The neutron-capture cross sections of 186,187Os have been recently measured at the CERN neutron time-of-flight facility n_TOF for an improved evaluation of the Re/Os cosmo-chronometer. This experimental information was complemented by nuclear model calculations for obtaining the proper astrophysical reaction rates at s-process temperatures. The calculated results and their implications for the determination of the time-duration of nucleosynthesis during galactic chemical evolution is discusse

Fujii, K.

Käppeler, F.

Mengoni, A.

Mosconi, M.

RERO DOC Digital Library

CSIRO PUBLISHINGPublications of the Astronomical Society of Australia, 2009, 26, 250–254 www.publish.csiro.au/journals/pasaTuning the Re/Os Clock: Stellar-Neutron Cross SectionsA. MengoniA,F, M. MosconiB, K. FujiiC, F. KäppelerD, and The n_TOF CollaborationEA International Atomic Energy Agency, Vienna, Austria and CERN, Geneva, SwitzerlandB Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, GermanyC INFN, Sezione di Trieste and Universitá degli Studi di Padova, ItalyD Forschungszentrum Karlsruhe, GermanyE CERN (www.cern.ch/ntof), Geneva, SwitzerlandF Corresponding author. Email: a.mengoni@iaea.orgReceived 2009 January 9, accepted 2009 March 12Abstract: The neutron-capture cross sections of 186,187Os have been recently measured at the CERN neutrontime-of-ﬂight facility n_TOF for an improved evaluation of the Re/Os cosmo-chronometer. This experimentalinformation was complemented by nuclear model calculations for obtaining the proper astrophysical reactionrates at s-process temperatures. The calculated results and their implications for the determination of thetime-duration of nucleosynthesis during galactic chemical evolution is discussed.Keywords: nuclear reactions, nucleosynthesis, abundances — galaxy: evolution — stars: neutron1 IntroductionThe use of the slow β-decay of 187Re into 187Os as cos-mochronometer was proposed by Don Clayton in 1963(see Figure 1). It was immediately noted that the neutroncapture cross sections of the two s-only isotopes, 186Osand 187Os would be key quantities for the determinationof the s-process component of the 187Os abundance (Clay-ton 1964), and hence essential for isolating the radiogeniccomponent. Estimates of these quantities, or of their ratioRσ ≡ 〈σ(186)〉〈σ(187)〉 , (1)were made from capture cross section systematics(Rσ ≈ 0.5), till the ﬁrst direct measurements were per-formed in the 1980 (Browne & Berman 1981; Winters &Macklin 1982).In parallel, it became clear that the experimental datahad to be corrected for the basic formulation of the clockdue to thermal effects in the stellar plasma. It turned outthat the role of low-lying states in 187Os was particularlycrucial for obtaining the (n, γ) cross section at the tem-peratures of the s-process site, which are of the order of3× 108 K. Under these conditions low-lying states arepopulated by excitation in the hot thermal photon bath.Therefore, the measured (n, γ) results for the ground statehave to be corrected for the contribution of the excitedstates to the effective stellar capture cross section.This contribution complements improved experimentalstudies of the (n, γ) cross sections of 186,187Os (Mosconi2007; Mosconi et al. 2008; Segawa et al. 2008) and ofthe (n, n′) cross section of 187Os (Mosconi 2007) by anupdated and consistent set of calculations to quantify thecorrections for the effect of thermally populated nuclearstates at the high temperatures of the stellar interior.Direct information on capture rates from excited statesis impossible to obtain by laboratory experiments. How-ever, theoretical model calculations, which are necessaryto evaluate the effective stellar cross sections of 186Os and187Os, can be constrained by a number of experimentaldata. In this contribution the methods and informationsused in these calculations are reviewed on the basis ofrecent experimental results, i.e. the measured (n, γ) crosssections from