Measurement of the radiative neutron capture cross section of 206 Pb and its astrophysical implications

PHYSICAL REVIEW C 76, 045805 (2007) Measurement of the radiative neutron capture cross section of 206Pb and its astrophysical implications C. Domingo-Pardo,1,2,*U. Abbondanno,3G. Aerts,4H. ´ Alvarez,5F. Alvarez-Velarde,6S. Andriamonje,4J. Andrzejewski,7 P. Assimakopoulos,8L. Audouin,1G. Badurek,9P. Baumann,10 F. Beˇ cv´ aˇ r,11 E. Berthoumieux,4S. Bisterzo,12,1F. Calvi ˜ no,13 M. Calviani,14 D. Cano-Ott,6R. Capote,15,16 C. Carrapic¸o,17 P. Cennini,18 V. Chepel,19 E. Chiaveri,18 N. Colonna,20 G. Cortes,13 A. Couture,21 J. Cox,21 M. Dahlfors,18 S. David,10 I. Dillman,1R. Dolfini,22 W. Dridi,4I. Duran,5 C. Eleftheriadis,23 M. Embid-Segura,6L. Ferrant,24 A. Ferrari,18 R. Ferreira-Marques,19 L. Fitzpatrick,18 H. Frais-Koelbl,25 K. Fujii,3W. Furman,26 R. Gallino,12 I. Goncalves,17 E. Gonzalez-Romero,6A. Goverdovski,27 F. Gramegna,14 E. Griesmayer,25 C. Guerrero,6F. Gunsing,4B. Haas,28 R. Haight,29 M. Heil,1A. Herrera-Martinez,18 M. Igashira,30 M. Isaev,24 E. Jericha,9F. K¨ appeler,1Y. Kadi,18 D. Karadimos,8D. Karamanis,8M. Kerveno,10 V. Ketlerov,27,18 P. Koehler,31 V. Konovalov,26,18 E. Kossionides,32 M. Krtiˇ cka,11 C. Lamboudis,23 H. Leeb,9A. Lindote,19 I. Lopes,19 M. Lozano,16 S. Lukic,10 J. Marganiec,7S. Marrone,20 C. Massimi,33 P. Mastinu,14 A. Mengoni,34,18 P. M. Milazzo,3C. Moreau,3 M. Mosconi,1F. Neves,19 H. Oberhummer,9M. Oshima,35 S. O’Brien,21 J. Pancin,4C. Papachristodoulou,8C. Papadopoulos,36 C. Paradela,5N. Patronis,8A. Pavlik,37 P. Pavlopoulos,38 L. Perrot,4R. Plag,1A. Plompen,39 A. Plukis,4A. Poch,13 C. Pretel,13 J. Quesada,16 T. Rauscher,40 R. Reifarth,29 M. Rosetti,41 C. Rubbia,22 G. Rudolf,10 P. Rullhusen,39 J. Salgado,17 L. Sarchiapone,18 I. Savvidis,23 C. Stephan,24 G. Tagliente,20 J. L. Tain,2L. Tassan-Got,24 L. Tavora,17 R. Terlizzi,20 G. Vannini,33 P. Vaz,17 A. Ventura,41 D. Villamarin,6M. C. Vincente,6V. Vlachoudis,18 R. Vlastou,36 F. Voss,1S. Walter,1 H. Wendler,18 M. Wiescher,21 and K. Wisshak1 (n TOF Collaboration) 1Forschungszentrum Karlsruhe GmbH (FZK), Institut f¨ ur Kernphysik, Germany 2Instituto de F´ ısica Corpuscular, CSIC-Universidad de Valencia, Spain 3Istituto Nazionale di Fisica Nucleare (INFN), Trieste, Italy 4CEA/Saclay - DSM/DAPNIA, Gif-sur-Yvette, France 5Universidade de Santiago de Compostela, Santiago de Compostela, Spain 6Centro de Investigaciones Energeticas Medioambientales y Technologicas, Madrid, Spain 7University of Lodz, Lodz, Poland 8University of Ioannina, Ioannina, Greece 9Atominstitut der ¨ Osterreichischen Universit¨ aten, Technische Universit¨ at Wien, Wien, Austria 10Centre National de la Recherche Scientifique/IN2P3 - IReS, Strasbourg, France 11Charles University, Prague, Czech Republic 12Dipartimento di Fisica Generale, Universit` a di Torino, Torino, Italy 13Universitat Politecnica de Catalunya, Barcelona, Spain 14Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Legnaro, Legnaro, Italy 15International Atomic Energy Agency, NAPC/Nuclear Data Section, Vienna, Austria 16Universidad de Sevilla, Sevilla, Spain 17Instituto Tecnol´ ogico e Nuclear (ITN), Lisbon, Portugal 18CERN, Geneva, Switzerland 19LIP - Coimbra & Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal 20Istituto Nazionale di Fisica Nucleare (INFN), Bari, Italy 21University of Notre Dame, Notre Dame, Indiana, USA 22Universit` a degli Studi di Pavia, Pavia, Italy 23Aristotle University of Thessaloniki, Thessaloniki, Greece 24Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France 25Fachhochschule Wiener Neustadt, Wiener Neustadt, Austria 26Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia 27Institute of Physics and Power Engineering, Kaluga region, Obninsk, Russia 28Centre National de la Recherche Scientifique/IN2P3 - CENBG, Bordeaux, France 29Los Alamos National Laboratory, Los Alamos, New Mexico, USA 30Tokyo Institute of Technology, Tokyo, Japan 31Oak Ridge National Laboratory, Physics Division, Oak Ridge, Tennessee, USA 32NCSR, Athens, Greece 33Dipartimento di Fisica, Universit` a di Bologna, and Sezione INFN di Bologna, Bologna, Italy 34International Atomic Energy Agency (IAEA), NAPC/Nuclear Data Section, Vienna, Austria 35Japan Atomic Energy Research Institute, Tokai-mura, Japan 36National Technical University of Athens, Athens, Greece 37Institut f¨ ur Isotopenforschung und Kernphysik, Universit¨ at Wien, Wien, Austria 38Pˆ ole Universitaire L´ eonard de Vinci, Paris La D´ efense, France 0556-2813/2007/76(4)/045805(10) 045805-1 ©2007 The American Physical Society C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 76, 045805 (2007) 39CEC-JRC-IRMM, Geel, Belgium 40Department of Physics and Astronomy - University of Basel, Basel, Switzerland 41ENEA, Bologna, Italy (Received 25 July 2007; published 31 October 2007) The (n, γ ) cross section of 206Pb has been measured at the CERN n TOF facility with high resolution in the energy range from 1 eV to 620 keV by using two optimized C6D6detectors. In the investigated energy interval about 130 resonances could be observed, from which 61 had enough statistics to be reliably analyzed via the R-matrix analysis code SAMMY. Experimental uncertainties were minimized, in particular with respect to (i) angular distribution effects of the prompt capture γ-rays, and to (ii) the TOF-dependent background due to sample-scattered neutrons. Other background components were addressed by background measurements with an enriched 208Pb sample. The effect of the lower energy cutoff in the pulse height spectra of the C6D6detectors was carefully corrected via Monte Carlo simulations. Compared to previous 206Pb values, the Maxwellian averaged capture cross sections derived from these data are about 20% and 9% lower at thermal energies of 5 keV and 30 keV, respectively. These new results have a direct impact on the s-process abundance of 206Pb, which represents an important test for the interpretation of the cosmic clock based on the decay of 238U. DOI: 10.1103/PhysRevC.76.045805 PACS number(s): 25.40.Lw, 27.80.