshold effects 3.5 3.5 Beam spot size 2.5 2.5 Anisotropy 1 2 Total 4.6 4.9 Because the PPACs are position sensitive, the distributions could be determined from the trajectory reconstruction. However, we did not use this because of the limited angular range covered by our system. Instead, we used the parametrization given in Ref. [14] for the anisotropy in neutronand protoninduced fission of 209Bi and 238U. We extended the data above 200 MeV up to 1 GeV by means of a simple function (see Fig. 3) assuming that the anisotropy decreases in a manner analogous to 232Th and 238U[15]. Assuming that the angular distribution W(θ)ofnatPb is very similar to that of 209Bi, the correction factor for the detection efficiency is fθ=1 xW(θ)d(cos θ) 1 0W(θ)d(cos θ) ,(5) where xis the cosine of the maximum acceptance angle in each case. For example, the correction due to the angular distribution effect reaches a maximum of 10% at 30 MeV in the cross section ratio of 209Bi and 238U. IV. SYSTEMATIC UNCERTAINTIES The total systematic uncertainty in the cross section is determined by the uncertainties associated with the different terms in Eq. (2). The mass of the targets, measured according to the explanation given in Sec. II B, introduces a systematic uncertainty of 1.2% [10]. The detection efficiency ratio contributes the largest systematic uncertainty due to differences in material thickness and detector thresholds. This uncertainty was previously estimated for this experiment by analyzing samples of the same isotope, where systematic effects could be separated [3]. The uncertainty in the anisotropy correction is less than 1% in the energy region below 100 MeV, where the anisotropy is largest. At higher energies, the anisotropy is not well known, so a 2% uncertainty was adopted. The different sample sizes add another systematic uncertainty of 2.5%, as was explained in Sec. III B. The total systematic uncertainty is shown in Table Ias the quadratic sum of the different contributions. V. EXPERIMENTAL RESULTS In this work, we determined the cross section ratios for neutron-induced fission of natPb and 209Bi. For the first time, 044620-4 NEUTRON-INDUCED FISSION CROSS SECTION OF ... PHYSICAL REVIEW C 83, 044620 (2011) En (eV) 8 10 9 10 Ratio 0 0.2 0.4 0.6 0.8 1 This work Smirnov 2004 (Protons) Kotov 2006 Bi(n,f) 209 Pb(n,f)/ nat FIG. 4. (Color online) Fission cross section ratio of σf(natPb)/σf(209Bi). Recent data obtained using neutrons [17] and high-energy protons [18] are also shown. the energy range under investigation could be extended to 1 GeV. It should be stressed, also, that our results do not rely on any normalization to previous results or evaluations, because all the numerical factors were calculated as explained. Comparisons of our results with available data in the Experimental Nuclear Reaction Data (EXFOR) database [16]areshownfor all cases. A. Cross section ratios The measured σf(natPb)/σf(209Bi) ratio is plotted in Fig. 4. Comparison with recent results of Smirnov et al. [17] exhibits good agreement in the energy range below 200 MeV. Above this energy there are only data