the n_TOF facility at CERN as well asthe inelastic scattering cross section obtained at FZKKarlsruhe (Section 2.1). Up-to-date calculations with theHauser–Feshbach statistical model are presented in Sec-tion 2.2 for different assumptionsmade in the evaluation ofthemodel parameters. The implications of these results forthe determination of the time-duration of nucleosynthesis(and ultimately of the age of the universe) are discussed insomedetail in Section 3. Itwill become clear that themajoruncertainty on the age determination based on this radio-active decay is now due to the modeling of the GalacticalChemical Evolution (Clayton 1988).2 Neutron Cross Sections2.1 MeasurementsThe neutron-capture cross sections of 186,187Os have beenrecently measured at the CERN neutron time-of-ﬂightfacility n_TOF. Details of the measurement techniqueand data analysis have been reported elsewhere (Mosconi2007; Mosconi et al. 2008). Here it sufﬁces to report theﬁnalMaxwellian-averaged capture cross sections,MACS,for the two isotopes in Table 1.©Astronomical Society of Australia 2009 10.1071/AS09005 1323-3580/09/03250https:/www.cambridge.org/core/terms. https://doi.org/10.1071/AS09005Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 15:57:46, subject to the Cambridge Core terms of use, available atTuning the Re/Os Clock: Stellar-Neutron Cross Sections 251Figure 1 The front page of theWashington Post of 23 April 1963 where the proposal of using the Re/Os clock by Don Clayton was reportedafter the announcement at the meeting of theAmerican Physical Society. The story, while written in non-specialistic language, correctly reportsthe basic principle on which the clock is based (courtesy of Don Clayton, 2008).Table 1. Maxwellian-averaged capture cross sections atkT = 30 keV and cross-section ratios, RσA B C186Os 414± 17 418± 16 438± 30187Os 969± 32 874± 28 919± 43Rσ 0.43± 0.02 0.48± 0.02 0.48± 0.04A, Mosconi et al. (2008); B, Winters & Macklin (1982); C, Browne &Berman (1981).The energy dependence of the cross section is impor-tant in this context since the parametrization of the modelcalculation, which is necessary to deduce the stellar rates,can be validated by comparison of the calculations withthemeasured cross sections. The relevant energy range forthis comparison from 0.1 keV≤En ≤ 1MeV is perfectlycovered by the high-resolution results of the n_TOF mea-surement. The new n_TOF data are shown in Figure 2together with the results of previous capture cross sectionmeasurements and the updated calculations.2.2 CalculationIn the mass range A≈ 185, the Hauser–Feshbach statis-tical model (HFSM) is best suited in the energy range ofinterest for this work. The model relies on the assump-tion that the reaction proceeds through formation of acompound nucleus and its subsequent statistical decay,following well established statistical properties. In partic-ular, the nearest level spacings correspond to a Wignerdistribution and the width for neutron decay to a Porter–Thomas distribution. The decay probabilities for γ-rayemission can be deduced from time-reversal invariance(detailed balance) and the Brink–Axel hypothesis.Then, the simple HFSM formula holds:σn,γ (En) = πk2n∑J,πgJ∑ls Tn,lsTγ,J∑ls Tn,ls +∑ls Tn′,ls + Tγ,JWγ,Jwhere En is the incident neutron energy, kn the wavenumber for the neutron-nucleus relative motion, s= 12the intrinsic spin of the neutron, and l the orbital angu-lar momentum of the relative motion. The statisticalweighting factor for target nuclei in states of spin I andcompound states of total angular momentum J compat-ible with spin and parity conservation laws is indicatedby gJ = (2J + 1)(2s+ 1)−1(2I + 1)−1. Finally, Wγ is afactorwhich takes the different statistical ﬂuctuation prop-erties of the γ-decay channel compared to the neutronelastic (n) and inelastic (n′) channels into account.https:/www.cambridge.org/core/terms. https://doi.org/10.1071/AS09005Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 