Resonance neutron-capture cross sections of stable magnesium isotopes and their astrophysical implications

PHYSICAL REVIEW C 85, 044615 (2012) Resonance neutron-capture cross sections of stable magnesium isotopes and their astrophysical implications C. Massimi,1,2,*P. Koehler,3S. Bisterzo,4N. Colonna,5R. Gallino,4F. Gunsing,6F. K ¨ appeler,7G. Lorusso,5A. Mengoni,8,9 M. Pignatari,10 G. Vannini,1,2U. Abbondanno,11 G. Aerts,6H. ´ Alvarez,12 F. ´ Alvarez-Velarde,13 S. Andriamonje,6 J. Andrzejewski,14 P. Assimakopoulos,15,†L. Audouin,16 G. Badurek,17 M. Barbagallo,5P. Baumann,18 F. Beˇ cv´ aˇ r,19 F. Belloni,11 M. Bennett,20 E. Berthoumieux,6M. Calviani,9F. Calvi ˜ no,21 D. Cano-Ott,13 R. Capote,8,22 C. Carrapic¸o,23,6 A. Carrillo de Albornoz,23 P. Cennini,9V. Chepel,24 E. Chiaveri,9G. Cortes,25 A. Couture,26 J. Cox,26 M. Dahlfors,9S. David,16 I. Dillmann,7R. Dolfini,27 C. Domingo-Pardo,28 W. Dridi,6I. Duran,12 C. Eleftheriadis,29 M. Embid-Segura,13 L. Ferrant,16,†A. Ferrari,9R. Ferreira-Marques,24 L. Fitzpatrick,9H. Frais-Koelbl,8K. Fujii,11 W. Furman,30 I. Goncalves,23 E. Gonz´ alez-Romero,13 A. Goverdovski,31 F. Gramegna,32 E. Griesmayer,8C. Guerrero,13 B. Haas,33 R. Haight,34 M. Heil,35 A. Herrera-Martinez,9F. Herwig,36 R. Hirschi,20 M. Igashira,37 S. Isaev,16 E. Jericha,17 Y. Kadi,9 D. Karadimos,15 D. Karamanis,15 M. Kerveno,18 V. Ketlerov,30 V. Konovalov,29 S. Kopecky,38 E. Kossionides,39 M. Krtiˇ cka,19 C. Lampoudis,29,6H. Leeb,17 C. Lederer,40 A. Lindote,24 I. Lopes,24 R. Losito,9M. Lozano,22 S. Lukic,18 J. Marganiec,14 L. Marques,23 S. Marrone,5T. Mart´ ınez,13 P. Mastinu,32 E. Mendoza,13 P. M. Milazzo,11 C. Moreau,11 M. Mosconi,7F. Neves,24 H. Oberhummer,17 S. O’Brien,26 M. Oshima,41 J. Pancin,6C. Papachristodoulou,15 C. Papadopoulos,42 C. Paradela,12 N. Patronis,15 A. Pavlik,40 P. Pavlopoulos,43 L. Perrot,6M. T. Pigni,17 R. Plag,7A. Plompen,38 A. Plukis,6A. Poch,25 J. Praena,22 C. Pretel,25 J. Quesada,22 T. Rauscher,10 R. Reifarth,34 G. Rockefeller,34 M. Rosetti,44 C. Rubbia,27 G. Rudolf,18 J. Salgado,23 C. Santos,23 L. Sarchiapone,9R. Sarmento,23 I. Savvidis,29 C. Stephan,16 G. Tagliente,5 J. L. Tain,28 D. Tarr´ ıo,12 L. Tassan-Got,16 L. Tavora,23 R. Terlizzi,5P. Vaz,23 A. Ventura,44 D. Villamarin,13 V. Vlachoudis,9 R. Vlastou,42 F. Voss,7S. Walter,7H. Wendler,9M. Wiescher,26 and K. Wisshak7 (n_TOF Collaboration) 1Dipartimento di Fisica, Universit` a di Bologna, Bologna, Italy 2Istituto Nazionale di Fisica Nucleare, Bologna, Italy 3Oak Ridge National Laboratory, Physics Division, Oak Ridge, Tennessee 37831-6369, USA 4Dipartimento di Fisica Generale, Universit` a di Torino, Torino, Italy 5Istituto Nazionale di Fisica Nucleare, Bari, Italy 6CEA/Saclay, IRFU, Gif-sur-Yvette, France 7Karlsruhe Institute of Technology (KIT), Campus Nord, Institut f¨ ur Kernphysik, Germany 8International Atomic Energy Agency (IAEA), Nuclear Data Section, Vienna, Austria 9CERN, Geneva, Switzerland 10Department of Physics, University of Basel, Switzerland 11Istituto Nazionale di Fisica Nucleare, Trieste, Italy 12Universidade de Santiago de Compostela, Santiago de Compostela, Spain 13Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, Madrid, Spain 14University of Lodz, Lodz, Poland 15University of Ioannina, Ioannina, Greece 16Centre National de la Recherche Scientifique/IN2P3-IPN, Orsay, France 17Atominstitut der ¨ Osterreichischen Universit¨ aten, Technische Universit¨ at Wien, Vienna, Austria 18Centre National de la Recherche Scientifique/IN2P3-IReS, Strasbourg, France 19Charles University, Prague, Czech Republic 20Keele University, Newcastle-under-Lyme, Staffordshire, United Kingdom 21Universidad Politecnica de Madrid, Madrid, Spain 22Universidad de Sevilla, Seville, Spain 23Instituto Tecnol´ ogico e Nuclear (ITN), Lisbon, Portugal 24LIP-Coimbra and Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal 25Universitat Politecnica de Catalunya, Barcelona, Spain 26University of Notre Dame, Notre Dame, USA 27Universit` a degli Studi Pavia, Pavia, Italy 28Instituto de F´ ısica Corpuscular, CSIC-Universidad de Valencia, Valencia, Spain 29Aristotle University of Thessaloniki, Thessaloniki, Greece 30Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia 31Institute of Physics and Power Engineering, Kaluga region, Obninsk, Russia 32Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Padua, Italy 33Centre National de la Recherche Scientifique/IN2P3-CENBG, Bordeaux, France 34Los Alamos National Laboratory, New Mexico, Los Alamos 87545, USA 35GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Darmstadt, Germany 36Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 044615-1 0556-2813/2012/85(4)/044615(15) ©2012 American Physical Society C. MASSIMI et al. PHYSICAL REVIEW C 85, 044615 (2012) 37Tokyo Institute of