from proton-induced fission [18], which are systematically lower. This ratio can be given with a fairly small uncertainty because no correction due to the different beam spot has to be applied, and the ratio of detection efficiency is assumed to be equal to unity. This ratio is especially interesting because En (eV) 8 10 9 10 Ratio -4 10 -3 10 -2 10 -1 10 U (This work) 235 Bi/ 209 U (This work) 235 Pb/ nat U (Laptev 2007) 235 Bi/ 209 U (Shcherbakov 2001) 235 Pb/ nat U (Protons) (Kotov 2006) 235 Pb/ nat U (Protons) (Kotov 2006) 235 Bi/ 209 U (Protons) (Prokofiev 2001) 235 Bi/ 209 U (Protons) (Prokofiev 2001) 235 Pb/ nat FIG. 5. (Color online) Fission cross section ratios for natPb/235U and 209Bi/235U vs neutron incident energy. Our results are compared with previous references using neutrons [19,20] and protons [18]. Systematics from Ref. [21] for proton-induced fission are also shown. En (eV) 8 10 9 10 Ratio -4 10 -3 10 -2 10 -1 10 U (This work) 238 Pb/ nat U (This work) 238 Bi/ 209 U (Smirnov 2004) 238 Bi/ 209 U (Prokofiev 2001) 238 Bi/ 209 U (Protons) (Kotov 2006) 238 Pb/ nat U (Protons) (Kotov 2006) 238 Bi/ 209 U (Protons) (Prokofiev 2001) 238 Bi/ 209 U (Protons) (Prokofiev 2001) 238 Pb/ nat FIG. 6. (Color online) Fission cross section ratios for natPb/238U and 209Bi/238U vs neutron incident energy. Our results are compared with previous references using neutrons [17,23] and protons [18]. Systematics from Ref. [21] are also shown. 209Bi is likely to become a new reference for neutron-induced fission in the region of subactinides [2], so cross section ratios for fission in subactinides would be measured relative to it. Ratios of natPb and 209Bi with respect to 235U are shown in Fig. 5. Data published by Laptev et al. [19]forthe209Bi/235U ratio and by Shcherbakov et al. [20]fornatPb/235U are also shown. In the region above 200 MeV, the proton-induced cross sections by Kotov et al. [18] and the systematics for protoninduced fission [21] are indicated for comparison. The present 209Bi/235U ratio is clearly lower than the data of Ref. [19], but the natPb results are in good agreement with the data set of Ref. [20]. In both cases, the proton-induced cross sections exhibit an energy dependence that is very different from the present results (except at very high energies). Although the statistical accuracy is limited at high energies because of the lower flux, our results indicate a trend to saturation around 600 and 700 MeV for 209Bi and natPb, respectively. En (eV) 8 10 9 10 (b) f σ -4 10 -3 10 -2 10 -1 10 This work Nolte 2007 Ryzhov 2006 Smirnov 2004 Shcherbakov 2002 Goldanskiy 1955 (Protons) Kotov 2006 (Protons) Prokofiev 2001 This work Pb(n,f) nat FIG. 7. (Color online) Neutron-induced fission cross section for natPb obtained at the n TOF facility. Previous results using neutrons [17,20,26–28] are shown. The parametrization of Ref. [17] is compared with the new parametrization proposed in this work (see Sec. VI). Experimental results [18] and a systematics [21]for high-energy protons are also indicated. 