15:57:46, subject to the Cambridge Core terms of use, available at252 A. Mengoni et al.0.11100.001 0.01 0.1 1Capture cross section [b]Neutron energy [MeV]186OsBrowne & Berman (1981)Winters & Macklin (1980)TIT (2007)n_TOF (2004)Calc (spherical OMP)Calc (deformed OMP)0.11101000.0001 0.001 0.01 0.1 1Capture cross section [b]Neutron energy [MeV]187OsBrowne & Berman (1981)Winters & Macklin (1980)TIT (2007)n_TOF (2004)Calc (spherical OMP)Calc (deformed OMP)Calc (optimized spherical OMP) 00.511.5 210 20 30 40 50 60 70Inelastic cross section [b]Neutron energy [keV]Calc (spherical OMP)Calc (optimized spherical OMP)Mosconi (2007)Litvinsky (1995)Macklin (1983)Hershberger (1983)Figure 2 Top andMiddle: neutron-capture cross sections of 186Osand 187Os as a function of neutron energy. Calculations were per-formed in this work within the HFSM theory, as described in thetext. In the legend TIT refers to Segawa et al. (2008) and n_TOFto Mosconi et al. (2008). Bottom: the inelastic cross section for theﬁrst excited state in 187Os at 9.75 keV (Mosconi 2007).The nuclear input data for the HFSM theory canbe calculated using different nuclear structure and de-excitation models. It is here that the various HFSMapproaches used so far differ among each other. Examplesof widely used approaches to the HFSM parameterizationfor nuclear astrophysical applications are those of Holmeset al. (1976), Harris (1981) and the most recent versionsof non-smoker (Rauscher & Thielemann 2001), most(Arnould & Goriely 2006), and talys (Koning, Hilaire &Duijvestijn 2005). Most of these references include alsoHFSM computer codes for calculation of reaction crosssections. A repository of parameters and systematics ofnuclear structure quantities can be found in the ‘RIPL’initiative1.The present calculations of the neutron capture crosssections of 186Os and 187Oswere performedusing the stan-dard optical model parameters (OMP) ofMoldauer (1975)and of the code talys. The level density parametrizaionis that of Gilbert and Cameron with parameters, whichare adjusted to reproduce the low-lying cumulative num-ber of levels available from the data library ensdf2 at lowexcitation energies and the average level spacings at theneutron binding energy deduced from the n_TOF crosssectionmeasurements. The parameters for the γ-ray trans-mission coefﬁcients were adopted from photo-neutroncross section data for the giant dipole resonance and themethodology used in talys.Additional calculations were performed using adeformedoptical potential, considering the coupling of therotational states in the target such as the 0+, 2+, 4+ statesin 186Os and the 1/2−, 3/2−, and 5/2− states in 187Os.The coupling strengths were deduced from the ground-state quadrupole and octupole deformations, which arealso available from the ensdf data library.Both sets of calculations are included in Figure 2. Thecalculated cross sections were normalized to reproducethe MACS at kT = 30 keV given in Table 1. The plots ofFigure 2 show that the use of the deformed OMP doesnot result in a better reproduction of the capture crosssections in the energy range of interest, but that the crosssections obtained with the spherical OMP are closer to theexperimental data. This can be due to an overestimation ofthe coupling strength deduced from the static quadrupoledeformations. In the actual situation, a smaller couplingstrength could be more appropriate for the descriptionof the experiemental data, a situation comparable to thatdescribed by a spherical OMP set.A similar behaviour is also seen in the comparisonwith the experimental data for the inelastic cross section.Again, the deformed OMP calculations do no seem toimprove the results obtained with spherical OMPs. In fact,a small adjustment of the spherical OMPs seems producethe best results, for the neutron capture as well as for theinelastic channel. This adjustement consists in a simplereduction of the strength for the real part