+w, 97.10.Cv I. INTRODUCTION Similar to the majority of the stable isotopes beyond iron, 206–208Pb and 209Bi are synthesized by the rapid (r-) and slow (s-) neutron capture processes. However, this mass region is particularly interesting because the r-process abundances are dominated by the decay of the short lived α-unstable transbismuth isotopes [1]. This feature provides an important consistency check for the r-process abundance calculations in the actinide region, since the integrated rresiduals are constrained by the difference between the solar abundance values and the respective s-process components. Reliable r-process calculations are required for the interpretation of the observed Th and U abundances in the ultra metal-poor (UMP) stars of the Galactic halo. Since these stars are considered to be as old as the Galaxy, the observed Th and U abundances can be used as cosmo-chronometers, provided the original Th and U abundances are inferred from r-process models. This dating mechanism has the advantage of being independent of the yet uncertain r-process site [1–3]. Apart from its relevance for establishing the basic constraints for the r-process chronometry in general, 206Pb contains also dating information in itself. The 206Pb/238U cosmochronometer was first introduced by Clayton in 1964 [4]. The 238U produced by the rprocess decays with a half-life of t1/2=4.5×109yr over a chain of αand βdecays ending at 206Pb. Therefore, its radiogenic abundance component, N206 c, can be used to constrain the age of the parent isotope 238U, and hence the age (r)ofther-process. Unlike the more direct r-process abundance predictions derived from the Th and U abundances in UMP stars, this procedure requires a Galactic evolution model, which describes the supernova rate or the frequency of the r-process events [5]. The drawback of this clock arises from the difficulty to isolate the cosmoradiogenic component of 206Pb accurately enough from the additional abundance components. *Corresponding author: cesar[email protected] Apart from these astrophysical aspects, the neutron capture cross section of 206Pb is also of importance for the design of fast reactor systems based on a Pb/Bi spallation source. Because 24.1% of natural lead consists of 206Pb, its (n, γ ) cross section influences the neutron balance of the reactor [6]. There have been several measurements of the 206Pb(n, γ ) cross section, which show discrepancies that are difficult to understand (see Sec. IV A). The aim of this work is to perform a new independent measurement with higher accuracy and in this way to determine the s-process contribution to the 206Pb abundance, N206 s, more reliably. In fact, the s-process abundance of this isotope is almost completely determined by the stellar (n, γ ) cross section, nearly independent of the stellar model used [7]. Therefore, the uncertainty of N206 sarises mostly from the cross section uncertainty. Potential sources of systematic error have been substantially reduced in the present measurement, which was performed at the CERN n TOF installation. The new setup, and in particular the detectors themselves, were optimized for very low neutron sensitivity. Furthermore, the detectors were mounted at ∼125◦ with respect to the incident neutron beam in order to minimize the correction for angular distribution effects. The experimental details are presented in Sec. II, followed by the adopted data analysis procedures and an evaluation of the various systematic uncertainties in Sec. III. The deduced resonance parameters and the corresponding Maxwellian averaged capture cross sections in the stellar temperature regime are presented in Sec. IV. Based on these new data, first astrophysical implications for the s-process abundance of 206Pb are discussed in Sec. V. II. MEASUREMENT The time-of-flight (TOF) measurement was performed at the CERN n TOF installation [8] using a set of two C6D6 detectors. Neutrons were produced by a 20 GeV proton beam on a lead spallation target. The spallation source was 045805-2 MEASUREMENT OF THE RADIATIVE NEUTRON CAPTURE . . . PHYSICAL REVIEW C 76, 045805 (2007) surrounded by a 6 cm thick water layer, which served as a coolant and as a moderator for the initially fast neutron spectrum. The beam was characterized by intense bunches of (3 to 7)×1012 protons, a width of 6 ns (rms), and a repetition rate of only 0.4 Hz. This extremely low duty-cycle allows one to perform (n, γ ) measurements over a broad neutron energy interval from 1 eV up to 1 MeV and to achieve favorable background conditions. Data were recorded by means of an advanced acquisition system with zero dead time, based on 8-bit flash-analog-to-digital converters (FADC), with 500 MHz sampling rate and 8 MB buffer memory [9]. The measurement was performed with an enriched metal sample 8.123 g in mass and 20 mm in diameter. The sample was enriched to 99.76% in 206Pb with small impurities of 207Pb (0.21%) and 208Pb (0.03%). Capture events were registered with two C6D6γ-ray