New measurement of neutron capture resonances in 209 Bi

PHYSICAL REVIEW C 74, 025807 (2006) New measurement of neutron capture resonances in 209Bi C. Domingo-Pardo,1,∗U. Abbondanno,2G. Aerts,3H. ´ Alvarez-Pol,4F. Alvarez-Velarde,5S. Andriamonje,3J. Andrzejewski,6 P. Assimakopoulos,7L. Audouin,8G. Badurek,9P. Baumann,10 F. Beˇ cv´ aˇ r,11 E. Berthoumieux,3F. Calvi ˜ no,12 D. Cano-Ott,5 R. Capote,13,14 A. Carrillo de Albornoz,15 P. Cennini,16 V. Chepel,17 E. Chiaveri,16 N. Colonna,18 G. Cortes,12 A. Couture,19 J. Cox,19 M. Dahlfors,16 S. David,20 I. Dillman,8R. Dolfini,21 W. Dridi,3I. Duran,4C. Eleftheriadis,22 M. Embid-Segura,5 L. Ferrant,20 A. Ferrari,16 R. Ferreira-Marques,17 L. Fitzpatrick,16 H. Frais-Koelbl,13 K. Fujii,2W. Furman,23 R. Gallino,24 I. Goncalves,17 E. Gonzalez-Romero,5A. Goverdovski,25 F. Gramegna,26 E. Griesmayer,13 C. Guerrero,5F. Gunsing,3 B. Haas,27 R. Haight,28 M. Heil,8A. Herrera-Martinez,16 M. Igashira,29 S. Isaev,20 E. Jericha,9Y. Kadi,16 F. K ¨ appeler,8 D. Karamanis,7D. Karadimos,7M. Kerveno,10 V. Ketlerov,16,25 P. Koehler,30 V. Konovalov,16,23 E. Kossionides,31 M. Krtiˇ cka,11 C. Lamboudis,7H. Leeb,9A. Lindote,17 I. Lopes,17 M. Lozano,14 S. Lukic,10 J. Marganiec,6L. Marques,15 S. Marrone,18 P. Mastinu,26 A. Mengoni,13,16 P. M. Milazzo,2C. Moreau,2M. Mosconi,8F. Neves,17 H. Oberhummer,9M. Oshima,32 S. O’Brien,19 J. Pancin,3C. Papachristodoulou,7C. Papadopoulos,33 C. Paradela,4N. Patronis,7A. Pavlik,34 P. Pavlopoulos,35 L. Perrot,3R. Plag,8A. Plompen,36 A. Plukis,3A. Poch,12 C. Pretel,12 J. Quesada,14 T. Rauscher,37 R. Reifarth,28 M. Rosetti,38 C. Rubbia,21 G. Rudolf,10 P. Rullhusen,36 J. Salgado,15 L. Sarchiapone,16 I. Savvidis,22 C. Stephan,20 G. Tagliente,18 J. L. Tain,1 L. Tassan-Got,20 L. Tavora,15 R. Terlizzi,18 G. Vannini,39 P. Vaz,15 A. Ventura,38 D. Villamarin,5M. C. Vincente,5 V. Vlachoudis,16 R. Vlastou,33 F. Voss,8S. Walter,8H. Wendler,16 M. Wiescher,19 and K. Wisshak8 (n TOF Collaboration) 1Instituto de F´ ısica Corpuscular, CSIC-Universidad de Valencia, Spain 2Istituto Nazionale di Fisica Nucleare, Trieste, Italy 3CEA/Saclay-DSM, Gif-sur-Yvette, France 4Universidade de Santiago de Compostela, Spain 5Centro de Investigaciones Energeticas Medioambientales y Technologicas, Madrid, Spain 6University of Lodz, Lodz, Poland 7University of Ioannina, Greece 8Forschungszentrum Karlsruhe GmbH (FZK), Institut f¨ ur Kernphysik, Germany 9Atominstitut der ¨ Osterreichischen Universit¨ aten,Technische Universit¨ at Wien, Austria 10Centre National de la Recherche Scientifique/IN2P3-IReS, Strasbourg, France 11Charles University, Prague, Czech Republic 12Universitat Politecnica de Catalunya, Barcelona, Spain 13International Atomic Energy Agency, NAPC-Nuclear Data Section, Vienna, Austria 14Universidad de Sevilla, Spain 15Instituto Tecnol´ ogico e Nuclear(ITN), Lisbon, Portugal 16CERN, Geneva, Switzerland 17LIP-Coimbra & Departamento de Fisica da Universidade de Coimbra, Portugal 18Istituto Nazionale di Fisica Nucleare, Bari, Italy 19University of Notre Dame, Notre Dame, USA 20Centre National de la Recherche Scientifique/IN2P3-IPN, Orsay, France 21Universit` a degli Studi Pavia, Pavia, Italy 22Aristotle University of Thessaloniki, Greece 23Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia 24Dipartimento di Fisica, Universit` a di Torino and Sezione INFN di Torino, Italy 25Institute of Physics and Power Engineering, Kaluga region, Obninsk, Russia 26Istituto Nazionale di Fisica Nucleare(INFN), Laboratori Nazionali di Legnaro, Italy 27Centre National de la Recherche Scientifique/IN2P3-CENBG, Bordeaux, France 28Los Alamos National Laboratory, New Mexico, USA 29Tokyo Institute of Technology, Tokyo, Japan 30Oak Ridge National Laboratory, Physics Division, Oak Ridge, USA 31NCSR, Athens, Greece 32Japan Atomic Energy Research Institute, Tokai-mura, Japan 33National Technical University of Athens, Greece 34Institut f¨ ur Isotopenforschung und Kernphysik, Universit¨ at 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 0556-2813/2006/74(2)/025807(10) 025807-1 ©2006 The American Physical Society C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 74, 025807 (2006) 38ENEA, Bologna, Italy 39Dipartimento di Fisica, Universit` a di Bologna, and Sezione INFN di Bologna, Italy (Received 1 December 2005; published 23 August 2006) The neutron capture cross section of 209Bi has been measured at the CERN n TOF facility by employing the pulse-height-weighting technique. Improvements over previous measurements are mainly because of an optimized detection system, which led to a practically negligible neutron sensitivity. Additional experimental sources of systematic error, such as the electronic threshold in the detectors, summing of γ-rays, internal electron conversion, and the isomeric state in bismuth, have been taken into account. γ-Ray absorption effects inside the sample have been corrected by employing a nonpolynomial weighting function. Because 209Bi is the last stable isotope in the reaction path of the stellar s-process, the Maxwellian averaged capture cross section is important for the recycling of the reaction flow by αdecays. In the relevant stellar range of thermal energies between kT =5 and 8 keV our new capture rate is about 16% higher than the presently accepted value used for nucleosynthesis calculations. At this low temperature an important part of the heavy Pb-Bi isotopes are supposed to be synthesized by the s-process in the He shells of low mass, thermally pulsing asymptotic giant branch stars. With the improved set of cross sections we obtain an s-process fraction of 19±3% of the solar bismuth abundance, resulting in an r-process residual of 81±3%. The present (n, γ ) cross-section measurement is also of relevance for the design of accelerator driven systems based on a liquid metal Pb/Bi spallation target. DOI: 10.1103/PhysRevC.74.025807 PACS number(s): 25.40.Lw, 25.40.Sc, 27.80.