Technology, Tokyo, Japan 38EC-JRC-IRMM, Geel, Belgium 39NCSR, Athens, Greece 40University of Vienna, Faculty of Physics, Vienna, Austria 41Japan Atomic Energy Research Institute, Tokai-mura, Japan 42National Technical University of Athens, Athens, Greece 43Pˆ ole Universitaire L´ eonard de Vinci, Paris La D´ efense, France 44ENEA, Bologna, Italy (Received 9 January 2012; revised manuscript received 22 February 2012; published 20 April 2012) We have measured the neutron capture cross sections of the stable magnesium isotopes 24,25,26Mg in the energy range of interest to the sprocess using the neutron time-of-flight facility n_TOF at CERN. Capture events from a natural metal sample and from samples enriched in 25Mg and 26Mg were recorded using the total energy method based on C62H6detectors. Neutron resonance parameters were extracted by a simultaneous resonance shape analysis of the present capture data and existing transmission data on a natural isotopic sample. Maxwellian-averaged capture cross sections for the three isotopes were calculated up to thermal energies of 100 keV and their impact on s-process analyses was investigated. At 30 keV the new values of the stellar cross section for 24Mg, 25Mg, and 26Mg are 3.8±0.2 mb, 4.1±0.6 mb, and 0.14±0.01 mb, respectively. DOI: 10.1103/PhysRevC.85.044615 PACS number(s): 26.20.Kn, 28.20.Np, 29.30.Hs, 21.10.Hw I. INTRODUCTION The slow neutron-capture process (sprocess) [1–4]instars is responsible for the origin of about one half of the elemental abundances beyond iron that we observe today. In this process most of the neutrons are provided by the 13C(α, n)16O reaction and by the 22Ne(α, n)25Mg reaction. Most of the produced neutrons are captured by light species in competition with 56Fe, that is the main seed for s-process nucleosynthesis on heavy elements. Among light neutron poisons, 25Mg and 26Mg may have a relevant impact on neutron balance, and their neutroncapture cross sections need to be known with high precision, in order to obtain robust s-process calculations. Additionally, these results yield some constraints for the yet poorly known 22Ne(α, n)25Mg cross section by studying the states of the 25Mg +ncompound nucleus. Another aspect of the capture cross section of the stable magnesium isotopes is related to the open question of the production of the radioisotope 26Al in the cosmos. The sensitivity study of Iliadis et al. [5] has demonstrated that the cross section of the 24Mg(n, γ ) reaction is important for the origin of 26Al, because its main production mechanism in massive stars is strongly affected by the uncertainties of several cross sections, including that of 24Mg(n, γ ). The capture cross sections of the Mg isotopes in current nuclear data libraries exhibit deficiencies in the resolved resonance region (RRR), in particular concerning the assignment of resonance spins. The respective evaluations are based on the Japanese Evaluated Nuclear Data Library (JENDL) 3.2 [6] version, which adopted the Brookhaven National Laboratory compilation [7]intheRRR. Because the energy range of interest for s-process temperatures is slightly larger than the one covered by the evaluation, Koehler [8] recently reanalyzed *[email protected] †Deceased. existing data [9] to derive an improved set of resonance parameters. His analysis included very high resolution data for the total cross section obtained with a metallic sample of natural Mg and high-resolution capture data measured with an enriched 25Mg sample, both from experiments at the Oak Ridge Electron Linear Accelerator (ORELA) neutron time-of-flight facility [10]. Although the evaluation of Ref. [8] is more accurate than that in Ref. [6], there are three problems [11] with the former work (Ref. [8]). First, the scattering widths given in Tables I and II of Ref. [8] are actually nand not gn, where gis the statistical spin factor. Second, and more importantly, the sample thickness used in the transmission analysis was 10% too small. Third, the transmission data used in that analysis were too much averaged near the 475-keV resonance, so the quoted parameters for that resonance are not very accurate. Previous experiments comprise a series of neutron time- of-flight (TOF) measurements on natMg as well as on enriched samples. Typically, these experiments covered only a limited energy region, and capture data were taken with large detectors, less suited for capture cross-section studies on isotopes in the mass region of Mg, where the cross sections are by far dominated by the elastic-scattering channel. While the most abundant isotope 24Mg has been investigated several times [12–15], there are few neutron data for 25,26Mg. Because the resonance-dominated capture cross sections of all three Mg isotopes are relatively