detectors optimized for very low neutron sensitivity [10]. A sketch of the experimental setup is shown in Fig. 2 of Ref. [11]. The absolute value of the neutron fluence was determined by regular calibration measurements with an 0.5 mm thick gold sample and by using the saturated resonance technique [12]for the first gold resonance at En=4.9 eV. The energy differential neutron flux was determined with a relative uncertainty of ±2% from the flux measurement with a 235,238U fission chamber calibrated by Physikalisch-Technische Bundesanstalt (PTB) [13]. The neutron intensity at the sample position was also monitored by means of a 200-µg/cm2thick 6Li foil in the neutron beam about 2.5 m upstream of the capture sample. The 6Li foil was surrounded by four silicon detectors outside of the beam for recording the 3H and αparticles from the (n, α) reactions. Compared to previous measurements [14,15], the present setup had the advantage that the detectors were placed at ∼125◦with respect to the incident neutron beam. In this way, the corrections for angular distribution effects of the prompt capture γ-rays were strongly reduced. This configuration led also to a substantial reduction of the background from in-beam γ-rays scattered in the sample [16]. III. CAPTURE DATA ANALYSIS The response function of the C6D6detectors needs to be modified such that the detection probability for capture cascades becomes independent of the cascade multipolarity. This was accomplished by application of the pulse height weighting technique (PHWT) [17]. Based on previous experience [11,18,19], the weighting functions (WFs) for the gold and lead samples were obtained by means of Monte Carlo calculations. The accuracy of the WFs was verified with the method described in Ref. [18], by which the calculated WFs were applied to Monte Carlo simulated capture γ-ray spectra. Using this procedure, the uncertainty of the WFs was estimated to be smaller than 0.5% for the samples used in the present experiment. The weighted count rate Nwis then transformed into an experimental yield, Yexp =fsat Nw NnEc ,(1) where the yield-normalization factor fsat is determined by calibration measurements using the saturated 4.9 eV resonance in gold. Nndenotes the neutron flux and Ecthe effective binding energy. The yield in Eq. (1) is still subject to several corrections. The common effects of the background and of the low energy cutoff in the pulse height spectra of the γdetectors are described in Secs. III A and III B, respectively. The measurement on 206Pb is particularly sensitive to the angular distribution of the prompt capture γ-rays. The impact of this effect is described in Sec. III C. A. Backgrounds A major source of background is due to in-beam γ-rays, predominantly from neutron captures in the water moderator, which travel along the neutron flight tube and are scattered in the 206Pb sample. This background exhibits a smooth dependence on neutron energy, with a broad maximum around En≈10 keV. The shape of this background was determined from the spectrum measured with an isotopically pure 208Pb sample, which contains practically no resonances in the investigated neutron energy range. This spectrum was properly scaled and used as a point-wise numerical function in the R-matrix analysis of the 206Pb capture yield (see Sec. IV). Another type of background arises in the analysis of resonances with a dominant neutron scattering channel, n γ. In such cases, there are about n/ γscattered neutrons per capture event. These scattered neutrons can be captured in the detectors or in surrounding materials, thus mimicking true capture events. This effect was estimated to be negligible for all the resonances reported in Sec. IV. B. Digital threshold As mentioned in Sec. II, FADCs were used for recording directly the analog output signals of the C6D6detectors. Without any further discrimination, 8 MB of data would have been acquired per proton pulse in each detector. Depending on the sample, this enormous amount of data could be reduced by factors of 20 to 100 by using a zero suppression algorithm (see Ref. [9] for details). By this method events below a certain pulse-height are discriminated by a constant digital threshold analogous to conventional data acquisition systems, where an electronic threshold is used to reduce backgrounds and dead time effects. Due to this threshold, the pulse height spectra of the C6D6 detectors exhibit a low energy cutoff at a certain value of the signal amplitude (see Fig. 1). In this experiment the threshold was set at a γ-ray energy of 320 keV. If the pulse height spectra of the 206Pb sample and of the gold sample used for normalization would have the same shape, the fraction of weighted counts below this threshold would nearly cancel out in the expression for the yield Yexp ∝320 keV 0keV WPb iRPb i+Ec 320 keV WPb iRPb i 320 keV 0keV WAu iRAu i+Ec 320 keV WAu iRAu i ≈Ec 320 keV WPb iRPb i Ec 320 keV WAu iRAu i .