+w, 97.10.Cv I. INTRODUCTION 209Bi is the end-point isotope of the s-process path. Its observed abundance has been finally understood in terms of the main s-process component, operating in the He-shell of low mass, low metallicity, thermally pulsing asymptotic giant branch (AGB)stars[1,2]. However, the complex production pattern at the end of the s-process path still hides important information, that can be unraveled by means of accurate neutron capture measurements. Capture on bismuth leads to the ground state of 210Bi, which βdecays to 210Po that is α-unstable, producing 206Pb (see Fig. 1). However, given the 210Po half-life of 138 days it can also act as a branching point by capturing another neutron and enhancing the abundance of 207Pb instead. Another contribution to 207Pb may be because of a long-lived isomer in 210Bi at 271 keV. Neutron capture on this isomer leads to 211Bi with an α-decay half-life of 2.17 min. The two branchings, at 210Po and 210Bi, depend strongly on the stellar conditions of neutron density and temperature. Given an appropriate stellar model and accurate neutron capture cross sections, the sabundances of the Pb/Bi isotopes can be more reliably determined, thus providing a better decomposition of the respective r-process abundances and of the radiogenic contributions because of the Th/U αdecays. The latter information represents a viable constraint on the Th/U abundances calculation and its use as cosmochronometers [3,4]. For the discussion of these astrophysical aspects, the present status of the 209Bi capture data is rather unsatisfactory [5]. Previous experiments exhibit significant discrepancies suggesting the existence of systematic uncertainties, which must be clearly reduced for a more quantitative assessment of the Pb/Bi abundances. Two capture resonance studies on ∗Electronic address: Cesar[email protected] 209Bi have been reported so far, one at ORNL [6] and the other at GELINA [7,8]. In the former measurement, two strong s-wave resonances at low neutron energy could not be measured because of a low-neutron-energy cutoff at 2.6 keV. In addition, substantial corrections were needed for some of the resonances in order to account for the neutron sensitivity of the experimental setup employed. The GELINA measurement was also affected by significant corrections for neutron sensitivity. The 209Bi (n, γ ) cross section has also a very practical application. Thanks to its properties of chemical inertness, high boiling point, low neutron moderation, and large scattering cross section, an eutectic mixture of lead and bismuth is presently considered as a very appropriate material for the spallation target and as the coolant for accelerator driven systems (ADS). In a first sensitivity study of the neutron cross sections of the main materials used in this type of hybrid reactor [9], severe discrepancies were found between different evaluated nuclear data files. As a consequence, a list of isotopes was tagged for high priority measurements. Initially, most of the requested cross sections corresponded to the fuel and cladding materials and were focused on the elastic, inelastic, and (n, xn) channels. However, a recent extension of the same study [10] includes additional requests for the capture reactions in the spallation/coolant materials lead and bismuth. Comparing two evaluated data files, ENDF/B-VI.8 and JENDL 3.3, discrepancies in the neutron balance of 12.5% were identified to result from the uncertainties of the (n, γ ) cross section of 209Bi alone. Hence, the precise knowledge of the neutron capture cross sections of the lead and bismuth isotopes turned out to be of key relevance for the design of an ADS suited for the transmutation of radioactive residues and for energy production. Apart from its contribution to the neutron balance, neutron capture on 209Bi affects the radiotoxicity as well. Buildup of the α-emitters 210Bim(t1/2=3×106yr) and 210Po (t1/2= 025807-2 NEW MEASUREMENT OF NEUTRON CAPTURE . . . PHYSICAL REVIEW C 74, 025807 (2006) 202 203 204 205 203 204 205 206 207 208 209206205204 210 210 Hg Hg HgHg Tl Tl Tl Tl Pb Pb Pb Pb Pb Pb Bi Po 29.86 46.59d 6.87 29.524 70.476 1.4 24.1 22.1 52.4 3.253h 138.38d Po 211 3Ma 25.2s 0.516s α 5.013d Bi 211 Tl 207 s—process path 15Myr 3.78yr 5.2min 4.2min 4.77min 2.17min Bi 209 100 FIG. 1. (Color online) The s-process reaction network terminates at 209Bi. Shaded boxes designate stable isotopes. Decays from the α-unstable 210,211Po isotopes are represented with dashed lines. Quantities below the isotopic symbols show natural abundances or half-lives. 