small, the measurements can be strongly affected by various kinds of background and exhibit, therefore, rather large discrepancies. For instance, spin and parity of the first neutron resonance in 25Mg +nhave been reported as Jπ=3+[16], 3−[17], and 2+[18] but was assigned as 2− in the JENDL evaluation, although the parity assignment of Ref. [18] is consistent with an independent 26Mg(γ,n)25Mg experiment [19]. Concerning 26Mg +nreaction, the observed differences between the only TOF data from Ref. [9] and activation experiments by Mohr et al. [20,21] are consistent with the 044615-2 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) TABLE I. Characteristics of the Mg samples. Sample Isotopic abundance (%) Total Areal density ID 24Mg 25Mg 26Mg mass (g) (atoms/b)a natMg 78.7 10.13 11.17 5.2393 0.03415 25Mg 3.05 95.75 1.20 3.1924 0.01234 26Mg 2.46 1.28 96.26 3.2301 0.01219 aAreal density of the Mg isotopes. direct radiative capture (DRC) component [22] that is not covered by the TOF technique. For this part, the thermal capture cross section reported in Ref. [23] provides an additional constraint for normalization of the 1/v slope of the cross section (vbeing the neutron velocity). In view of the uncertain and incomplete cross-section data of the Mg isotopes, which may be due to the neutron sensitivity of previous experiments, a set of capture measurements was performed at n_TOF to update the (n, γ ) cross sections of 24,25,26Mg. In these measurements particular care was devoted to minimizing systematic uncertainties due to scattered neutrons. In addition, enriched samples were used to improve the assignment of some doubtful resonances. The experiment and the procedure for the data reduction are described in Secs. II and III, respectively. The resonance analysis is discussed in Sec. IV and the corresponding stellar cross sections are given in Sec. V. The astrophysical implications are illustrated in Sec. VI and the conclusions are in Sec. VII. II. EXPERIMENT The capture experiment was performed at n_TOF, the neutron time-of-flight facility at CERN [24], which provides a white neutron spectrum from thermal to about 1-GeV neutron energy. Neutrons are produced in a massive lead target by a pulsed 20-GeV proton beam from the CERN/PS accelerator complex. This spallation neutron source is characterized by the high intensity of 7 ×1012 protons per pulse, a short pulse width of 6 ns, a low repetition rate of 0.4 Hz, and a long flight path of 185 m. Two collimators are present in the neutron beam. They provide a nearly symmetric Gaussian-shaped beam profile at the sample position, with an energy-dependent standard deviation, which is about 0.77 cm at low neutron energies. A full description of its characteristics and performance can be found in Refs. [25,26]. The background level is kept low, in the experimental area, thanks to several massive concrete and iron shieldings and by means of a strong sweeping magnet. A. Capture apparatus The capture apparatus consisted of two C62H6liquid scintillators. The deuterated benzene liquid scintillators used in the present measurement consisted of cylindrical cells 127.3 mm in diameter and 78 mm in length with an active volume of about 1000 cm3. Deuterated benzene was chosen for its very small neutron sensitivity. The neutron sensitivity of FIG. 1. (Color online) Sketch of sample changer and detectors in the experimental area at a flight path of 185 m (D denotes deuterium, 2H). the detectors was further minimized by coupling a thin carbonfiber cell directly to the EMI 9823QKA photomultipliers [27]. The detectors were placed perpendicular to the beam, 9.2 cm upstream from the sample center in order to reduce the background due to scattered photons. This geometrical configuration also allowed us to reduce the effects of the angular distribution from primary neutron capture γrays following neutron capture in =1p-wave resonances. The setup of the sample-detector geometry is sketched in Fig. 1. The total energy detection method in combination with the pulse height weighting technique (PHWT)[28] was used for this experiment. The neutron fluence at the sample position, about 185 m from the neutron source, was measured with a well-calibrated 6Li-based neutron monitor [29]. It is an in-beam detector, consisting of a 6Li deposit (300 mg/cm2and 6 cm in diameter) on a Mylar foil and four off-beam silicon (6 ×4cm 2) detectors measuring the particles from the 6Li(n, α)3H reaction. The monitor was located about 3 m upstream of the sample position. The detector signals were recorded using fast digitizers with a sampling rate of 500 Msamples/s[30]. This configuration made it possible to record the detector signals over the entire TOF interval from relativistic neutron energies down to approximately 