(2) 045805-3 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 76, 045805 (2007) (MeV) dep E 012345678 Counts 1 10 2 10 3 10 4 10 5 10 0 0.05 0.1 0.15 0.2 0.25 0.3 50 100 150 200 3 10 × FIG. 1. Pulse height spectra for the 4.9 eV resonance in gold (grey) and for the 3.3 keV resonance in 206Pb (black), arbitrarily scaled. The dashed lines are the MC-calculated γ-ray spectra for the two resonances. The linear scale used in the inset illustrates the large difference between the simulated spectra below a threshold of 300 keV. Here, the Wiand Riare the corresponding weighting factors and response functions for a certain time of flight channel, respectively. However, this approximation is only valid within 4 to 5%, because the pulse height spectra of captures on 206Pb and 197Au differ significantly near threshold (Fig. 1). This effect has been taken into account in the determination of the experimental capture yield by simulating the capture cascades of each isotope as described in detail in Refs. [11,18, 19]. Figure 1shows that the experimental spectra above the digital threshold are well reproduced by the simulations. With this correction the experimental yield becomes Yexp ∝ft Pb ft Au Ec 320 keV WPb iRPb i Ec 320 keV WAu iRAu i .(3) For the adopted digital threshold the yield of the 4.9 eV resonance in 197Au needs to be scaled by a factor ft Au = 1.071(3), whereas the yield of the resonances in 206Pb required a correction of ft Pb =1.021(5) due to their harder spectrum. Hence, the correction factor of the final experimental yield was ft=ft Pb/f t Au =0.952(4). C. Angular distribution effects Neutron capture with orbital angular momentum l>0 leads to an aligned state in the compound nucleus, perpendicular to the direction of the incident neutron. Given the small multiplicity (m=1 to 2) of the capture cascades in 206Pb, most of the prompt γ-rays registered with the C6D6detectors still carry this anisotropy, which affects the measured yield. The angular distribution is in general given by W(θ)= k AkPk(cos θ)=1+A2P2(cos θ) +A4P4(cos θ)+A6P6(cos θ),(4) (a) (b) 6738.2 0.0 897.5 569.6 2623.1 6737.9 6168.6 4114.5 5/2+ 3/2− 5/2− 1/2− 5840.8 JΠ (d) (c) FIG. 2. Level scheme and decay patterns for 207Pb [14]. All energies are in keV. where Pk(cos θ) are the Legendre polynomials of order kand Akare coefficients, which depend on the initial (J) and final (J) spin values, on the multipolarity (l) of the transition, and on the degree of alignment. The angular distribution effects in the capture yield are minimized (although not avoided) by setting the detectors at 125◦. Since each C6D6detector covers a substantial solid angle, capture γ-rays are registered around 125◦±θ. For the actual setup of the present measurement one finds θ ≈28◦. 1. Resonances with spin J =1/2 For resonances with J=1/2 it can be assumed that they decay directly to the ground state (Jπ=1/2−)ortothefirst or second excited states with Jπ=5/2−and Jπ=3/2−, respectively (see also Fig. 2). In these cases, one finds that A2=A4=A6=0. Therefore, only resonances with spin J>1/2 may be affected by angular distribution effects. 2. Resonances with spin J =3/2 In order to quantify the uncertainty due to the angular distribution of the prompt γ-rays emitted from excited states with Jπ=3/2−the de-excitation patterns reported in Ref. [14] have been used (Table I). For the first resonance at 3.36 keV, fair agreement has been found between the relative intensities of Ref. [14] and the rather coarse values deduced from the experimental pulse height spectrum (Table Iand Fig. 1), which suffer from uncertainties due to background subtraction, limited counting statistics and poor energy resolution of the C6D6detectors. Therefore, an uncertainty of about 20% has to be ascribed to the quoted γ-ray intensities. The estimated effect of the angular distribution on the capture yield (σ3/2− θ) is given in the last column of Table I. These values were obtained via Monte Carlo simulations of the experimental setup, using the energies and intensities listed in 045805-4 MEASUREMENT OF THE RADIATIVE NEUTRON CAPTURE . . . PHYSICAL REVIEW C 76, 045805 (2007) TABLE I. Measured decay patterns from resonances with spin J=3/2[14]. The systematic uncertainty in the yield of each resonance due to the angular distribution of the involved transitions are given in the last column. E◦(keV) Intensity Iγ(%) Eγ(keV) σ3/2− θ 6737.9 6168.6 5840.8 4114.5 3.36 76.0(27) 2.5(8) 8.58(11) 13.0(8) ±10% 3.36a60 2.5 24.5 13 ±8% 10.86 100 ±2% 21.87 100 ±2% 42.07 100 ±10% aThis work. Table Iand the prescription of Ref. [20]. The main uncertainty in the calculation of the angular distribution effects arises from the unknown admixtures of different multipolarities (M1+E2) for the transitions connecting the original excited state Jπ=3/2−with any of the three lowest states [paths (a), (b), and (c) in Fig. 2]. As shown in Table I, the decay pattern and the corresponding effect on the capture yield σ3/2− θvary abruptly from one resonance to another. It is therefore difficult to assess a common systematic uncertainty for the remaining 3/2−resonances. Assuming that the four resonances listed in Table Iconstitute a representative sample, one may consider their standard deviation of σ=4% as a realistic estimate of the systematic uncertainty due to angular distribution effects. Resonances with Jπ=3/2+can be assumed to decay directly to the ground state through an E1 transition. In this case we have estimated an effect of 10% in the capture yield with respect to the isotropic case. However, since 3/2+ resonances appear at a relatively high neutron energy, the final effect in the MACS is practically negligible (see below Sec. IV B). 