138 d) contributes to the longand short-term radiotoxicity of the spallation target and of the coolant. These hazards can only be evaluated on the basis of a precise (n, γ ) cross section of bismuth and with accurate data concerning the partial cross sections leading to 210Bimand 210Po. II. CROSS-SECTION MEASUREMENT The neutron energy differential capture cross section of 209Bi has been measured at the n TOF installation of CERN using the time-of-flight (TOF) technique. Because this facility has been described in detail elsewhere [11], only the main features are summarized in Sec. II A. The major motivation for this measurement was to overcome the systematic uncertainty related to the neutron-scattering background, which arises in measurements on isotopes with a dominant scattering channel. Sample scattered neutrons are easily captured in the materials surrounding the detector or in the sensitive detector volume itself, producing γ-rays, which appear as a prompt, TOF-dependent background. This effect becomes particularly crucial for the broad s-wave resonances in bismuth at low-neutron energies between 0.8 and 12 keV, resulting in corrections as large as 50% in previous measurements [6]. For this reason the reaction yield of this isotope has been measured with a set of total energy detectors consisting of optimized C6D6liquid scintillation detectors (Sec. II B). This setup turned out to be of pivotal importance for the efficient suppression of the background from scattered neutrons. Other sample-related corrections were significantly reduced by choosing a comparably small bismuth sample 20 mm in diameter and 6.1 mm in thickness. The cross section is determined relative to the 4.9 eV 198Au resonance by employing the saturated resonance technique [12]. For this purpose a gold sample 1 mm in thickness and 20 mm in diameter was measured in regular intervals. A thorough analysis of the capture data, including extensive Monte Carlo simulations of the necessary corrections to the experimental data, allowed us to determine the final cross section with a systematic uncertainty of better than 3%. A. The n TOF installation At n TOF, neutrons are produced via spallation reactions induced by 20 GeV protons in a lead target. Pulses of (3–7)×1012 protons with a duration of 6 ns (rms) hit the Pb-block with a typical repetition rate of 0.4 Hz. This very low duty cycle combined with the very high intensity in the beam pulses makes n TOF an ideal facility for TOF measurements on radioactive samples. The low repetition rate has allowed to implement an advanced data acquisition system with zero dead time based on Flash-amplitude-to-digital converters [13]. The number of neutrons arriving at the sample are monitored by means of a 200-µg/cm2-thick 6Li foil centered in the beam. The particles emitted in the 6Li(n, α)3H reaction are registered with four silicon detectors surrounding the 6Li foil outside of the beam. The neutron monitor [14] is mounted in an evacuated carbon fiber chamber 3 m upstream of the samples. The samples, which are positioned at a flight path of 185 m, are fixed on a sample changer, which is also made of carbon fiber. The neutron intensity has been determined by means of two independent measurements, performed with the Si-monitor described above and with a calibrated fission chamber [15]. Two measurements were carried out with the latter detector, employing foils of 235U and 238U. Calibration of the absolute yield in (n, γ ) measurements via the saturated resonance method requires actually only the shape of the neutron flux, which can be directly determined from the Si-monitor and fission chamber measurements with an uncertainty below ±2% [16]. The beam profile at the sample position has been determined to exhibit an approximate Gaussian shape with σ= 7 mm, slightly off centered (x=1.5 mm) [17]. The samples used in this measurement cover about 60% of the neutron beam. The excellent neutron energy resolution of the n TOF facility is because of the long flight path of 185 m and the short proton pulse width. The resolution function was determined by means of Monte Carlo simulations [18] and has been validated experimentally by measuring narrow pand d-wave capture resonances on a sample of natFe. B. Experimental setup A general view of the experimental setup is shown in Fig. 2. The detection system used with the pulse-height-weighting technique (PHWT) [19] had been optimized with respect to the sensitivity for scattered neutrons, the most crucial source of background in (n, γ ) studies on neutron magic nuclei, which are characterized by particularly large scattering-to-capture ratios. Scattered neutrons may be subsequently captured in the detectors or in nearby materials, where they produce γ-rays, which are likely to be registered with high probability, thus mimicking true capture events in the sample. In an effort to reduce the neutron sensitivity as much as possible, special