1 eV. The effective length of the flight path, L=185.07 ±0.01 m, was calibrated using the first s-wave resonances of Au as explained in Ref. [31]. The TOF data were converted to neutron energy by En=mnc2⎡ ⎣ c c2−L t 2−1⎤ ⎦,(1) where mnis the neutron mass and cthe speed of light. The TOF interval of a neutron t was determined by the time between the start signal, based on the reference signal provided by the prompt γ-flash tγ, and the stop signal tn(both 044615-3 C. MASSIMI et al. PHYSICAL REVIEW C 85, 044615 (2012) detected in the C62H6detectors) according to the following: t =tn−tγ+L/c. B. Samples and measurements Enriched samples of 25Mg and 26Mg were borrowed from the Science-Technical Centre “Stable Isotopes” (Obninsk, Russia) in the form of magnesium oxide powder. The powder was sealed in very thin aluminum cans with total masses of 350 mg. The enriched samples were complemented by a metal disk of natural magnesium. All samples were 22 mm in diameter. The composition of the samples is listed in Table I.The specified impurities of the enriched samples included traces of Be, Sb, Fe, Al, Sn, Mn, Cu, Ca, Mo, Ni, Ag, and Pb [32]. From the resonance shape analysis (RSA) of the capture data, some traces of In were found in addition. The concentration of impurities was verified and it resulted to be very low. For instance, the most important impurities (115In, 121,123Sb, 117Sn, and 95Mo) were at the level of tens of ppm. The mass of the samples was quoted in the accompanying documentation without uncertainties. Furthermore, no information was available on the procedure used for the preparation, nor on the final homogeneity of the powder samples. Because MgO is highly hygroscopic, the Mg content might have been overestimated by the absorption of moisture before the powder was sealed in the Al cans. Unfortunately, it was not possible to heat the samples for removing absorbed water as described in Ref. [20]. In fact, the comparative analysis of the first s-wave resonance at 19.86 keV in the 25Mg(n,γ) cross section, which was observed with the enriched 25MgO sample and with the metallic natural sample, provided clear evidence that the quoted 25Mg mass was overestimated by about 30% (see Sec. IV B). An alternative explanation could be possible inhomogeneities of the sample, related to the spatial distribution of the powder inside the canning. Nevertheless, a procedure described in the analysis section allowed determination of the 25Mg mass with an uncertainty of approximately 12%. Unfortunately, the same procedure could not be applied to the 26Mg sample. Therefore, the cross section presented herein may be underestimated by as much as 30% for this isotope. Additional samples of Au, Pb, and C (all 22 mm in diameter) have been used in the experiment. The Pb and C (corresponding to an areal density of 2.99 ×10−3atoms/b and 2.018 ×10−2atoms/b, respectively) disks were used to determine various background components. A gold sample, 0.25 mm in thickness (corresponding to an areal density of 1.498 ×10−3atoms/b), served to normalize the capture data via the saturated resonance technique [33]. This technique can be applied when the macroscopic total cross section is much larger than unity. In this particular case, all incoming neutrons, with energies in the vicinity of the resonance energy, interact with the sample. Therefore, since all neutrons are absorbed in the sample, the probability of a capture event in the sample is 1. The measurements with the different samples were cycled every 2 days and they were interspersed with energy calibration of the scintillators. III. DATA REDUCTION The use of the PHWT, by which the TOF spectrum is modified on the basis of the signal amplitude, requires a careful energy calibration of the capture detectors in combination with proper study of the detector resolution [34]. During the entire experiment, the pulse height response of the C62H6detectors was calibrated in regular intervals with standard sources, i.e., with 137Cs, 60Co, and a composite 238Pu/C source, which yields 6.13-MeV γrays through the 13C(α,n)16O∗reaction. Data were taken with a digitizer threshold corresponding to a deposited energy of about 160 keV, but a fixed threshold of 200 keV was later applied in the off-line processing. By the use of fast digitizers for data acquisition the dead time could be reduced to an effective value of less than 25 ns, related to the pulse reconstruction algorithm. In the off-line event processing, we applied a fixed dead time of 30 ns and used this value in the calculation of the correction due to counting-rate losses. When an event was observed, all subsequent signals occurring within the dead time of 30 ns in both detectors were discarded in order to eliminate coincidence counting. The