3. Resonances with spin J =5/2 For resonances in 207Pb with Jπ=5/2+the most probable decay would be through an electric dipole transition to the first excited state with Jπ=5/2−and/or to the second excited state with Jπ=3/2−[paths (b) and (c) in Fig. 2]. Under these assumptions, the effect on the capture yield would be −12% for path (b) and 9% for path (c). However, mixtures of both decay paths would partly compensate the correction for angular distribution effects. Adopting one standard deviation of the two extreme cases σ5/2+ θ≃10% would, therefore, represent a rather conservative estimate of the corresponding uncertainty. Nevertheless, even such a relatively large uncertainty for the cross section of Jπ=5/2+resonances would have negligible consequences for the Maxwellian averaged cross section because these resonances contribute very little to the total capture cross section (see Sec. IV B). D. Summary of uncertainties With the WFs calculated via the Monte Carlo technique, the accuracy of the PHWT has been investigated in detail by the nTOF collaboration [18]. It has been shown that the capture yield can be determined from the measured raw data with an accuracy better than 2%. Other sources of systematic uncertainty pertaining to this measurement are due to the energy dependence of the neutron flux (±2%) and to the background due to in-beam γ-rays (±1%). In the particular case of the (n, γ ) cross section of 206Pb, the uncertainty introduced by the angular distribution of the capture γ-rays has to be considered as well. This effect has been estimated to contribute an uncertainty of ±4% for resonances with Jπ=3/2−and less than ±10% for resonances with Jπ=3/2+,5/2+. IV. RESULTS A total of 61 capture levels were analyzed in the neutron energy range from 3 keV up to 570 keV using the R-matrix code SAMMY [21]. In the analysis, the orbital angular momenta land the resonance spins Jwere adopted from Ref. [22]. Some of the land Jparameters listed in Table II are tentative or arbitrary if missing in Ref. [22]. We list all the parameters used in our analysis so that the final values can be recalculated if necessary. The capture yield Y(E◦, n, γ) was parametrized with the Reich-Moore formalism, and a channel radius of 9.5 fm was used for all partial waves. This parameterized yield was fitted to the corrected experimental yield by variation of the capture width γand/or neutron width n, ft×Yexp =B+Y(E◦, n, γ),(5) where ftis the global yield correction factor given in Sec. III B.ThetermBdescribing the background was parametrized as an analytical function of the neutron energy in the range between 1 eV and 30 keV. Beyond 30 keV, Bwas best described by means of a numerical function (pointwise) determined from the measurement of the 208Pb sample (see Ref. [23] for details). The uncertainties quoted for the energy of each resonance are only the statistical errors obtained from the fits of the capture data performed with SAMMY. A. Comparison to previous work The radiative neutron capture cross section of 206Pb has been measured at ORNL [14,15,24], at RPI [25], and at IRMM [26]. As representative examples of these measurements we consider in this section two measurements made at ORELA [14,15], a more complete analysis [27] of the ORELA capture data [15] made in combination with transmission data [28] and the recent experiment made at IRMM [26]. In order to compare these four data sets with the present results (Table II), the ratio of the capture kernels are shown in Fig. 3. The values reported in Ref. [15] show a relatively good agreement with our results, except for the first two resonances at 3.3 keV and 14.25 keV, which are lower by ∼50% (see Fig. 3). However, these two resonances and the resonance at 16.428 keV are important because of their dominant contribution to the MACS in the energy range between 5 keV and 20 keV. It is difficult to determine the source of discrepancy, thus no correlation has been found between the discrepancies 045805-5 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 76, 045805 (2007) TABLE II. Resonance parameters derived from the R-matrix analysis of the 206Pb(n, γ ) data. E◦lJ γγnnKraKr (eV) (meV) (%) (meV) (%) (meV) (%) 3357.93(0.04) 1 3/2 78.1 3 235 117 2 10865.0(0.4) 1 3/2 64.9 9 44.1 8 52.5 6 11296.0(0.5) (1) (1/2) 455 44.6 7 40.6 7 14220.0(0.6) 1 (1/2) 152 6 1560 139 5 16428.0(0.4) 0 1/2 2268 9 936 5 662 5 19744.0(1.3) 1 (1/2) 156 7 2581 147 6 19809.0(0.9) 1 (3/2) 295 71.6 8 115 6 21885.0(0.9) 1 3/2 121 6 875 212 5 25112.0(0.9) 1 3/2 438 9 326 8 374 6 25428(5) 1 1/2 254 7 48901 253 7 36200(6) 1 1/2 312 14 35700 309 13 37480.0(1.9) 1 (3/2) 151 15 890 258 13 39028(2) 1 (1/2) 346 93.0 36 73.3 28 40647(2) 1 (1/2) 163 23 884 138 19 42083.0(1.7) 1 (3/2) 419 21 1419 91 647 26 47534(2) (1) (1/2) 184 34 1000 155 29 59233.0(0.2) (2) (3/2) 322 16 1000 487 12 63976(3) (2) 5/2 151 17 1110 400 15 65990(10) 0 1/2 1186 9 82200 1169 9 66590(6) 1 3/2 198 19 9530 387 19 70352(7) 1 1/2 163 34 10780 161 34 80388(4) 2 3/2 1490 8 7005 2457 6 83699(6) (2) (3/2) 351 16 8000 673 15 88509(6) 2 5/2 375 13 7996 1076 12 91740(4) (1) (3/2) 298 25 1000 460 19 92620(13) 0 1/2 991 15 32000 961 15 93561(6) 2 3/2 125 37 7001 246 37 94743(7) 2 (3/2) 241 20 7000 465 20 101220(7) 2 (5/2) 119 26 8000 351 25 114380(5) 1 (3/2) 655 24 2500 1037 19 114602(6) 2 (5/2) 366 19 5600 1030 18 118100(6) 2 (5/2) 390 16 5100 1087 15 124753(47) 1 3/2 2972 9 300000 5886 9 125312(7) 2 (3/2) 2783 10 21005 4915 9 126138(38) (1) (3/2) 319 32 100000 635 32 140570(23) 2 3/2 1387 11 103000 2736 11 145201(6) (2) (3/2) 518 30 3100 888 26 146419(24) 0 1/2 6092 8 176000 5888 8 150880(7) (1) (1/2) 554 48 4400 492 43 151290(13) 2 5/2 457 23 19000 1340 22 191217(48) (1) (1/2) 767 28 96977 761 27 196990(37) 1 1/2 584 45 64000 579 44 198618(34) 2 3/2 2730 10 132108 5350 10 274630(22) 1 (1/2) 514 65 32000 506 64 276984(49) 2 3/2 2481 13 112000 4854 13 313400(18) 2 (3/2) 1020 32 22000 1950 31 314340(84) 2 5/2 964 24 179000 