C6D6liquid scintillation detectors [20] have been developed consisting of materials with low-neutroncapture cross sections. The main features of these detectors are thin-walled scintillator cells made of carbon fiber, which are 025807-3 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 74, 025807 (2006) directly glued onto the photomultiplier tubes, thus eliminating dead materials, e.g., the common quartz window of the scintillator cells. To avoid the additional material of a support, the detectors were hanging on thin cords fixed at the ceiling. Similarly, the sample changer was made of carbon fiber as was the frame of the sample-holder. The samples were mounted on thin Kapton foils, which were glued on the frame that was much larger than the diameter of the neutron beam. In this way, the neutron sensitivity in the critical energy range from 1 to 100 keV could be reduced by factors of 3–10 [20]. The two detectors were placed at an angle of ∼125◦with respect to the sample to minimize the angular distribution effects of the primary capture γrays. Also the background resulting from in-beam γ-rays scattered in the sample was considerably reduced in this configuration [21]. III. DATA ANALYSIS In this section, the PHWT principle is reviewed together with the related systematic uncertainties of relevance for this type of capture measurements, followed by the determination of the weighting factors. We describe the calculation of accurate yield corrections and the analysis procedure to determine resonance parameters. A. Pulse-height-weighting technique and systematic uncertainties The PHWT is based on two conditions: (i) that the detector efficiency εγ1 so that at most only one γray per capture cascade is registered and (ii) that εγis proportional to the energy of the registered γ-ray, εγ≈αEγ. Under these two conditions, the efficiency εcfor detecting a capture event, i.e., a cascade composed of mγrays, becomes proportional to the sum energy Ecof that cascade. In this case one obtains εc=1− m  j=1 (1 −εγj)≈ m  j=1 εγj ≈αEc,(1) which is a constant independent of the actual deexcitation pattern of the nucleus produced in the capture reaction. It is worth noting that the approximations in Eq. (1) are the better justified the better conditions (i) and (ii) are fulfilled. The validity of Eq. (1) can be challenged by several experimental problems. In particular, condition (i) is violated if more than one γray of the cascade is registered in the same detector. Moreover, the product as well as the sum over the mγrays of the cascade is always incomplete because of the unavoidable loss of γrays because of electronic threshold applied to the detector signals, converted transitions, and partial population of the isomeric state in 210Bi at 271 keV. For all these effects, which may influence the validity of Eq. (1), appropriate corrections have to be determined as is shown in the following subsections. As far as condition (ii) is concerned, the proportional increase of the efficiency with γ-ray energy is enforced by an appropriate modification of the detector energy response distribution R(E). This is achieved by application of a pulseheight-dependent weighting factor Wi, such that the weighted sum of the response for a γ-ray j,Rij , becomes proportional to its energy Eγj,  i WiRij =αEγj.(2) The second approximation in Eq. (1) depends directly on the accuracy of the calculated weights Wi, which can be tested as discussed below. B. Weighting factors It has been shown [22,23] that realistic response functions Rij for mono-energetic γrays with energies Eγj can be determined by means of Monte Carlo simulations for any particular setup for (n, γ ) measurements. A set of expressions of the form of Eq. (2) can then be used to derive the weighting factors Wi. The detailed geometry and chemical composition of the experimental setup has been implemented in the Monte Carlo simulation using GEANT4 [24] (see Fig. 2). The composition of the carbon fiber, which is by far the dominant structural material, was determined by an RBS analysis [25], yielding C/O/N/Ca/Br =2.0/0.2/0.16/0.012/0.016. Also, the capture γrays were carefully traced, assuming a radial distribution for the emission probability inside the sample according to the neutron beam profile described in Sec. II A. The depth distribution was included as well because it changed significantly from a practically uniform to a surface peaked shape between weak and strong resonances, respectively. The weighting function (WF) of the gold calibration sample was obtained using the conventional approximation by a polynomial function of order k=4,W i=k=4 k=0akEk i.The values of the coefficients akwere derived from a least-squares minimization, min  j i WiRij −Eγj2 .(3) Because of the higher γ-ray absorption in the 6.1-mmthick bismuth sample the proportionality condition (ii) could FIG. 2. (Color online) The geometry of the experimental setup used in the GEANT4 simulation of the weighting functions. 