dead time correction never exceeded 1%. A. Capture yield The capture yield Y(En), which represents the probability of a neutron to be captured by the sample, can be deduced from the background-subtracted counts in the TOF spectrum C(En) registered by the C62H6array, C(En)=Y(En)(En)Aεc,(2) where (En) represents the intensity of the neutron beam, A the sample area, and εcthe efficiency for detecting a capture event. In the PHWT, the proportionality of the capture efficiency to the total γenergy released in the capture event εc∝ Ec, where Ecis the sum of the neutron separation energy and the kinetic energy (Ec=Sn+Kc.m.), is obtained by a weighting function, which modifies the detection efficiency so εcbecomes independent of the γcascade. The weighted count rate spectrum is CW(En)=NY(En)(En)Ec,(3) where the absolute normalization Nof the capture data is obtained by means of the saturated resonance in Au at 4.9 eV. Since the Au disk was 0.25 mm in thickness, the attenuation of the γrays in the Au sample was considered as described in Ref. [28]. The corresponding correction of the normalization constant was of the order of 1%. The measured capture yields are shown in Fig. 2. B. Background studies The background components have been determined by comparison of the Mg capture yields with the respective yields measured with the Pb and C samples as illustrated in Fig. 3. The main source of background in the keV region is generated by in-beam γrays, which are scattered from the 044615-4 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 10 102103104105106 natMg(n,γ) 25Mg(n,γ) 26Mg(n,γ) Neutron energy (eV) Capture yield (in units of 102) FIG. 2. (Color online) Capture yield of the natMg(n,γ), 25Mg(n, γ), and 26Mg(n,γ) reactions. sample and detected by the capture setup. These γrays arise mainly from neutron capture on hydrogen in the water moderator surrounding the spallation target and are responsible for most of the background in the keV region. This component is most pronounced in the yield of the Pb sample, which is particularly sensitive to in-beam γrays due to high atomic number of lead. Accordingly, the effect for the C and Mg samples is much weaker as illustrated in Fig. 3. Another important background is produced by samplescattered neutrons, which are captured in the detection setup and in surrounding materials. This background component is studied with the C sample that can be considered as a pure neutron-scatterer sample. The shape of the carbon yield is very similar to that of 25Mg, because the nonresonant elastic cross section σn(the so-called potential scattering) is smooth for both elements in this region and the elastic yield nσn(where nis the areal density in atoms per barn) is similar for both samples. The comparison of the two components shows that the overall background was dominated by the effect of sample- 10-5 10-4 10-3 1 10 102103104105106 25Mg + n natC + n natPb + n Neutron energy (eV) Yield (not normalized) FIG. 3. (Color online) Capture yield of the 25Mg +nreaction together with the spectra of the C and Pb measurements. scattered neutrons. Since the background displays a smooth, nonresonant behavior as a function of energy, it was not subtracted but was fitted in the resonance analysis. In this way, the uncertainty related to the background was included in the uncertainty of the resonance parameters. IV. SIMULTANEOUS RESONANCE SHAPE ANALYSIS The present capture data were analyzed together with transmission data from ORELA [9], available from the Experimental Nuclear Reaction Data (EXFOR) database [35], using the R-matrix code SAMMY [36]. A simultaneous resonance shape analysis of capture and transmission data results in much more reliable resonance parameters than can be obtained through independent analyses of the various data sets. Experimental effects due to neutron multiple scattering in the sample, self-shielding (i.e., shielding of the inner atoms in the sample by the outer atoms closer to the surface), Doppler broadening, and experimental resolution are properly taken into account within the SAMMY code. As shown in Eq. (3), the efficiency, and, hence, the calculated capture yield, is inversely proportional to Ec. However, only a single Sn(typically chosen to be that of the most abundant isotope in the sample) can be used in weighting the data. Therefore, in the analysis of the capture data, the abundances of the other Mg isotopes in the sample must be scaled according to their Snvalue. In particular, the neutron separation energies used were 7.33, 11.09, and 6.44 MeV for 25Mg, 26Mg, and 27Mg, respectively. Resonance parameters reported in Ref. [8]wereusedas initial values in the RSA, with the following exceptions. An average reaction width γ=3.5 eV was kept fixed to fit