A
The Astrophysical Journal, 673:434Y 444, 2008 January 20 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
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Lu/176Hf: A SENSITIVE TEST OF s-PROCESS TEMPERATURE AND NEUTRON DENSITY IN AGB STARS M. Heil,1 N. Winckler,1 S. Dababneh,2 F. Ka¨ppeler, and K. Wisshak Forschungszentrum Karlsruhe, Institut f u¨r Kernphysik, Postfach 3640, D-76021 Karlsruhe, Germany;
[email protected]
S. Bisterzo and R. Gallino Dipartimento di Fisica Generale, Universita` di Torino, Via P. Giuria 1, I-10125 Torino, Italy
A. M. Davis Enrico Fermi Institute and Department of the Geophysical Sciences, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637
and T. Rauscher Departement f u¨r Physik, Universita¨t Basel, CH-4056 Basel, Switzerland Received 2007 July 3; accepted 2007 September 21
ABSTRACT The s-process branching at A ¼ 176 has been analyzed on the basis of significantly improved experimental cross sections. This work reports on activation measurements of the partial (n; ) cross section of 176 Lu feeding the isomeric state in 176 Lu. In total, six irradiations were performed at the Karlsruhe 3.7 MV pulsed Van de Graaff accelerator, and the induced activities were measured with HPGe clover detectors. In combination with previous data, partial cross sections of 3185 156 and 1153 30 mbarn were deduced at kT ¼ 5:1 and 25 keV, respectively. With these results and a recent time-of-flight measurement of the total stellar (n; ) cross section, the isomeric ratio was found to be constant in the relevant thermal energy range of the main s-process component. Based on these new data, a comprehensive analysis of the branching at 176 Lu was carried out for testing the temperature and neutron density conditions during He shell flashes in thermally pulsing low-mass asymptotic giant branch stars. It was found that the long-standing problem of the mother/daughter ratio of the two s-only isotopes 176 Lu and 176 Hf could be solved, if the temperaturedependent -decay half-life of 176 Lu was considered with sufficient resolution over the temperature profile of the convective He shell flashes. Subject headingg s: nuclear reactions, nucleosynthesis, abundances — stars: AGB and post-AGB — stars: interiors Online material: color figures
1. INTRODUCTION
asymptotic giant branch (AGB) stars (Gallino et al. 1998; Busso et al. 1999). In this context, lutetium is an especially attractive example for the intricate way in which nuclear physics can affect the actual s-process production yields. This is illustrated in Figure 1, showing that the reaction path in the vicinity of lutetium is determined not only by the stellar neutron capture cross sections of 175;176 Lu and 176 Hf, but also by the thermal coupling of isomer and ground state in 176 Lu. Due to its long half-life of 37.5 Gyr, 176 Lu was initially considered as a potential nuclear chronometer for the age of the s-elements (Audouze et al. 1972). This possibility is based on the fact that 176 Lu, as well as its daughter 176 Hf, are of pure s-process origin, since both are shielded against the r-process -decay chains by their stable isobar 176 Yb. In a straightforward approach, the reaction flow in the branching at A ¼ 176 and, therefore, the surviving s abundance of 176 Lu and of 176 Hf would be determined by the partial (n; ) cross sections of 175 Lu feeding the ground and isomeric state of 176 Lu. Since transitions between the two states are highly forbidden by selection rules, the isomer rapidly decays (t1=2 ¼ 3:7 hr) only by -transitions directly to 176 Hf. Therefore, both states could be considered as separate species in the description of the s-process branching at A ¼ 176 ( Fig. 1). In this way the s-process yield of 176 Lu appeared well defined and could be used to estimate the age of the s-elements by comparison with the actual solar system value.