025807-4 NEW MEASUREMENT OF NEUTRON CAPTURE . . . PHYSICAL REVIEW C 74, 025807 (2006) (MeV) dep E 012345 Counts 1 10 2 10 3 10 n_TOF Exp. Stat. Model (MeV) dep E 012345678 Counts 1 10 2 10 3 10 n_TOF Exp. Stat. Model FIG. 3. Comparison of experimental (dashed) and simulated (solid) pulse height spectra of 210Bi (left) and 198Au (right) illustrating the quality of the simulations. not be satisfied with the polynomial WF approach. In this case an accurate, pointwise WF was obtained by means of a linear regularization method for solving the inverse problem of Eq. (2)[16]. In this way the uncertainty connected with the polynomial WF has been reduced to 0.3%, an improvement by an order of magnitude. The systematic uncertainty introduced by the WF was determined as described in Ref. [23], basically by performing Monte Carlo simulations of the capture cascades at a certain resonance. The deexcitation pattern is modeled by combining the experimentally known levels at low excitation energy with a statistical model of the nucleus to complete the cascade up to the capture energy. These simulated capture events can be used to estimate the uncertainty of the calculated WF. To illustrate the performance of the cascade event generator for the samples measured in this experiment, the simulated pulse-height spectra RC ifor the 802 eV resonance in 210Bi and for the 4.9 eV resonance in 198Au are compared in Fig. 3with the corresponding experimental spectra measured at n TOF. The spectra based on the simulated cascades show in general a good agreement with the experimental spectra. The small differences at higher energy can be ascribed to the employed statistical model and to a lesser extent to the uncertainties in the calibration of the C6D6detectors. In principle, these differences could be minimized by modifying the relative strength of M1 and E1 transitions in the statistical part of the cascades and/or the instrumental resolution. However, the effect on the weighted sum iWiRC iand, therefore, on the estimated uncertainty becomes absolutely negligible in both cases. In summary, it was found that the simulated pulse height spectra can be employed for the determination of the uncertainty of the WF. By computing the weighted sum of each capture cascade with the calculated weighting functions, we obtain values, which deviate by less than 0.3% from the corresponding capture energies. This means that condition (ii) is fulfilled within 99.7%, leading to a practically negligible uncertainty because of the calculated WF. C. Yield correction factors The corrections for the electronic threshold, γ-summing, internal conversion, and the effect of the isomeric state (see Sec. III A) have been estimated by detailed Monte Carlo simulations of the capture events in a similar manner as in Ref. [23]. Although internal conversion and summing of cascade γrays were found to have a minor effect of less than 2% on the capture yield of the bismuth sample, more significant corrections are required for the electronic threshold and for the isomeric state in 210Bi. The isomeric state is included in the simulation by assigning a null branching ratio to the level of 271 keV, so that the deexcitation cascade ends at that level whenever it is reached. The yield correction factor including all these effects can be calculated as ft,s,ce,m =nEc i=tWiRC i ,(4) where RC iis the total response of the detection system for n simulated capture events. For a threshold tof 200 keV, the yield correction factors calculated with this procedure for the bismuth sample are listed in the third column of Table I. Because the simulated spectra for resonances with same spin and parity are very similar, i.e., almost independent of the resonance energy, the correction factors could be classified according to spin and parity of the resonance (first column in Table I). The population of the isomeric state calculated with our statistical model of the nucleus is shown in the second column of Table I. For comparison, and to illustrate the possible uncertainty of the calculation, the correction factor of the hypothetic case, where the isomer is populated with 100% probability is shown in the last column. The differences were found to range between 1% and 2.5%. As mentioned before, the cross section is determined relative to the 4.9-eV resonance in 197Au. Therefore, the capture yield measured with the gold sample had to be corrected for experimental effects of threshold, γ-ray summing, and internal conversion. The corresponding correction factor for a threshold of 200 keV is ft,s,ce Au =1.046(2). Hence, the final correction for each resonance is the ratio between the corresponding factor ft,s,ce,m from Table I and ft,s,ce Au . This ratio oscillates between 5% and 7%. It can be concluded, that the threshold, γ-summing, and internal TABLE I. Yield correction factors for the bismuth sample calculated for a threshold of 200 keV. JπIsom. popul.