capture data when a resonance was not visible in the transmission data. Spin-parity assignment of resonances above 500 keV were taken from known results of a neutron elasticscattering experiment [13]. All resonances up to 700 keV were included in the Rmatrix. The availability of capture data in the full energy range allowed us to assign the observed resonances to the respective isotopes in the fit of the transmission data up to 700 keV. The RSA of the capture data was limited to below about 700-keV neutron energy, where inelastic scattering starts to interfere. In the fitting procedure, the resonance energy and the partial widths (nand γ) were allowed to vary while spin and angular momentum were kept fixed. The nuclear radii for 24Mg +nand 25Mg +nwere allowed to vary in the fits of the transmission data as explained in Ref. [8]. The results are radii of 5.4 and 3.8 fm for sand pwaves in 24Mg +n, respectively, and 5.1 fm common to sand pwaves in 25Mg +n. Figure 4 shows the quality of the fit to the transmission data. Parameters of the resonances at negative energy were changed with respect to the assumptions in Ref. [6] to reproduce the thermal-neutron capture cross section reported in Ref. [23]. Their energy was taken from the level scheme in Ref. [37]. A. 24Mg +nresonances The capture yield considered for this analysis was obtained from the natMg +nmeasurement. The problems described in 044615-5 C. MASSIMI et al. PHYSICAL REVIEW C 85, 044615 (2012) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 100 200 300 400 500 600 700 natMg+nI SAMMY RSA Neutron energy (keV) Transmission FIG. 4. (Color online) natMg +ntransmission data (red symbols) and the SAMMY fit (blue line). Sec. II B for the oxide samples do not apply for this metal sample. In Table II the results of the RSA are reported together with the uncertainties from the fitting procedure. Examples of the fits are given in Figs. 4and 5. In the present analysis, the 68.5-keV resonance, assigned to 24Mg in the literature, has been found to be a 26Mg resonance. Indeed, it was visible in the 26Mg(n, γ ) data and with much reduced size in the natMg(n, γ ). Moreover, the doubtful resonance at 177 keV was confirmed as belonging to 24Mg. The capture kernels ωγ =gγn/(γ+n),(4) calculated from present resonance parameters, are compared to those from Ref. [9]inFig.6. In particular ratios of the capture kernels as a function of neutron energy and of the gn/ γ values are shown. It has been shown [38] that some kernels TABLE II. 24Mg +nresonance parameters extracted from the simultaneous R-matrix analysis. The quoted uncertainties were obtained by the SAMMY fit.SpinandparityfromRef.[8]andRef.[13]. En(keV) J πγ(eV) n(eV) −100 0 0.5+13 3000 46.347 ±0.001 (1) (0.5−) 1.4 ±0.2 1.44 ±0.06 83.940 ±0.004 1 1.5−4.1 ±0.2 7607 ±4 176.67 ±0.01 (1) (0.5−) 3.5a0.4 ±0.2 257.182 ±0.001 (2) (1.5+) 1.8 ±0.1 20.9 ±0.5 267.48 ±0.01 1 0.5−7±3 83270 ±20 430.79 ±0.01 1 1.5−6.7 ±0.6 28180 ±20 475.359 ±0.004 2 2.5+1.2 ±0.2 13.9 ±0.5 498.285 ±0.004 1 1.5−0.25 ±0.1 752 ±2 551.04 ±0.03 (2) (2.5+)8±7 1.2 ±0.4 642.012 ±0.004 1 0.5−1.5 ±0.3 1459 ±8 659.95 ±0.01 0 0.5+(13 ±1) 17470 ±40 aAssumed reaction width. See text for details. 0 0.005 0.01 0.015 0.02 45 45.5 46 46.5 47 24Mg(n,γ)I SAMMY RSA (a) Incoming neutron energy (keV) Capture yield 0 0.05 0.1 0.15 260 280 300 24Mg(n,γ)I SAMMY RSA (b) Incoming neutron energy (keV) Capture yield (in units of 102) FIG. 5. (Color online) Fits of the capture yield of the 24Mg +n reaction in different energy regions. from previous ORELA measurements for resonances having large gn/ γwere systematically too large, presumably due to an underestimation of the neutron-scattering background (so-called neutron sensitivity effect). The differences between the present capture kernels and those of Ref. [9] do not appear to indicate this neutron sensitivity effect. B. 25Mg +nresonances The capture yield of 25Mg was obtained from the spectrum measured with the enriched oxide sample after its areal density was scaled to reproduce the resonance parameters determined from the natural Mg sample, where the first s-wave resonance in 25Mg +nat 19.86 keV is well isolated. Without that correction, γvalues of 1.7 ±0.2 and 1.16 ±0.06 eV were found using the data measured with the natural and the enriched MgO sample, respectively. This disagreement suggested that the areal density of the oxide sample was 27.5% too high, indicating a significant water contamination of the oxide sample. 