2875 24 356098(22) 2 (5/2) 676 35 31000 1985 35 357465(87) 2 3/2 1998 24 455000 3979 24 406200(55) 2 5/2 656 51 102000 1955 51 407200(41) 2 3/2 2906 24 71000 5583 23 416370(127) 2 5/2 2722 16 307000 8096 16 433340(32) 2 (5/2) 4122 17 47000 11368 16 434604(37) (2) (3/2) 4695 23 58000 8687 21 443412(13) (2) (5/2) 2375 21 14000 6092 18 TABLE II. (Continued.) E◦lJ γγnnKraKr (eV) (meV) (%) (meV) (%) (meV) (%) 466320(49) (1) (3/2) 5413 15 90000 10211 14 469080(76) 2 3/2 3222 19 161000 6317 19 471789(28) (3) (5/2) 792 36 41000 2330 35 476310(172) 0 1/2 5252 18 374000 5180 17 510690(51) (2) (3/2) 3123 18 86000 6026 18 572245(181) 2 5/2 3838 13 793194 11460 13 aCapture kernel Kr=gγn/, with g=J+1/2. and the spins of the resonances. The latter could probably help to determine if there is any effect related to the angular distribution of the prompt capture γ-rays or to the WF used in the previous measurement. In the second measurement at ORELA [14] the discrepancies versus our present results are smaller (see Fig. 3), but the capture kernels are systematically larger, on average 20 ±5% higher. This could probably reflect that the WF used in Ref. [14] is overweighing the relatively hard pulse height spectrum of 207Pb. Indeed, similar discrepancies have been found in the past for 56Fe [29], where the pulse height spectrum is also considerably harder than that of the 197Au sample used for yield normalization. The posterior analysis [27] of the ORELA capture data [15] in combination with transmission [28] shows, on average, better agreement with the capture areas reported here (see Fig. 3). Finally, the results reported in the measurement at IRMM [26] show the best agreement with the capture kernels of nTOF (see Fig. 3). At En⩽40 keV both measurements agree ORNL’73/nTOF 0 1 2 3 ORNL’79/nTOF 0 0.5 1 1.5 2 ORNL’80/nTOF 0 0.5 1 1.5 2 4 10 5 10 IRMM/nTOF 0 0.5 1 1.5 2 (eV) n E FIG. 3. (Color online) Ratio between the capture kernels reported in Refs. [15] (top), [14] (second), [27] (third), and [26] (bottom) and the kernels determined here. 045805-6 MEASUREMENT OF THE RADIATIVE NEUTRON CAPTURE . . . PHYSICAL REVIEW C 76, 045805 (2007) (keV) n E 3.35 3.36 3.37 Yield 0.05 0.1 0.15 This Work IRMM, 2007 ORELA, 1979 Mughabghab 2006 This Work IRMM, 2007 ORELA, 1979 Mughabghab 2006 (keV) n E 15 20 25 Yield 0.01 0.02 0.03 0.04 FIG. 4. (Color online) (left) The bold red line represents an R-matrix fit to our experimental capture yield starting from the initial parameters (solid green line) in Ref. [22]. The dashed and dot-dashed curves correspond to the capture yields determined in Refs. [26]and[14], respectively. (right) The fitted capture yield in the 10–30 keV energy range (thin red line). within a few percent. At higher energy the fluctuations are larger, but the agreement is still good within the quoted error bars. As an illustrative example, the capture yield measured at nTOF for the first resonance at 3.3 keV is compared in the top panel of Fig. 4versus the yield calculated from the resonance parameters reported in Refs. [14,22,26]. Obviously, the IRMM and n TOF results show good agreement in both the capture area and the resonance energy. B. Maxwellian averaged capture cross section The Maxwellian averaged cross section (MACS) was determined using the SAMMY code in the range of thermal energies relevant for stellar nucleosynthesis, i.e., from kT = 5 keV up to kT =50 keV. As discussed in the previous section, our results agree best with the values reported in Ref. [26]. The latter data set seems also to be the most complete in terms of number of analyzed resonances, with about 283 levels. Therefore our results were complemented with resonances from Ref. [26] in order to avoid any discrepancy due to resonances missing in Table II. The contribution of these supplementary resonances to the MACS is <0.1% at kT = 5 keV and 6% at kT =25 keV. The fact that this correction starts to be significant toward kT > ∼25 keV is not relevant for the study of the nucleosynthesis of 206Pb. Indeed, as it is discussed below in Sec. V,206Pb is mostly synthesized between the He-shell flashes of the asymptotic giant branch stars. These intervals between pulses provide about 95% of the neutron exposure via the 13C(α, n)16O reaction, which operates at a thermal energy of kT =8 keV. At this stellar temperature less than 0.5% of the MACS is due to the supplemented resonances. The uncertainties shown in Fig. 5are only statistical. The systematic uncertainties of the MACS quoted in Table III include all contributions discussed in Sec. III D. Assuming systematic uncertainties of 4% and 10% for 3/2− and 5/2−resonances, respectively, the final uncertainties are completely dominated by the 4% uncertainty of the 3/2− resonances. A change of 10% in the cross section of the fewer 5/2+resonances has a negligible influence on the MACS at kT =5 keV, it contributes only 0.5% at kT =25 keV and increases linearly up to 1% at kT =50 keV. An effect of 10% in the capture yield of the 3/2+resonances makes only a 1% difference in the MACS at kT =25 keV and it becomes also negligible toward lower stellar temperatures. The 3% systematic uncertainty of the experimental method itself originates from the PHWT, the neutron flux shape, and the use of the saturated resonance technique. In summary, the MACS of 206Pb can now be given with total uncertainties of 5% and 4% at the stellar temperatures corresponding to 5 keV and 25 keV thermal energies, respectively. This improvement with respect to the previously recommended values