(%) ft,s,ce,m ft,s,ce,100%m 3+6 1.124(2) 1.103(2) 4−8 1.131(2) 1.118(2) 4+9 1.143(2) 1.116(2) 5−23 1.137(2) 1.109(2) 5+22 1.142(2) 1.119(2) 6+44 1.134(2) 1.114(2) 025807-5 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 74, 025807 (2006) conversion effects do not cancel out by measuring with respect to a reference sample. Neglecting these corrections could lead to systematic deviations in the yield determination of > ∼5%. D. Neutron sensitivity For a certain resonance at energy E◦with capture and neutron widths, γand n, the probability that a signal in the C6D6scintillator is caused by a neutron scattered in the sample and eventually captured in the detector is given by Pns =εn εcn γ,(5) where εndenotes the probability of detecting a γ-ray produced by sample-scattered neutrons in or near the detector and εcthe probability to register a γ-ray from a true capture cascade. This requires a correction of the experimental resonance yield by fns =1 1+Pns .(6) Equation (5) can be rewritten as, Pns =εn εγεγ εcn γ,(7) where εγis the detection probability for a γ-ray of a given energy. For an energy Eγ=600 keV, εn/εγhas been calculated by means of Monte Carlo simulations for comparison with the experimentally determined value reported in Ref. [20]. The second factor, εγ/εc, has been determined by a detailed Monte Carlo simulation of the present experimental setup. The efficiency εγwas obtained for γrays of 600 keV, whereas εcwas determined using simulated capture cascades (see Secs. III B and III C). Finally, n/ γis to be determined by an iterative procedure of correcting and fitting the value of γof the corresponding resonance. In case of the s-wave resonance at 12.1 keV, which has the largest n/ γof all analyzed bismuth resonances, the corresponding ratios were found to be εγ/εc=0.446 (this work) and (εn/εγ)12.1keV =1.5841 ×10−5[20]. Because of the very low neutron sensitivity the required correction for the 12.1-keV resonance of 3.6±0.7% is relatively small and practically negligible for the rest of the s-wave resonances in bismuth. The 20% uncertainty of this correction results from neutron captures in the quartz window of the photomultiplier tube because of the uncertain silicon cross sections, which contribute a 10% uncertainty to εn/εγ, and from the resonance parameters nand γ, which exhibit uncertainties of 8% and 10%, respectively. E. R-matrix analysis The experimental yield Yexp =ft,s,ce,mfnsfsat Nw NnEc (8) was determined by the weighted net count rate (Nw), the effective binding energy Ec, the integrated neutron flux Nn (obtained from the Si-monitor and from the shape of the neutron flux, Sec. II A), and the corrections discussed before. The factor fsat corresponds to the absolute normalization via the analysis of the saturated resonance at 4.9 eV in 198Au. The yield has been analyzed with the multilevel R-matrix code SAMMY [26]. Using an iterative procedure based on Bayes’s theorem, Yexp is fitted with a function of the type, Yexp =Yf(E◦, n, γ)+B, (9) where Yfcorresponds to a parametrization as a function of the resonance parameters E◦, n, and γaccording to the Reich-Moore formalism. For all partial waves a channel radius of 9.6792 fm was used. Whereas the well-known nvalues from transmission measurements were adopted, the resonance energies E◦and capture widths γhave been fitted to the experimental data. The background below the resonance is described by the constant term B. In the fits with SAMMY, sample effects (single and double neutron scattering inside the sample) as well as thermal broadening are taken into account. The resolution function of the facility (Sec. II A) has been considered in the fits using the RPI parametrization. The present results are illustrated in Fig. 4at the example of the first two s-wave resonances in 210Bi. The comparison with the capture yields calculated with the corresponding resonance parameters quoted in the ENDF/B-VI.8 evaluation demonstrates the improvement because of the reduced systematic uncertainties of the n TOF data. IV. RESULTS In total, 21 resonances were identified in the 209Bi(n, γ ) data in the energy range from 800 to 23150 eV. The respective capture widths and areas are listed in Table II. Beyond 23 keV further resonances could not be observed because of the in-beam γ-ray background [21], which was the major limitation in this experiment. However, this background (eV) n E 700 800 900 Yield 0.01 0.02 (keV) n E 2.2 2.3 2.4 2.5 Yield 0.004 0.006 0.008 0.01 FIG. 4. (Color online) R-matrix analysis of the first two resonances in bismuth. The dashed line corresponds to the yield calculated with the resonance parameters quoted by the ENDF/BVI.8 evaluation. 025807-6 NEW MEASUREMENT OF NEUTRON CAPTURE . . . PHYSICAL REVIEW C 74, 025807 (2006) TABLE II. Resonance parametersaand radiative kernelsbfor 209Bi. E◦(eV) lJn(meV) γ(meV) gγn/(meV) 801.6(1) 0 5 4309(145) 33.3(12) 18.2(6) 2323.8(6) 0 4 17888(333) 26.8(17) 12.0(8) 3350.83(4) 1 5 87(9) 18.2(3) 9.5(2) 4458.74(2) 1 5 173(13) 23.2(22) 11.3(11) 5114.0(3) 0 5 5640(270) 65(2) 35.3(11) 6288.59(2) 1 4 116(18) 17.0(17) 6.7(7) 6525.0(3) 1 3 957(100) 25.3(14) 8.6(5) 9016.8(4) 1 6 408(77) 21.1(14) 13.0(9) 9159.20(7) 1 5 259(45) 21.4(21) 10.9(11) 9718.910(1) 1 4 104(22) 74(7) 19.5(21) 9767.2(3) 1 3 900(114) 90(8) 28.7(26) 12098 65(4)c 15649.8(1.0) 1 5 1000 47(4) 20.2(17) 17440.0(1.3) 1 6 1538(300) 32(3) 20.4(18) 17839.5(9) 1 5 464(181) 43(4) 21.7(20) 20870 1 5 954(227) 34.4(33) 18.3(17) 21050 1 4 7444(778) 33(3) 14.8(13) 22286.0(9) 1 5 181(91) 