044620-5 D. TARRIO et al. PHYSICAL REVIEW C 83, 044620 (2011) TABLE II. Cross section ratios for neutron-induced fission and statistical uncertainties. Energy natPb/209Bi natPb/235UnatPb/238U209Bi/235U209Bi/238U (eV) 4.37 ×1070.18 ±0.14 (1.73 ±2.0) ×10−4(1.86 ±3.0) ×10−4(9.46 ±5.0) ×10−4(1.02 ±0.7) ×10−3 4.79 ×1070.47 ±0.22 (5.47 ±4.0) ×10−4(5.99 ±6.0) ×10−4(1.16 ±0.6) ×10−3(1.27 ±0.8) ×10−3 5.25 ×1070.18 ±0.09 (3.91 ±4.0) ×10−4(4.15 ±5.0) ×10−4(2.17 ±0.8) ×10−3(2.30 ±1.0) ×10−3 5.76 ×1070.28 ±0.09 (9.49 ±6.0) ×10−4(1.01 ±0.7) ×10−3(3.34 ±1.0) ×10−3(3.55 ±1.0) ×10−3 6.32 ×1070.24 ±0.07 (1.07 ±0.6) ×10−3(1.11 ±0.8) ×10−3(4.41 ±1.0) ×10−3(4.60 ±1.0) ×10−3 6.93 ×1070.42 ±0.09 (2.46 ±0.9) ×10−3(2.57 ±1.0) ×10−3(5.91 ±1.0) ×10−3(6.17 ±2.0) ×10−3 7.59 ×1070.36 ±0.07 (3.08 ±1.0) ×10−3(3.24 ±1.0) ×10−3(8.65 ±2.0) ×10−3(9.09 ±2.0) ×10−3 8.33 ×1070.38 ±0.06 (4.03 ±1.0) ×10−3(4.36 ±2.0) ×10−3(1.06 ±0.2) ×10−2(1.15 ±0.2) ×10−2 9.13 ×1070.35 ±0.06 (4.41 ±1.0) ×10−3(4.50 ±2.0) ×10−3(1.27 ±0.2) ×10−2(1.29 ±0.3) ×10−2 1.00 ×1080.39 ±0.05 (7.16 ±2.0) ×10−3(7.32 ±2.0) ×10−3(1.83 ±0.2) ×10−2(1.87 ±0.3) ×10−2 1.10 ×1080.42 ±0.05 (7.78 ±2.0) ×10−3(7.86 ±2.0) ×10−3(1.85 ±0.3) ×10−2(1.87 ±0.3) ×10−2 1.20 ×1080.45 ±0.05 (1.19 ±0.2) ×10−2(1.21 ±0.3) ×10−2(2.64 ±0.3) ×10−2(2.70 ±0.4) ×10−2 1.32 ×1080.49 ±0.05 (1.30 ±0.2) ×10−2(1.36 ±0.3) ×10−2(2.66 ±0.3) ×10−2(2.80 ±0.4) ×10−2 1.45 ×1080.44 ±0.04 (1.45 ±0.3) ×10−2(1.45 ±0.3) ×10−2(3.27 ±0.4) ×10−2(3.28 ±0.4) ×10−2 1.59 ×1080.46 ±0.04 (1.70 ±0.3) ×10−2(1.74 ±0.4) ×10−2(3.70 ±0.4) ×10−2(3.79 ±0.5) ×10−2 1.74 ×1080.48 ±0.04 (2.01 ±0.3) ×10−2(2.07 ±0.4) ×10−2(4.22 ±0.4) ×10−2(4.33 ±0.5) ×10−2 1.91 ×1080.50 ±0.04 (2.37 ±0.3) ×10−2(2.43 ±0.4) ×10−2(4.73 ±0.5) ×10−2(4.86 ±0.6) ×10−2 2.09 ×1080.55 ±0.05 (2.68 ±0.4) ×10−2(2.71 ±0.5) ×10−2(4.92 ±0.5) ×10−2(4.97 ±0.6) ×10−2 2.29 ×1080.49 ±0.04 (2.97 ±0.4) ×10−2(2.97 ±0.5) ×10−2(6.07 ±0.5) ×10−2(6.07 ±0.7) ×10−2 2.51 ×1080.63 ±0.05 (3.61 ±0.4) ×10−2(3.68 ±0.6) ×10−2(5.75 ±0.5) ×10−2(5.86 ±0.7) ×10−2 2.76 ×1080.48 ±0.04 (3.45 ±0.4) ×10−2(3.51 ±0.6) ×10−2(7.21 ±0.6) ×10−2(7.33 ±0.8) ×10−2 3.02 ×1080.60 ±0.04 (4.38 ±0.5) ×10−2(4.38 ±0.6) ×10−2(7.27 ±0.6) ×10−2(7.28 ±0.8) ×10−2 3.31 ×1080.51 ±0.04 (4.34 ±0.5) ×10−2(4.21 ±0.6) ×10−2(8.50 ±0.7) ×10−2(8.23 ±0.8) ×10−2 3.63 ×1080.60 ±0.04 (5.16 ±0.6) ×10−2(5.12 ±0.7) ×10−2(8.66 ±0.7) ×10−2(8.59 ±0.9) ×10−2 3.99 ×1080.60 ±0.04 (5.19 ±0.6) ×10−2(5.16 ±0.7) ×10−2(8.70 ±0.7) ×10−2(8.65 ±0.9) ×10−2 4.37 ×1080.61 ±0.04 (6.28 ±0.7) ×10−2(6.14 ±0.8) ×10−2(1.02 ±0.08) ×10−1(1.00 ±0.1) ×10−1 4.79 ×1080.61 ±0.04 (6.30 ±0.7) ×10−2(6.12 ±0.8) ×10−2(1.02 ±0.08) ×10−1(9.95 ±1.0) ×10−2 5.25 ×1080.60 ±0.04 (6.74 ±0.7) ×10−2(6.43 ±0.9) ×10−2(1.13 ±0.09) ×10−1(1.08 ±0.1) ×10−1 5.76 ×1080.60 ±0.04 (7.13 ±0.8) ×10−2(7.32 ±1.0) ×10−2(1.19 ±0.09) ×10−1(1.22 ±0.1) ×10−1 6.32 ×1080.63 ±0.04 (7.71 ±0.8) ×10−2(7.30 ±0.9) ×10−2(1.23 ±0.1) ×10−1(1.17 ±0.1) ×10−1 6.93 ×1080.73 ±0.04 (8.14 ±0.8) ×10−2(8.34 ±1.0) ×10−2(1.11 ±0.09) ×10−1(1.14 ±0.1) ×10−1 7.59 ×1080.68 ±0.04 (9.01 ±0.9) ×10−2(8.57 ±1.0) ×10−2(1.32 ±0.1) ×10−1(1.25 ±0.1) ×10−1 8.33 ×1080.69 ±0.04 (8.11 ±0.9) ×10−2(8.00 ±1.0) ×10−2(1.17 ±0.1) ×10−1(1.16 ±0.1) ×10−1 9.13 ×1080.64 ±0.04 (8.33 ±0.9) ×10−2(8.49 ±1.0) ×10−2(1.30 ±0.1) ×10−1(1.32 ±0.1) ×10−1 1.00 ×1090.81 ±0.07 (9.07 ±1.0) ×10−2(9.10 ±2.0) ×10−2(1.12 ±0.1) ×10−1(1.13 ±0.2) ×10−1 The ratios of natPb and 209Bi with respect to 238Uareshown in Fig. 6. We compared our results with earlier data of Smirnov et al. [17] (based on the previous work of Eismont et al. [22]) as well as with the experimental data from Prokofiev [23]. These data agree well with ours within their measured energy ranges (up to 200 MeV). Dashed lines represent the systematics of Prokofiev [21] for proton-induced fission. Concerning the proton data, both for the Prokofiev systematics and for the Kotov et al. measurements, the same trend as for the ratios over 235U is observed. Numerical results for the fission cross section ratios are shown in Table II along with the statistical uncertainty. A logarithmic energy binning of 25 bins/decade was used. The (n,f ) standard cross sections of 235U and 238U[24] are limited to energies below 200 MeV. Therefore, we used the Japanese Evaluated Nuclear Data Library High Energy File (JENDL/HE-2007) [25] to obtain the cross sections of natPb(n,f ) and 209Bi(n,f ), because it covers our whole energy range. The experimental values of the cross sections for both natPb and 209Bi are listed in Table III. B. The natPb(n,f) cross section The final result for the neutron-induced fission cross section of natPb, extended up to 1 GeV for the first time, is shown in Fig. 7. Published data by Nolte et al. [26], Ryzhov et al. [27], Smirnov et al. [17], and Shcherbakov et al. [20] with neutrons below 200 MeV are available in the EXFOR database [16] and are in agreement with this work within the statistical uncertainties. However, this is not the case with the earlier measurement of Goldanskiy et al. at 380 MeV [28], which underestimates the cross section. Above 200 MeV, essentially only proton data [18] and the systematics of Prokofiev [21]are available for comparison. The latter is in agreement with our data only at the highest energies, where the (p,f ) and (n,f ) cross sections are expected to converge. 044620-6 NEUTRON-INDUCED FISSION CROSS SECTION OF ... PHYSICAL REVIEW C 83, 044620 (2011) TABLE III. Neutron-induced fission cross sections of natPb and 209Bi with their statistical uncertainties. Energy σf(natPb) σf(209Bi) (eV) (b) (b) 4.37 ×107(3.19 ±2.0) ×10−4(1.75 ±0.5) ×10−3 4.79 ×107(1.01 ±0.4) ×10−3(2.13 ±0.6) ×10−3 5.25 ×107(6.99 ±4.0) ×10−4(3.87 ±0.8) ×10−3 5.76 ×107(1.67 ±0.6) ×10−3(5.87 ±1.0) ×10−3 6.32 ×107(1.82 ±0.6) ×10−3(7.54 ±1.0) ×10−3 6.93 ×107(4.11 ±0.9) ×10−3(9.88 ±1.0) ×10−3 7.59 ×107(5.05 ±1.0) ×10−3(1.42 ±0.2) ×10−2 8.33 ×107(6.51 ±1.0) ×10−3(1.71 ±0.2) ×10−2 9.13 ×107(6.73 ±1.0) ×10−3(1.93 ±0.2) ×10−2 1.00 ×108(1.07 ±0.2) ×10−2(2.72 ±0.2) ×10−2 1.10 ×108(1.13 ±0.2) ×10−2(2.68 ±0.3) ×10−2 1.20 ×108(1.69 ±0.2) ×10−2(3.76 ±0.3) ×10−2 1.32 ×108(1.83 ±0.2) ×10−2(3.77 ±0.3) ×10−2 1.45 ×108(1.98 ±0.3) ×10−2(4.46 ±0.4) ×10−2 1.59 ×108(2.32 ±0.3) ×10−2(5.04 ±0.4) ×10−2 1.74 ×108(2.73 ±0.3) ×10−2(5.71 ±0.4) ×10−2 1.91 ×108(3.21 ±0.3) ×10−2(6.41 ±0.5) ×10−2 2.09 ×108(3.62 ±0.4) ×10−2(6.63 ±0.5) ×10−2 2.29 ×108(4.00 ±0.4) ×10−2(8.17 ±0.5) ×10−2 2.51 ×108(4.94 ±0.4) ×10−2(7.87 ±0.5) ×10−2 2.76 ×108(4.79 ±0.4) ×10−2(1.00 ±0.06) ×10−1 3.02 ×108(6.16 ±0.5) ×10−2(1.02 ±0.06) ×10−1 3.31 ×108(6.16 ±0.5) ×10−2(1.21 ±0.07) ×10−1 3.63 ×108(7.58 ±0.6) ×10−2(1.27 ±0.07) ×10−1 3.99 ×108(7.64 ±0.6) ×10−2(1.28 ±0.07) ×10−1 4.37 ×108(9.16 ±0.7) ×10−2(1.49 ±0.08) ×10−1 4.79 ×108(9.15 ±0.7) ×10−2(1.49 ±0.08) ×10−1 5.25 ×108(9.70 ±0.7) ×10−2(1.62 ±0.09) ×10−1 5.76 ×108(1.05 ±0.08) ×10−1(1.76 ±0.09) ×10−1 6.32 ×108(1.08 ±0.08) ×10−1(1.72 ±0.10) ×10−1 6.93 ×108(1.16 ±0.08) ×10−1(1.58 ±0.09) ×10−1 7.59 ×108(1.21 ±0.09) ×10−1(1.76 ±0.10) ×10−1 8.33 ×108(1.08 ±0.09) ×10−1(1.56 ±0.10) ×10−1 9.13 ×108(1.10 ±0.09) ×10−1(1.71 ±0.10) ×10−1 1.00 ×109(1.16 ±0.10) ×10−1(1.43 ±0.10) ×10−1 C. The 209Bi(n,f) cross section The final (n,f ) cross section for 209Bi, extended for first time up to 1 GeV, is shown in Fig. 8. Earlier results obtained by Laptev et al. [19], Nolte et al. [26], Ryzhov et al. [27], Smirnov et al. [17], Fomichev et al. [29], and Gondalskiy et al. [28] with neutrons from threshold energy up to 200 MeV are also provided and are in agreement with our data. Data from Fomichev et al. are available up to 400 MeV and are compatible with our results within the statistical uncertainties. However, there is a discrepancy between our findings and those of Goldanskiy et al. at 380 MeV. For energies above 200 MeV, previous experimental data for the (p,f ) reaction [18] are higher than the present results at all energies. As expected, the Prokofiev systematics [21]for proton-induced fission shows agreement with our data at the highest energies. VI. UPDATING FISSION CROSS SECTION SYSTEMATICS A universal parametrization for neutron-induced fission in the subactinides was proposed by Smirnov et al. [17]: σf(En)=P1exp[−(P2/En)P3],(6) where P1,P2, and P3are fitting parameters that depend on the target nuclei. This suggested set of parameters fits all the previous results and also our data below 200 MeV, but it underestimates the fission cross sections above that energy, as shown in Figs. 7and 8. As was mentioned before, the 209Bi(n,f ) cross section has been recommended as a standard by the International Atomic Energy Agency (IAEA) [2]. It was proposed as a substitution for the ENDF/HE-VI evaluation, which is based on the work of Fukahori and Pearlstein [30] and does not fit experimental results obtained since then. For the sake of simplicity in the graphs, we did not include this evaluation in the figure. The IAEA standard cross section based on the work of Carlson et al. [2] reproduces our results and the previous data below 200 MeV and even in the subthreshold region [28,31–34], but it underestimates the new data presented here and those of Fomichev et al. [29]. The original parametrization of Smirnov et al. [17] fits well up to 200 MeV, but above this energy it underestimates the cross section for both natPb and 209Bi. With the new set of parameters indicated in Table IV, we can use the same function [Eq. (6)] used by Smirnov et al. [17]to extend the parametrization of the