of Ref. [30] becomes particularly important for determining the s-process contribution to the production of lead and bismuth in the Galaxy. V. T H E s-PROCESS ABUNDANCE OF 206Pb AS A CONSTRAINT FOR THE U/TH CLOCK The s-process production of 206Pb takes place in low mass asymptotic giant branch (AGB) stars of low metallicity [31], TABLE III. Maxwellian averaged cross section for 206Pb. Thermal energy kT MACS σstat σsys (keV) (mbarn) (%) (%) 521.31.85 820.41.83 10 19.41.93 12 18.42.03 15 17.12.13 20 15.62.23 25 14.72.33 30 14.22.34 40 13.52.24 50 12.82.14 045805-7 C. DOMINGO-PARDO et al. PHYSICAL REVIEW C 76, 045805 (2007) Thermal energy (keV) 10 20 30 40 50 MACS (mb) 12 14 16 18 20 22 24 26 28 This work IRMM 2007 Mughabghab’06 Bao et al. FIG. 5. (Color online) Maxwellian averaged (n, γ ) cross sections for 206Pb from the resonance parameters of this work (bold red) compared to the IRMM measurement [26] (dashed), to the recommended data of Ref. [30] (grey), and to the compiled data of Ref. [22] (solid green). where about 95% of the neutron exposure is provided by the 13C(α, n)16O reaction at a thermal energy of kT ≈8keV. At this stellar temperature the present MACS is about 20% lower and two times more accurate (see Fig. 5) than the values from Ref. [30], which have been commonly used so far for stellar nucleosynthesis calculations. 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. With the new MACS the s-process abundance of 206Pb has been redetermined more accurately. A model calculation was carried out for thermally pulsing AGB stars of 1.5 and 3 M and a metallicity of [Fe/H] =−0.3. The abundance of 206Pb is well described by the average of the two stellar models, which represent the so-called main component [32]. Since the contribution of 206Pb by the strong component is only 2%, the main component can be used to approximate the effective production of 206Pb during Galactic chemical evolution (GCE) [31,33,34]. This approach yields an s-process abundance of 206Pb, which represents 70(6)% of the solar abundance value N206 =0.601(47)/106Si [35]. The same calculation made with the older MACS recommended by Bao et al. [30] yields 64%. The uncertainty on the calculated s-process abundance is mostly due to the uncertainty on the solar abundance of lead (7.8%) [36]. The contribution from the uncertainty on the MACS at 8 keV is less than 2%. Finally, the contribution from the s-process model is ±3%. The latter corresponds to the mean root square deviation between observed and calculated abundances for s-process only isotopes [32]. This uncertainty is justified for 206Pb because its nucleosynthesis is dominated by the main component and it is only marginally affected (∼2%) by the strong component [31–34]. Furthermore, because of the much lower cross sections of 208Pb and 209Bi, the synthesis of 206Pb remains practically unaffected by the α-recycling after 209Bi [7]. This lends further confidence that the production of 206Pb, and hence its uncertainty, follows the same trend as the main s-process component. In order to estimate a constraint for the r-process abundance of 206Pb one needs to take into account its radiogenic contribution, N206 c, due to the decay of 238U. As it is shown (years)∆ 051015 9 10× 238 /N c 206 R=N 0 0.5 1 1.5 2 2.5 3 3.5 Sudden 43% SN Rate Uniform r ∆ FIG. 6. Estimate of the radiogenic component of 206Pb using the Fowler’s model with different nucleosynthetic assumptions (see labels in curves) and the r-process age r=tU−4.6 Gyr (vertical dashed line) derived from the age of the Universe tU[37]. in the following, this component is relatively small but cannot be neglected. Based on the schematic model of Fowler, which assumes an exponential decrease of the r-process yield during GCE [4] supernova rate =(0.43t)−1Gyr−1] and using the current best estimates for the age of the Universe (tU= 13.7±0.2Gyr)[37], one obtains N206 c=0.027(2)/106Si (see Fig. 6and Table IV). This number, combined with our result for N206 s, yields an r-process residual, N206 r=N206 −N206 s−N206 c=0.153 ±0.063.(6) The uncertainty in this result includes contributions of 8.4% from N206 c(corresponding to the uncertainty on the solar abundance of 238U[36]), 7.8% from the total solar abundance of 206Pb, N206 [35,36], and 8.6% from the determination of N206 sas discussed above. This means that, apart from the uncertainties related with the simplified assumptions in the GCE model of Fowler, the r-process abundance can be reliably constrained between 16% and 36% of the solar 206Pb. The r-process residuals derived here are consistent with r-process model calculations available in the literature, i.e., N206 r=26.6% [1]. More recent calculations yield N206 rvalues between 27% and 35% [3]. One can also derive hard limits for the r-process abundance, considering the two extreme cases of sudden nucleosynthesis (→∞) and uniform nucleosynthesis (→0). This yields constraints between 10% and 37% of solar 206Pb (see Table IV). The situation is rather different for the corresponding 207Pb/235U ratio, which has been investigated as a potential clock in the past [38]. In this case, the s-process abundance TABLE IV. Radiogenic abundance of 206Pb, N206 c(Si =106), derived from the model of Fowler and the age of the Universe (see Fig. 6). r-Process residuals obtained via Eq. (6). GCE N206 c=RN238 N206 r=N206 −N206 s−N206 c (Fig. 6) 106Si 106Si N206 r/N206 (%) 43% SN rate 0.027(2) 0.15(6) 26(10) Sudden 0.058(5) 0.12(6) 20(10) Uniform 0.0161(14) 0.16(6) 27(10) 045805-8 MEASUREMENT OF THE