044615-6 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 (a) Neutron energy (keV) Kernel ratio (this work/Weigmann) 0 0.5 1 1.5 2 2.5 3 10 -2 10 -1 1 10 102103104 (b) gΓn/Γγ Kernel ratio (this work/Weigmann) FIG. 6. Capture kernel ratios of the present work to Weigmann [9] as functions of neutron energy (a) and gn/ γvalues (b) for 24Mg resonances. If the shape of a resonance is distorted by experimental effects, e.g., by Doppler and resolution broadening, the remaining observable is the capture kernel (proportional to the area under the resonance) and the areal density of the sample [39]. Accordingly, the RSA is sensitive to ngγn/(γ+n). Because nγfor the 19.86-keV resonance, this quantity reduces to ngγ, and because the statistical spin factor is known from previous measurements, the effective areal density ncan be derived via RSA from the capture data obtained with the oxide sample. This procedure is valid only if the resonance parameters, and in particular the reaction width, is kept fixed in the fit. In this way, the effective areal density turned out to be (8.6±1.0) ×10−3atoms/b, where the 12% uncertainty is given by the uncertainty on γ. This adjusted areal density was used in the RSA of the enriched 25Mg sample. As shown in Fig. 7, the capture yield of the oxide sample can be reproduced with the same accuracy either by fitting the reaction width or the areal density of the sample. On the contrary, the calculation of the yield 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15 20 25 30 25Mg(n,γ)I n=0.0118 atoms/b Γγ=1.7 eV n=0.0086 atoms/b Γγ=1.7 eV n=0.0118 atoms/b Γγ=1.16 eV Incoming neutron energy (keV) Capture yield (in units of 103) FIG. 7. (Color online) The capture yield of the 25Mg(n, γ ) resonance at 19.86 keV. The data measured with the oxide sample (symbols with error bars) are clearly overestimated with the resonance parameters obtained from the metallic sample and the originally declared areal density (black line). The resonance analysis with SAMMY shows that the data are reproduced treating the areal density nor the capture width γas free parameters (blue and green lines, respectively). Consistency with the result obtained with the metal sample requires adopting the reduced areal sample density. assuming n=0.01182 atoms/b (i.e., the originally declared value) and γ=1.7 eV (derived from the metallic sample) does not reproduce the data. It is obvious that the results for the 19.86-keV resonance can be reconciled only if the reduced areal density is adopted for the enriched sample. The corresponding results of the RSA are listed in Table III together with the uncertainties from the SAMMY fits. Examples of the RSA analysis are given in Figs. 4and 8. The parameters of the 19.86-keV resonance derived from the metallic natMg sample are in agreement with those of Ref. [9]. Moreover, the spin and parity assignment of this level was confirmed since the χ2/DOF (χ2is chi-squared and DOF is the number of degrees of freedom) value of the fit (in the energy range 15–30 keV) was 1.6 assuming Jπ=2+and 5.6 assuming Jπ=3+. The spin and parity of the 72.66 keV was confirmed as well: the χ2/DOF value of the fit (in the energy range 60–80 keV) was 4.6 assuming Jπ=2+and 7.9 assuming Jπ=3+. The parity of the 62.727-keV resonance was changed to negative according to a recent photoexcitation experiment by Longland et al. [40]. The doubtful resonances at ≈102 and 107 keV were found to improve the quality of the simultaneous RSA and are, therefore, included in Table III. However, they affect the resonance parameters of the large s wave at 100.03 keV and capture data with an enriched sample and very high statistic are required to solve this point. The spin and parity of the 211.14-keV resonance was changed from 3− [8]to2 −, because the simultaneous RSA of the transmission and capture data were more satisfactory. In particular, the χ2/DOF value of the fit (in the energy range 200–220 keV) was 1.1 assuming Jπ=2−and 3.5 assuming Jπ=3−.For the resonances above 450 keV the large statistical uncertainties prevented a meaningful RSA of the capture data. 044615-7 C. MASSIMI et al. PHYSICAL REVIEW C 85, 044615 (2012) TABLE III. 25Mg +nresonance parameters extracted from the simultaneous R-matrix analysis, uncertainties include the one from the sample mass. Spin and parity from Ref. [8]. Resonances and values in brackets must be considered with some caution. En(keV) J πγ(eV) n(eV) −154.25 0 2+6.5 30 000 19.86 ±0.05 0 2+1.7 ±0.2 2310 ±30 62.727 ±0.003 1a1+a4.1 ±0.7 28 ±5 72.66 ±0.03 0 2+2.5 ±0.4 5080 ±80 79.29 ±0.03 (0) (3+) 3.3 ±0.4 1560 ±80 81.117 ±0.001 0b(2)+3±2 0.8 ±0.7 93.60 ±0.02 (1) (1−) 2.3 ±2 0.6 ±0.2 100.03 ±0.02 0 3+1.0 ±0.1 5240 ±40 [101.997 ±0.009] [1] [2−] [0.2 ±0.1] [4 ±3] [107.60 ±0.02] [0]b[3+] [0.3 ±0.1] [2 ±1] 156.34 ±0.02 (1) (2−) 6.1 ±0.4 5520 ±20 188.347 ±0.009 0 (2)+1.7 ±0.2 590 ±20 194.482 ±0.009 (1) 4(−)0.2 ±0.1 1730 ±20 200.20 ±0.03 1b1−0.3 ±0.3 1410 ±60 200.944 ±0.006 (2) (2+) 3.0 ±0.3 0.7 ±0.7 203.878 ±0.001 (1) (2−) 0.8 ±0.3 2 ±1 [208.27 ±0.01] [1] [1−] [1.2 ±0.5] [230 ±20] 211.14 ±0.05 (1) (2−)d3.1 ±0.7 12400 ±100 226.255 ±0.001 (1) (1−)4±3 0.4 ±0.2 242.47 ±0.02 (1) (1−)6±4 0.3 ±0.2 244.60 ±0.03 1 1−c3.5 ±0.6 50 ±20 245.552 ±0.002 (1) (1−) 2.3 ±2 0.5 ±0.2 253.63 ±0.01 (1) (1−) 3.1 ±2.7 0.1 ±0.1 261.84 ±0.03 (1) 4(−)2.6 ±0.4 3490 ±60 279.6 ±0.2 (0) (2+) 1.9 ±0.7 3290 ±50 311.57 ±0.01 (2) (5+) (0.84 ±0.09) (240 ±10) 362.04 ±0.02 2 4+c2.2 ±0.2 2020 ±40 387.57 ±0.04 (3) (5−)c(1.7 ±0.3) (8910 ±80) 423.43 ±0.01 1 (1−)c(20 ±10) (25 ±10) 451.24 ±0.06 (1) (3−)c(6.6 ±0.8) (3000 ±100) 514.88 ±0.03 (1) (2−) (8.6 ±0.8) (1800 ±100) 536.0 ±0.02 (1) (4−) (2.7 ±0.3) (840 ±40) aSpin and parity assignment based on Ref. [40]. bParity assignment based on Ref. [19]. cObserved in 22Ne(α, n)25Mg reaction. dSpin assignment based on χ2. C. 26Mg +nresonances This analysis is based on the capture yield measured with the enriched 26MgO sample. The RSA results are reported in Table IV together with the uncertainties from the fitting procedure. As indicated by the capture yields in Fig. 2,the mass of the 26Mg sample seemed less affected by adsorption of moisture. Nevertheless, this possibility still implies a significant uncertainty, because none of the resonances could be seen with the natural Mg sample. Therefore, the γvalues (and, correspondingly, the capture cross section) may be underestimated by as much as 30%. It is worth noting that capture kernels have been estimated in Ref. [21] on the basis of activation data and a theoretical calculation for the DRC component. The ωγ values for the 68.5- and 219.4-keV resonances are given as 0.067 ±0.016 eV and 1.34 ±0.24 eV, respectively. In the present work we measured ωγ =0.09 ±0.02 eV for the 68.5-keV resonance and 2.17 ±0.12 eV for the 219.2-keV resonance. This disagreement would even be enhanced by a possible reduction of the sample mass. Examples of the simultaneous RSA analysis are given in Fig. 9. TABLE IV. 26Mg +nresonance parameters extracted from the simultaneous R-matrix analysis. The quoted uncertainties were obtained by the SAMMY fit. Spin and parity from Ref. [8]. En(keV) J πγ(eV) n(eV) −60 0 0.5+3 2400 68.529 ±0.001 (1) (0.5−) 0.09a±0.02 48 ±2 219.395 ±0.002 2 1.5+1.10a±0.06 80 ±2 302.34 ±0.1 ±0.08 1 0.5−6.3a±0.9 61200 ±200 427.23 ±0.02 (0) (0.5+) 2.7a±0.5 90 ±20 438.59 ±0.09 (1) (0.5−) 3.4a±0.9 11900 ±200 500.50 ±0.01 (1) (1.5−) 0.48a±0.08 260 ±10 aValues may be underestimated by as much as 30%. 044615-8 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) TABLE V. Maxwellian-averaged capture cross sections of 24,25,26Mg (in mb) for different temperatures compared with the values in the KADoNiS database [41]. Thermal energy This work KADoNiS [41] (keV) Resonances DRC Total Resonances Total 24Mg(n, γ )25Mg 5 0.17 ±0.01 0.04 0.21 ±0.01 0.11 8 0.38 ±0.02 0.05 0.43 ±0.02 10 0.67 ±0.04 0.06 0.71 ±0.04 0.48 15 1.7 ±0.1 0.08 1.71 ±0.1 1.3 20 2.7 ±0.1 0.09 2.7 ±0.1 2.3 23 3.1 ±0.2 0.1 3.2 ±0.2 25 3.3 ±0.2 0.1 3.4 ±0.2 2.9 30 3.7 ±0.2 0.1 3.8 ±0.2 3.3 ±0.4 40 3.8 ±0.2 0.1 3.9 ±0.2 3.6 50 3.6 ±0.2 0.1 3.7 ±0.2 3.4 60 3.2 ±0.2 0.2 3.4 ±0.2 3.1 80 2.6 ±0.2 0.2 2.8 ±0.2 2.7 90 2.4 ±0.3 0.2 2.6 ±0.3 100 2.1 ±0.2 0.2 2.3 ±0.3 2.1 25Mg(n, γ )26Mg 5 3.5 ±0.4 0.02 3.5 ±0.4 4.8 8 4.9 ±0.6 0.03 4.9 ±0.6 10 5.1 ±0.6 0.03 5.1 ±0.6 5.0 15 4.9 ±0.6 0.03 4.9 ±0.6 5.5 20 4.6 ±0.4 0.04 4.6 ±0.4 6.0 23 4.5 ±0.6 0.05 4.6 ±0.6 25 4.3 ±0.6 0.05 4.4 ±0.6 6.2 30 4.0 ±0.6 0.05 4.1 ±0.6 6.4 ±0.4 40 3.4 ±0.6 0.06 3.5 ±0.6 6.2 50 2.8 ±0.5 0.07 2.9 ±0.5 5.7 60 2.4 ±0.4 0.08 2.5 ±0.4 5.3 80 1.8 ±0.3 0.09 1.9 ±0.3 4.4 90 1.5 ±0.2 0.1 1.6 ±0.2 100 1.3 ±0.2 0.1 1.4 ±0.2 3.6 26Mg(n, γ )27Mg 5 0.067a±0.002 0.02 0.087b±0.002 0.103 8 0.050a±0.001 0.02 0.070b±0.001 10 0.047a±0.001 0.03 0.077b±0.001 0.091 15 0.056a±0.003 0.03 0.086b±0.003 0.098 20 0.069a±0.005 0.04 0.109b±0.005 0.110 23 0.07a±0.01 0.04 0.11b±0.01 25 0.08a±0.01 0.04 0.12b±0.01 0.124 ±0.008 30 0.09a±0.01 0.05 0.14b±0.01 0.084 ±0.005 0.126 ±0.009 40 0.12a±0.01 0.06 0.18b±0.01 0.143 50 0.17a±0.02 0.06 0.23b±0.02 0.161 60 0.21a±0.02 0.07 0.28b±0.02 0.165 80 0.29a±0.04 0.08 0.37b±0.04 0.226 90 0.31a±0.05 0.09 0.40b±0.05 100 0.34a±0.05 0.09 0.43b±0.05 0.265 aValues may be underestimated by as much as 30%. bValues may be underestimated by as much as 20%. V. STELLAR CROSS SECTIONS A. Resonance contributions The cross sections determined using the resonance parameters in Secs. IV A,IV B, and IV C have been convoluted with a Maxwellian neutron energy distribution to obtain the actual stellar cross section (MACS). The results are listed in the Table Vfor thermal energies between kT =5 and 100 keV, including the specific values for the common s-process sites, e.g., for kT =8 and 23 keV related to He shell burning in low-mass AGB stars and kT =25 and 90 keV for the case of core He and shell C burning in massive stars. The value 044615-9