natPb and 209Bi fission cross sections up to 1 GeV while maintaining the agreement below 200 MeV (see Figs. 7and 8). The resulting parametrization for the σf(natPb)/σf(209Bi) ratio is shown in Fig. 9. It agrees with the original parametrization of Smirnov et al. [17] between around 100 and 200 MeV, but it is higher above this energy. At around 1 GeV and above, our parametrization shows a tendency toward the Prokofiev systematics [21] for proton-induced fission, where the protonand neutron-induced cross sections are expected to converge. En (eV) 8 10 9 10 (b) f σ -3 10 -2 10 -1 10 This work Laptev 2007 Nolte 2007 Ryzhov 2006 Smirnov 2004 Fomichev 2004 Goldanskiy 1955 (Protons) Kotov 2006 IAEA standard (Protons) Prokofiev 2001 This work Bi(n,f) 209 FIG. 8. (Color online) Neutron-induced fission cross section for 209Bi obtained at the n TOF facility. Earlier results using neutrons [17,19,26–29] are shown for comparison. The parametrization of Ref. [17] and our parametrization are also shown (see Sec. VI). Experimental results [18] and a parametrization [21] for protons are indicated as well. The thick solid line corresponds to the IAEA standard fission cross section [2]. 044620-7 D. TARRIO et al. PHYSICAL REVIEW C 83, 044620 (2011) En (eV) 8 10 9 10 Ratio 0 0.2 0.4 0.6 0.8 1 This work Smirnov 2004 (Protons) Prokofiev 2001 Bi(n,f) 209 Pb(n,f)/ nat FIG. 9. (Color online) Fission cross section ratio σf(natPb)/σf(209Bi) given by different parametrizations [17,21] compared to the new one proposed in this work. VII. SUMMARY AND CONCLUSIONS The natPb(n,f ) and 209Bi(n,f ) cross sections were measured at the n TOF facility from threshold energy up to 1 GeV, the highest energy reached to date. A fission chamber was developed for this purpose and the fission fragments were detected in coincidence using PPACs. The cross sections were measured relative to 235U and 238U and were converted into absolute values using the JENDL/HE-2007 evaluation. The results obtained from both reference cross sections 235U and TABLE IV. Proposed parameters of the natPb(n,f ) 209Bi(n,f ) cross sections for Eq. (6). Nuclide P1P2P3χ2/ν natPb 198.9 379.20.839 0.65 209Bi 250.0 259.00.895 1.46 238U were compatible, so the average was used for the final values. The reliability of our method is also supported by results obtained for other nuclei in the same experiment, such as 234U and 237Np [3]. Our data are in good agreement with previous experimental data up to 200 MeV. Above this energy and up to 1 GeV, where no data were previously available, our results exhibit important differences when compared to recent parametrizations, such as those of Smirnov et al. [17] and the IAEA standard based on the work of Carlson et al. [2], which were fitted to the data available below 200 MeV. The results of this work are here proposed as a new parametrization for the natPb(n,f ) and 209Bi(n,f ) cross sections covering the energy range up to 1 GeV, for the purpose of updating existing neutron fission cross section evaluations in the intermediateand high-energy region. 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