RADIATIVE NEUTRON CAPTURE . . . PHYSICAL REVIEW C 76, 045805 (2007) TABLE V. Radiogenic abundance of 207Pb, N207 c(Si =106), derived from the model of Fowler and the age of the Universe. r-Process residuals obtained via Eq. (6). GCE N207 c=RN235 N207 r=N207 −N207 s−N207 c 106Si 106Si N207 r/N207 (%) 43% SN rate 0.150(13) 0.003(73) 0(11) 90% SN rate 0.08(7) 0.073(72) 11(11) Uniform 0.047(4) 0.106(72) 16(11) of 207Pb was recently determined to be N207 s=77(8)% [19]. A similar calculation to that shown in Fig. 6gives N207 c= 0.150(13) (see Table V). The latter value reflects the large relative radiogenic abundance of 207Pb, N207 c/N207 =22%, due to the much shorter half-life of 235U. From the total solar abundance of 207Pb [35] and the N207 sand N207 cvalues quoted above, the r-process residual becomes N207 r=0.003 ±0.073, which means that N207 rcan not be larger than 11% of the 207Pb abundance in the solar system, N207 =0.665(52) [35] (Table V). This result is in contrast with r-process model calculations, which yield values between 22.7% and 25.3%, with a relative uncertainty of 15–20% [1,3]. The s-process abundances of 206,207Pb are rather reliable and not very sensitive to details of the stellar models [7,39]. Therefore, this discrepancy indicates that r-process abundances might have been overestimated, possibly because the odd-even effect is not properly reproduced by the ETFSI-Q mass model implemented in the r-process calculations [1,3]. Indeed, one needs to increase the supernova rate in the standard Fowler model from 43% up to 90% [=(0.90t)−1Gyr−1] in order to achieve agreement between these r-process constraints and the latter r-process calculations [1,3]. Obviously the less realistic uniform scenario would also provide agreement with the abundances from these r-process models (see Table V). However the situation has been improved recently after more detailed r-process model calculations [40] predicted anewN207 rvalue, which is 35% lower than the previous one of Ref. [1]. This yields N207 r/N207 =16.8%, which is substantially closer (considering an uncertainty of 20%) to the upper limit of 11% derived here. In this case a good agreement would be found for a more reasonable increase of the supernova rate to 55% in the Fowler model. These constraints for the r-process abundances of 206,207Pb become relevant for the validation of r-process model calculations and hence, for the reliable interpretation of actinide abundances observed in UMP stars and their use as cosmochronometers. The s-process aspects will be more rigorously investigated in a comprehensive study of the Pb/Bi region [41], where the role of stellar modeling and GCE will be discussed with a complete set of new cross sections for the involved isotopes, including the present data for 206Pb, and recent results for 204Pb [23], 207Pb [19], and 209Bi [11]. VI. SUMMARY The neutron capture cross section of 206Pb as a function of the neutron energy has been measured with high resolution at the CERN n TOF installation using two C6D6detectors. Capture widths and/or radiative kernels could be determined for 131 resonances in the neutron energy interval from 3 keV up to 620 keV. Systematic uncertainties of 3%, 5%, and < ∼10% were obtained for resonances with spin-parities of 1/2±,3/2−, and 5/2+, respectively. The Maxwellian averaged cross sections were found to be significantly smaller by 10% to 20% compared to values reported earlier [30], resulting in a correspondingly enhanced s-process production of 206Pb. First calculations with a standard AGB model yield an s-process component of 70(6)% for the 206Pb abundance. Combined with an estimate of the radiogenic production of 206Pb, the r-process abundance is constrained between 16% and 36% of the solar 206Pb abundance, well in agreement with r-process model calculations reported in the literature [1,3]. A similar analysis for 207Pb shows agreement only with most recent r-process model calculations [40]. [1] J. J. Cowan, B. Pfeiffer, K.-L. Kratz, F.-K. Thielemann, C. Sneden, S. Burles, D. Tytler, and T. C. Beers, Astrophys. J. 521, 194 (1999). [2] H. Schatz, R. Toenjes, B. Pfeiffer, T. C. Beers, J. J. Cowan, V. Hill, and K.-L. Kratz, Astrophys. J. 579, 626 (2002). [3] K.-L. Kratz, B. Pfeiffer, J. J. Cowan, and C. Sneden, New Astron. Rev. 48, 105 (2004). [4] D. D. Clayton, Astrophys. J. 139, 637 (1964). [5] W. A. Fowler and F. Hoyle, Astron. J. 70, 345 (1960). [6] A. Herrera et al., in Workshop on Nuclear Data for the Transmutation of Nuclear Waste, edited by A. Kelic and K. Schmidt (GSI, Darmstadt, Germany, 2003). ISBN 3-00012276-1. [7] U. Ratzel, C. Arlandini, F. K¨ appeler, A. Couture, M. Wiescher, R. Reifarth, R. Gallino, A. Mengoni, and C. Travaglio, Phys. Rev. C 70, 065803 (2004). [8] U. Abbondanno et al.,CERNnTOF Facility: Performance Report, CERN/INTC-O-011 INTC-2002-037 CERN-SL-2002053ECT (2002). [9] U. Abbondanno et al., Nucl. Instrum. Methods Phys. Res. A 538, 692 (2005). [10] R. Plag, M. Heil, F. K¨ appeler, P. Pavlopoulos, R. Reifarth, and K. Wisshak, Nucl. Instrum. Methods Phys. Res. A 496, 425 (2003). [11] C. Domingo-Pardo et al., Phys. Rev. C 74, 025807 (2006). [12] R. Macklin, J. Halperin, and R. Winters, Nucl. Instrum. Methods Phys. Res. A 164, 213 (1979). [13] C. Borcea et al., Nucl. Instrum. Methods Phys. Res. A 513, 524 (2003). [14] M. Mizumoto, S. Raman, R. L. Macklin, G. G. Slaughter, J. A. Harvey, and J. H. Hamilton, Phys. Rev. C 19, 335 (1979). [15] B. Allen, R. Macklin, R. Winters, and C. Fu, Phys. Rev. C 8, 1504 (1973). 045805-9