The validity of the s-process concept implies that, for unbranched nuclides along the s-process path, the product of the abundances Ns produced in the s-process, and the corresponding neutron capture cross sections hi averaged over the thermal stellar spectrum, is a smooth function of mass number. In mass regions between magic neutron numbers this product is practically constant, thus confirming that reaction flow equilibrium is locally reached. This approximation holds best in the mass region of the rare earth elements (REEs). Because their relative solar abundances are accurately defined (Anders & Grevesse 1989) and because their large capture cross sections favor an efficient reaction flow (Arlandini et al. 1999), the REEs exhibit an almost constant hiNs product as a function of mass number. Consequently, the effect of temperature and neutron density on several prominent s-process branchings in the REE region can be evaluated without interference from constraints on the reaction flow, e.g., by the bottleneck effect due to the small cross sections of nuclei with magic neutron numbers. Hence, the REE branchings are well suited for testing the increasingly quantitative picture of the main s-process component that has been achieved with stellar models for thermally pulsing low-mass 1
Current address: GSI Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany. Current address: Faculty of Science, Al-Balqa Applied University, P.O. Box 7051, Salt 19117, Jordan. 2
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Lu /176Hf : SENSITIVE TEST OF AGB STARS
Fig. 1.— The s-process reaction flow in the Lu region. The strength of the lines indicates that neutron captures on 175 Lu leading to the isomeric state in 176 Lu are more probable than those to the ground state.
However, it was noted ( Ward & Fowler 1980) that ground state and isomer of 176 Lu are most likely connected by nuclear excitations in the hot stellar photon bath, since thermal photons at s-process temperatures in excess of 2 ; 108 K are energetic enough to populate higher lying states, which can decay to the long-lived ground state and to the short-lived 123 keV isomer as well (x 4.1.2). In this way, the strict forbiddenness of direct transitions between both states is circumvented, thus dramatically reducing the effective half-life to a few hours. As a result, most of the reaction flow could have been directly diverted to 176 Hf, resulting in a 176 Lu abundance much smaller than observed in the solar system. That this temperature dependence had indeed affected the information contained in the 176 Lu/176 Hf abundance ratio was found soon thereafter by Beer et al. (1981, 1984), thus changing its interpretation from a potential chronometer into a sensitive s-process thermometer. This temperature dependence was later confirmed on the basis of comprehensive investigations of the level structure of 176 Lu ( Klay et al. 1991a, 1991b; Doll et al. 1999). It turned out that such thermally induced transitions become effective at temperatures above 1:5 ; 108 K. Accordingly, ground state and isomer can be treated as separate species only at lower temperatures. In the stellar s-process model of thermally pulsing low-mass AGB stars this is the case between convective He shell flashes when the neutron production is provided by the 13 C(; n) 16 O reaction in the so-called 13 C pocket (see x 4.2). Under these conditions the partial cross sections populating ground state and isomer are directly determining the abundance of 176 Lu and have to be known for a full treatment of the branching at A ¼ 176 in the framework of the stellar s-process. During the He shell flashes, the higher temperatures at the bottom of the convective region lead to the activation of a second minor neutron source by the 22 Ne(; n) 25 Mg reaction. It is in this regime that the population of ground state and isomer, which is initially defined in the capture reactions, starts to be changed by thermally induced transitions. This affects the 176 Lug in the long-lived ground state that is actually produced by neutron capture on 175 Lu, as well as the Lu fraction circulating in the convective He shell flash with a turnover time of less than one hour. The latter part is only exposed for rather short times to the high bottom temperature and, therefore, less affected by the temperature dependence of the half-life. Once produced, by far most of the long-lived 176 Lug survives in the cooler layers outside of the actual burning zone. It is important to note that the capture cross
435
sections of both, ground state and isomer, are large enough that the final abundances are essentially determined during the freezeout phase at the decline of neutron density (see x 4.2). As far as the stellar neutron capture rates for describing the reaction flow sketched in Figure 1 are concerned, very accurate total (n; ) cross sections have been obtained for 175 Lu and 176 Lu in a recent time-of-flight (TOF) measurement using a 4 BaF2 array ( Wisshak et al. 2006a). The Maxwellian-averaged cross sections ( MACSs) deduced from these data are 5 times more accurate than the values listed in the compilation of Bao et al. (2000). However, in case of 175 Lu, it has to be considered that neutron captures may feed either the ground state or the isomer in 176 Lu. Therefore, the total (n; ) cross section (tot ) has to be complemented by a measurement of at least one of the two partial cross sections (pg , pm ). Since the