33.6(32) 15.1(15) 23149.1(1.3) 1 6 208(154) 25.3(25) 14.7(15) aAngular orbital momenta, l, resonance spins J, and neutron widths, n, are mainly from Refs. [27,28]. bUncertainties are given as 18.2(6)≡18.2±0.6. cThis area corresponds to the sum of the areas of the broad s-wave resonance at the indicated energy, plus two p-wave resonances at 12.092 and 12.285 keV. did not affect the initial aim of improving the systematic uncertainty of the broad s-wave resonances below 100 keV. The capture areas determined at n TOF are compared in Fig. 5with the previous measurements performed at ORNL [6] and GELINA [7]. For most of the resonances shown in Fig. 5, there is a fair agreement with the ORNL data. However, significantly higher values are reported in the latter measurement for the two resonances at 3.3 and 5.1 keV and a lower cross section for the resonance at 9.77 keV. The GELINA data show agreement Resonance Energy (eV) 0 5000 10000 15000 20000 (meV)Γ/ n Γ γ Γg 0 10 20 30 40 50 60 70 This work GELINA ORNL 0 5000 10000 15000 20000 Ratio 0 1 2 FIG. 5. (Color online) Comparison of the radiative capture kernels derived from the measurements at n TOF, GELINA, and ORNL. The capture area shown at 2.3 keV for ORNL corresponds to an estimation reported in Ref. [6]. The capture area shown at ∼12 keV corresponds to the sum of the three resonances in that region. with n TOF in several cases, but there is an average trend of lower cross sections. The largest differences in absolute values are for the resonances at 5.1 and 9.77 keV and the group at 12.1 keV. For these three resonances, the ORNL data show the opposite trend for the 5.1-keV resonance, agree with GELINA for the 9.77 keV resonance, and agree with the n TOF data for the 12.1 keV group. The general systematics of better average agreement with the ORNL data and lower average values of the GELINA data, might be related to the weighting functions used in the respective experiments, although threshold correction effects (see Sec. III C) could play a role as well. Moreover, systematic deviations because of the neutron sensitivity corrections applied to some particular resonances cannot be excluded. A. Discussion of uncertainties The measuring technique employed in this work and the data-analysis procedures described in Secs. III and III C have been validated experimentally at n TOF [23]. According to this study, the various contributions to the systematic uncertainty of the present data are about 2%. In addition, the energy dependence of the neutron flux has been found to exhibit an uncertainty of 2% as well, resulting in a total systematic uncertainty of better than 3%. In this discussion, the neutron sensitivity correction has to be considered separately because it has been applied only to one of the measured resonances. Although the uncertainty of the correction was 20%, the contribution to the systematic uncertainty of the capture kernel was only 0.7% in this case. 025807-7 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 74, 025807 (2006) V. IMPLICATIONS FOR THE S-ABUNDANCES IN THE PB-BI REGION The slightly higher cross sections for s-wave resonances measured at n TOF with respect to the values obtained at GELINA may affect the synthesis of the Pb/Bi. This holds preferentially at lower stellar temperature, because the neutron sensitivity correction becomes less relevant above 100 keV, where the relative contribution of the neutronscattering channel decreases. Qualitatively, the consequence of a higher 209Bi cross section would reduce the survival probability and, hence, the s-process abundance of this isotope, but this could be compensated to some extent through an enhanced production through α-recycling via 206,207Pb. In the calculation of the Maxwellian averaged cross sections (MACS), the n TOF resonances have been complemented between 25 and 31 keV with resonances from Ref. [7] and in the interval from 31 to 60 keV with capture areas from Ref. [27]. The additional resonances represent 2% and 7% of theMACSatkT =5 and 8 keV, respectively. At lower stellar temperature, comparison of the results in Table III with the MACS obtained at GELINA [8] shows that the new values are 16% larger. Beyond kT =20 keV, the MACS is strongly influenced by the average capture cross section above 80 keV, which has been determined experimentally in Ref. [8]. For this reason, the differences obtained in the strong s-wave resonances at lower neutron energy do not affect substantially the MACS at 20–25 keV. The MACS given in Table III refer to the lower temperature regime of the common stellar s-process site associated with thermally pulsing low mass AGB stars [29]. According to the Galactic chemical evolution (GCE) model described in Refs. [1,2], the s-process abundances of 208Pb and 209Bi are essentially produced in stars of low metallicity. In this model about 95% of the neutron exposure is because of the 13C(α, n)16O reaction, which operates during the interpulse phase between He shell flashes at temperatures around ∼108K, corresponding to a thermal energy of kT ≈8keV. The additional neutron irradiation provided by the 22Ne(α, n)25Mg reaction