of the sphericalpotential from V0 = 46MeV to V0 = 43MeV.As a conservative estimate of the uncertainties relatedto the OMP, the deviation of the cross sections calcu-lated with the three OMP sets from the mean valuewas adopted in the evaluation of the stellar enhancementfactors.1 RIPL-2 2007, see http://www-nds.iaea.org/RIPL-2.2 ENSDF, Evaluated Nuclear Structure Data File 2008, seehttp://www-nds.iaea.org/nsdd.https:/www.cambridge.org/core/terms. https://doi.org/10.1071/AS09005Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 15:57:46, subject to the Cambridge Core terms of use, available atTuning the Re/Os Clock: Stellar-Neutron Cross Sections 2532.2.1 Stellar Enhancement FactorsThe reaction rates under stellar conditions have to beevaluated by due consideration of the possibility that low-lying excited states can be thermally populated in theinvolved nuclei. Neutron capture rates are especially sen-sitive to this effect because the cross sections for excitedstates may well differ from that of the ground state.The capture cross section of excited states can be mod-eled as for the ground state. There are, however, additionalinelastic scattering channels, which have to be considered.In particular, the so-called super-elastic channel wherethe incident neutron is inelastically scattered to a lowerstate in the target, may contribute signiﬁcantly. In theabove HFSM equation, the transmission coefﬁcients forthe inelastic channels, Tn′,ls, must also include the opensuper-elastic channels. Comparison of the model calcu-lation with experimental data for the inelastic scatteringcross section provides a good benchmark for the neutron-nucleus interaction used to determine the transmissionfunctions.As a consequence of the compound nucleus reactionmechanism the compound nuclear states formed by cap-ture on excited states are the same (except for total angular11.11.21.31.41.51.60 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1SEFkT [MeV]Spherical OMPDeformed OMPSpherical optimized OMPFigure 3 Stellar enhancement factor (SEF) for the187Os(n, γ)188Os reaction. Three types of calculations areshown, using different sets of OMP, standard values from Moldauer(1975), a deformed optical model with channel coupling, and aspherical OMP with optimized parameters. The average value atkT = 30 keV has been adopted and the deviations from the meanwas assumed to represent the associated uncertainties.Table 2. Uncertainties of the Re/Os cosmo-chronometer associated with the Re/Os abundance ratios and the nuclear-physics inputQuantity Value Uncertainty (Gyr) Reference186Os/187Re abundance ratio 0.2845± 0.0071 Faestermann (1998)187Os/187Re abundance ratio 0.2254± 0.0057 Faestermann (1998)Total effect of abundances 0.49t1/2 187Re 41.2± 1.12 0.29 Galeazzi et al. (2001)MACS ratio Rσ (lab) 0.427± 0.023 0.40 Mosconi et al. (2008)SEF-30 (186Os) 1.025± 0.005 0.04SEF-30 (187Os) 1.28± 0.04 0.24Total combined uncertainty 0.74momentum) as those populated by capture on the ground-state. Since the modeling of the reaction cross sectionfor the ground-state can be tested against experimentalcapture cross sections measured in the laboratory, the con-straints from this comparison can help reduce, at leastin principle, the uncertainties related to the evaluationof stellar cross sections. In practice, the thermal effectsare expressed by the so-called stellar enhancement fac-tor (SEF), deﬁned as 〈σ〉∗ = SEF · 〈σ〉lab, where ∗ and‘lab’ indicate the MACS (i.e. averaged over a populationof excited states) and the laboratory (ground-state) crosssections, respectively.The SEFs of 186Os and 187Os represent crucial cor-rections with respect to the analysis of the Re/Os cosmo-chronometer. Especially the stellar cross section of 187Osis strongly inﬂuenced by the presence of low-lying excitedstates (Woosley&Fowler 1979). Figure 3 shows examplesof SEF calculations for this isotope.3 Tuning the ClockIn order to establish a chronology based