corresponding reaction channels could not be distinguished in the TOF measurement (Wisshak et al. 2006a), the activation technique has been employed in this work to determine the partial cross section to the isomeric state in 176 Lu at thermal energies of kT ¼ 5:1 and 25 keV. The available experimental information for the partial (n; ) cross section to the isomeric state in 176 Lu is limited to activation measurements at or near 25 keV neutron energy using the 7 Li( p; n) 7 Be reaction (Beer & Ka¨ppeler 1980; Allen et al. 1981; Zhao & Ka¨ppeler 1991) and a filtered neutron beam from a nuclear reactor (Stecher-Rasmussen et al. 1988). In all experiments the induced activity after irradiation was detected via the 88 keV -transition in the decay of 176 Lug . The decay of 176 Lu m was recorded by spectroscopy of the decay electrons in only one of these experiments (Zhao & Ka¨ppeler 1991) because of the large self-absorption of the 88 keV line. When these results at kT ¼ 25 keV were combined with the recent total (n; ) cross section of 175 Lu (Wisshak et al. 2006a) it turned out that the isomeric ratio IR(25 keV ) ¼ pm /tot was significantly larger than the value of 0:70 0:04 measured at the much lower thermal energies of reactor neutrons (kT ¼ 0:025 eV). Since the stellar model is based on two neutron sources operating at kT ¼ 8 and 23 keV, an experimental determination of the isomeric ratio near 8 keV was called for in order to avoid a systematic uncertainty due to the energy dependence of IR, in particular because most of the neutron exposure is provided by the 13 C(; n) 16 O source, which operates at kT ¼ 8 keV. The measurements and data analysis motivated by this request are described in xx 2 and 3. In x 4 the present results are combined with an updated set of all relevant nuclear physics quantities as well as with the most recent information on the half-life (Amelin 2005; Amelin & Davis 2005) and solar system abundance (de Laeter & Bukilic 2006) of 176 Lu, for a comprehensive analysis of the s-process branching at A ¼ 176. 2. MEASUREMENTS 2.1. Activation Technique The activation measurements on 175 Lu were carried out at the Karlsruhe 3.7 MV pulsed Van de Graaff accelerator using two reactions for producing quasi-stellar neutron spectra close to the characteristic temperatures of the relevant neutron source reactions of the s-process. Near the typical thermal energy of the 13 C(; n) 16 O reaction at kT ¼ 8 keV, a neutron spectrum corresponding to kT ¼ 5:1 0:1 keV was obtained via the 18O( p; n) 18 F reaction by choosing the proton energy 8 keV above the reaction threshold of Ep ¼ 2574 keV (Heil et al. 2005). This reaction, although hampered by a comparably low ( p; n) cross section, is an important complement to the more prolific 7 Li( p; n) 7 Be reaction. The neutron spectrum that can be produced via the 7 Li( p; n) 7 Be
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HEIL ET AL.
Fig. 2.— The -detection system consisting of two HPGe clover detectors in close geometry. The sample position is defined by an exactly dimensioned sample holder.
reaction represents the experimental counterpart of the second most important stellar neutron source provided by the 22 Ne(; n) 25 Mg reaction. In this case the spectrum mimics a thermal energy of kT ¼ 25 keV, rather close to the average 23 keV that is typical for He shell flashes in low-mass AGB stars. 2.2. Samples The Lu samples were cut from 0.1 and 0.2 mm thick metal foils of natural composition. During the irradiations, each foil was sandwiched between two 0.03 mm thick gold foils of the same diameter, since all activation measurements are normalized to gold. In spite of the large self-absorption correction for the 88 keV -ray line in the decay of 176 Lu m , the choice of the rather thick samples was dictated by the low neutron intensity of the 18 O( p; n) 18 F reaction. Correspondingly, special attention was paid to the reliable determination of the absorption correction (x 3.2). 2.3. Irradiations 18
The O targets were deposited on 0.2 mm thick tantalum disks by electrolysis of water enriched to 95% in 18 O. In total, four targets with an oxide layer about 2 m in thickness were produced. These targets were glued onto a 1 mm thick copper backing, which is cooled by lateral heat conduction to a water cooled copper ring. Since the proton energy is adjusted slightly above the reaction threshold, all neutrons are emitted in a forward cone of 140 opening angle. Thus, moderation effects in the cooling water are avoided by the ring geometry. Effects due to neutron scattering in the copper backing are negligible because of the 98% transmission for neutrons in the energy range of interest. The 7 Li targets consisted of metallic layers of natural lithium, which were directly evaporated onto the copper backings. The layers were 30 m in thickness. During the irradiations, the time history of the neutron flux was registered by means of a 6 Li glass detector, which was placed on the proton beam axis at a distance of 1 m from the target. This information is relevant in order to determine the factor fb for the proper correction for the fraction of nuclei that already decayed during irradiation (x 3.1). The proton beam of typically 40 A was wobbled across the neutron production targets to ensure homogeneous illumination. The irradiations were carried out by placing the samples in direct contact with the neutron target as described elsewhere (Ratzel et al. 2004).