at the higher thermal energy of kT =23 keV during the He shell flash is rather weak. Hence, the abundances of isotopes with small cross sections are still dominated by what has been produced at the lower-temperature of the interpulse phase. Therefore, the low-temperature part of the MACS is important for this stellar model. With respect to the solar abundance tables of Anders and Grevesse [30], the TABLE III. Maxwellian averaged cross sections of 209Bi compared to recent previous data. kT This work Mutti et al. [8] (keV) (mb) (mb) 5 13.05(84) 11.25(58) 8 8.62(54) 7.48(44) 20 3.41(50) 3.34(42) 25 2.89(50) 2.85(45) GCE model [2] provides s-process abundances of 206Pb, 207Pb, and 209Bi at the epoch of the solar system formation of 62%, 79%, and 19%, respectively. According to the sensitivity study reported in Ref. [5], the present result (see Table III) is not expected to affect the abundances of 206,207Pb by α-recycling from A=210. This was confirmed by a model calculation for a thermally pulsing AGB star with M=3Mand a metallicity [Fe/H] =−1.3, which yields a negligible difference for the abundances of 206Pb and 207Pb. The s-process abundance of 209Bi itself was found to decrease only slightly from 19% to 18.7%. To evaluate the uncertainty on the solar 209Bi s-process fraction, we have to consider first the uncertainty in the cross section of this isotope in the two temperature regimes of the stellar model. The main contribution because of the uncertainty of the bismuth cross section is dominated by the conditions during the He shell flash. At the higher temperature of the 22Ne(α, n)25Mg source (kT =23 keV) the reaction flow via 208Pb(n, γ )209Bi is strongly enhanced over the situation during the 13C(α, n)16O phase. This reflects the increase of the 208Pb cross section with stellar temperature [31]. The net effect of the uncertainty on the 209Bi cross section to its solar s-process abundance is found to be 6%. In the evaluation of the final s-process abundance of bismuth, three aditional uncertainties have to be considered: (i) the effect of the uncertainty in the 208Pb cross section, which directly affects the sproduction of 209Bi by 6.5% (see Table VII in Ref. [5]), (ii) the 7%–8% uncertainty of the solar bismuth abundance (Refs. [30,32]), and (iii) a further 10% for the uncertainties related to the s-process model and for modeling GCE [2]. In summary the s-process contribution to solar bismuth is obtained as 19±3%, corresponding to an r-process residual of 81±3%. This result is in agreement with the r-process calculation of Ref. [33] using the waiting point approximation and improved mass formulae, which yield an r-process contribution between 71% and 90%. A similar result is reported in Ref. [4], where the calculations give 77% and 92% r-process contributions depending on the initial seed composition. VI. ESTIMATION OF THE THERMAL CAPTURE CROSS SECTION The thermal neutron capture cross section of 209Bi can be expressed by the sum of the tails of all Breit-Wigner resonances, σth γ≈4.099 ×106A+1 A2N◦  i=1 gi n i ni γ (Ei ◦)2.(10) The result obtained with the resonance parameters from the present measurement (see Table II), is in agreement with that obtained from the GELINA measurement, as shown in Table IV. However, both values are around 40% smaller than the accepted value of 33.8(5) mb [27], which has been measured with the pile oscillator method. The direct 025807-8 NEW MEASUREMENT OF NEUTRON CAPTURE . . . PHYSICAL REVIEW C 74, 025807 (2006) TABLE IV. Comparison of the thermal neutron capture cross section from different sources. Cross section Source Ref. σth γ(mb) In-pile measurement [27] 33.8(5) From resonance parameters This work 23.6(9) GELINA [7] 24.6(9) ENDF 32.51 JENDL 32.51 capture process cannot account for this discrepancy. In fact, a preliminary estimate of this component leads to a negligible contribution to the thermal cross-section value [34]. The resonance parameters of the ENDF and JENDL libraries have been adjusted to reproduce the in-pile σth γ measurement by means of an expression such as Eq. (10). With the improved, present data for the s-wave resonances this inconsistency could be removed by introducing subthreshold resonances in the evaluated data files. VII. SUMMARY At the CERN n TOF facility the time-of-flight method has been employed with the pulse-height-weighting technique to determine the neutron-capture cross section of bismuth in the resolved resonance region. The main improvement with respect to previous measurements is because of an optimized detection setup, by which the crucial neutron sensitivity could be considerably reduced. All remaining sources of systematic uncertainties have been thoroughly treated by detailed Monte Carlo simulations. Resonance energies (E◦), widths (γ), and capture areas have been determined by an R-matrix analysis covering the energy range from 0.8 to 23 keV. The results show larger capture areas for the s-wave resonances, yielding a 16% enhancement of the stellar neutron capture rate at thermal energies between 5 and 8 keV compared with recent data [8]. 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