the cosmora-diogenic production of 187Os, one needs to develop aproper GCE model describing the production rate of187Re. This programwas started by Clayton (1988). How-ever, the implications of the different uncertainties of theRe/Os cosmo-chronometer can be analyzed with respectto their impact on the galactic age (or on the time-durationof nucleosynthesis) using the schematic model for anexponentially decreasing production of 187Re with timeproposed by Fowler & Hoyle (1960). The discussion ofthe various effects is summarized in Table 2, which refersto the uncertainties of the galactic age due to the Re/Osabundance ratios and the nuclear quantities entering themodel.The uncertainty of the SEF-30 value of 187Os was esti-mated to ±4% from the difference of the results obtainedwith a spherical and a deformed optical model potentialfor the neutron-nucleus interaction. This corresponds to a17% uncertainty for the contribution of the excited statesto the overall cross section. While this is justiﬁed for thewell studied case of 187Os, in general SEF correctionscan be estimated with uncertainties of ≈5% if the capturecross sections for the ground-state (lab) are known withsufﬁcient accuracy and if the other model parameters inHFSM calculations can be ﬁxed by measured quantities.https:/www.cambridge.org/core/terms. https://doi.org/10.1071/AS09005Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 15:57:46, subject to the Cambridge Core terms of use, available at254 A. Mengoni et al.It is interesting to note in closing that the various com-ponents of the uncertainty on the age add up to less than1Gyr. In other words, it appears that the uncertainties onthe nuclear physics quantities as well as on the observedabundances, are contributing a relatively minor compo-nent to the uncertainty of the age determination based onthe Re/Os clock. It is, however, all the most clear that atthis point a proper GCE modeling of the production rateof 187Re, and/or of its destruction by astration (Arnould,Takahashi & Yokoi 1984, and references therein), needto be accounted for in order to determine a meaning-ful chronology based on this interesting decay. A workwhich has been initiated (Clayton 1988) and that can benow exploited and brought to a much improved degree ofaccuracy.AcknowledgmentsIt is an honour and a pleasure to dedicate this contributionto Roberto Gallino. Some of us have been collaboratingwith Roberto over the course of a few decades and a smallcontribution on ‘age’ might perhaps be appropriate as asmall present at the occasion of his 70th birthday. BuonCompleanno Roberto!ReferencesArnould, M. & Goriely, S., 2006, NuPhA, 777, 157Arnould, M., Takahashi, K. &Yokoi, K., 1984, A&A, 137, 51Browne, J. C. & Berman, B. L., 1981, PhRvC, 23, 1434Clayton, D. D., 1964, ApJ, 139, 637Clayton, D. D., 1988, MNRAS, 234, 1Faestermann, T., 1998, Proceedings of the 9th Workshop onNuclear Astrophysics, Ringberg Castle, Tegernsee (Garching:Max Planck Institute for Astrophysics), 171Fowler, W. A. & Hoyle, F., 1960, AnPhy, 10, 280Galeazzi, M. et al., 2001, PhRvC, 63, 014302Harris, M., 1981, Ap&SS, 77, 357Holmes, J. A., Woosley, S. E., Fowler, W. A. & Zimmerman, B. A.,1976, ADNDT, 18, 305Koning,A., Hilaire, S. & Duijvestijn, M. C., 2005,AIPC, 769, 1154Moldauer, P. A., 1975, PhRvC, 11, 426Mosconi, M., 2007, PhD Thesis, University of KarlsruheMosconi, M. et al. (The n_TOF Collaboration), 2008, JPhG, 35,014015Rauscher, T. & Thielemann, F.-K., 2001, ADNDT, 79, 47Segawa, M. et al., 2007, PhRvC, 76, 022802Winters, R. R. & Macklin, R. L., 1982, PhRvC, 25, 208Woosley, S. E. & Fowler, W. A., 1979, ApJ, 233, 411https:/www.cambridge.org/core/terms. https://doi.org/10.1071/AS09005Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 15:57:46, subject to the Cambridge Core terms of use, available at

Tuning the Re/Os Clock: Stellar-Neutron Cross Sections

Abstract

Similar works

Full text

Available Versions

RERO DOC Digital Library