Vol. 673
Fig. 3.— The -ray spectrum of the activated Lu sample with the 88 keV line used in data analysis. The lines at 202 and 307 keV are due to the ground state decay of 176 Lu contained in the sample. [See the electronic edition of the Journal for a color version of this figure.]
2.4. Induced Activity After irradiation, the induced activity was measured with a -detection system consisting of two high-purity germanium clover detectors as shown in Figure 2. Each clover consists of four independent HPGe n-type crystals in a common cryostat. The crystals are 50 mm in diameter and about 70 mm in length. The front part of the crystals in one of the two clovers is tapered. The total crystal volume of the detector system is about 1000 cm3. The two clover detectors were placed face to face in close proximity such that they were in contact with the 5.2 mm thick sample holder. This holder is designed to guarantee an exact and reproducible positioning of the sample in the very center of the system. The whole assembly, which forms nearly a 4 geometry, was shielded with 10 cm of lead. The independent outputs of the eight crystals were connected to a set of 8K analog-to-digital converters (ADCs) via spectroscopy amplifiers with 6 s shaping time. A typical example of the resulting -ray spectra is shown in Figure 3. The intensities of the relevant -transitions were determined by a fit of the spectrum region containing the corresponding lines and the related background. 3. DATA ANALYSIS 3.1. Overview At the end of each irradiation, the number of activated nuclei in the sample and in the gold foils are A ¼ T N fb :
ð1Þ
Rt In this expression T ¼ 0 b (t) dt is the time integrated neutron flux, N is the number of sample atoms per cm 2, and is the capture cross section. The factor R tb (t)ek(tb t) dt fb ¼ 0 R tb ð2Þ 0 (t) dt accounts for the decay and for the variation of the neutron flux during the irradiation time tb . After a waiting time tw , which is the time required to transfer the sample from the irradiation position to the clover setup,
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No. 1, 2008
Lu /176Hf : SENSITIVE TEST OF AGB STARS
TABLE 1 Decay Properties of the Produced Nuclei
Product Nucleus
Half-Life
-Ray Energy ( keV )
198
Au .................. 2.69517 0.00021 days Lu m ................ 3.664 0.019 hr 176 Lu m ................ 37.5 0.1 Gyrc 176
a b c
411.80 88.36 88.36
TABLE 2 Correction Factors K Used in Data Analysis I per Decay (%) 95.58 0.12 8.90 0.44b 14.508 0.56b
-rays are counted during the measuring time tm . For a given -ray line, the number of counts is ð3Þ C ¼ AK Kcasc Kgeo " I 1 ektm ektw ; where " is the clover efficiency and I is the -ray intensity per decay. The correction factors K , Kgeo , and Kcasc account for the -ray self-absorption in the sample, the extended geometry of the sample, and the summing effect of the detector due to cascade transitions, respectively. These correction factors have been calculated by means of Monte Carlo simulations using the GEANT4 toolkit.3 Since Kgeo was found to be less than 0.5% and Kcasc was practically negligible, these effects are included in the fairly large self-absorption correction K discussed in x 3.2. Since all measurements are relative to 197 Au, equation (1) yields Ai i Ni fbi ¼ : AAu Au NAu fbAu
ð4Þ
The activities Ai and AAu are determined by the measured decay intensities. For 176 Lu, the analysis was based on the most intense line in the decay of the isomeric state with E ¼ 88:36 keV. The decay properties of all relevant states used in the analysis were adopted from Chunmei (1995) and Browne & Junde (1998), as listed in Table 1. The decay of the isomeric state has to be distinguished from the decay of the ground state. Therefore, the activity of the irradiated Lu samples was first measured at time tw1 in order to determine the total counts Ctot ¼ Cg þ Cm , including the decay of the isomer plus the decay of the 176 Lug contained in the natural sample, Ctot ¼ Cg þ Cm
¼ Ag K I; g 1 ekg tm1 ekg tw1 þ Am K I; m 1 ekm tm1 ekm tw1 :
ð5Þ
After an additional waiting time tw2 3 t1=2 ( 176 Lum ), all 176 Lum had decayed and the correction for the ground-state contribution could be obtained. This contribution is then subtracted from the first measurement: tm1 Cg : tm2 2
ð6Þ
The -energy scale and the -efficiencies were calibrated with a set of standard sources. An interpolation of the measured efficiency values by a GEANT4 simulation was then used to establish the efficiency as a function of -ray energy. The absolute efficiency at 88.36 keV, ¼ 0:572 0:017, could be directly nor3
See http://geant4.web.cern.ch /geant4/.
Nucleus
a
See Chunmei (1995). See Browne & Junde (1998). See Amelin (2005).
Cm ¼ Ctot Cg1 ’ Ctot
437
-Ray Energy ( keV )
Sample Diameter (mm)
Sample Thickness (mm)
Correction Factor K
176
Lum .................
88.36
15 15 12 10
0.2 0.1 0.2 0.2
0.461 0.652 0.463 0.463
198
Au ...................
411.80
10, 12, 15
0.03
0.990
malized to the calibration point measured at 88.033 keV with a Cd source. The fb factors were determined from the neutron flux history recorded during the irradiations by the 6 Li glass detector.
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3.2. Self-Absorption Correction For a distant point source the correction for self-absorption can be obtained as K ¼
1 ed ; d
where is the self-absorption coefficient and d is the sample thickness ( Beer & Ka¨ppeler 1980). The close geometry of the present experiment, which was necessary because of the weak activities produced in the 5.1 keV irradiations, required us, however, to evaluate K by a full GEANT4 simulation of the clover setup. In these simulations minor effects due to the extended sample size and cascade summing have been included as well. The resulting correction factors are listed in Table 2. By far the largest contribution to K is due to self-absorption. Since the correction factors have been obtained by means of GEANT4, it was important to normalize the simulations by a measurement of the -ray transmission, T ¼ ed , which constitutes the essential information for calculating K . The transmission measurement was performed by placing the 109 Cd source exactly at the sample position between the clover detectors and comparing the measured line intensities at E ¼ 88:033 keV before and after the source was sandwiched between 0.1 mm thick Lu foils. Because of the identical setup, systematic effects are automatically taken into account by normalizing the simulations to the measured transmission of 39:2% 0:2%. With this approach, K could be determined with an uncertainty of less than 1%. Another check was carried out by means of an additional activation at kT ¼ 25 keV. In this case, the absorption correction could be verified by the excellent agreement with the results of Zhao & Ka¨ppeler (1991), which were obtained by spectroscopy of the decay electrons as well as by detecting the 88 keV transition in far geometry from a much thinner Lu foil of 0.03 mm. This comparison is most important since the decay intensity of the 88 keV line had been revised recently. While Zhao & Ka¨ppeler (1991) had used a value of I ¼ 8:90% 0:15% (Browne 1990), the most recent reference contains a 3 times more uncertain value of 8:90% 0:44% (Browne & Junde 1998). However, this additional uncertainty can be avoided by normalization of the present measurement to the data based on spectroscopy of the decay electrons as discussed in x 3.3. 3.3. Results and Discussion The cross sections of 175 Lu and of 197 Au exhibit a very similar dependence on neutron energy. Hence, MACSs can be directly
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TABLE 3 Spectrum-Averaged Cross Sections of the Reaction
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Vol. 673 TABLE 4 Compilation of Uncertainties for the Partial (n; ) Cross Section to 176 Lum at kT ¼ 5:1 keV
Lu(n; ) 176 Lu m
Uncertainties Uncertainties (%) Thickness (mm)
Sample
hi (mbarn)
Statistical (%)
Systematic (%)
Thermal energy kT ¼ 5:1 keV Lu1 ................................. Lu2 ................................. Lu3 ................................. Lu4 ................................. Lu5 ................................. Weighted Average......
0.2 0.2 0.2 0.1 0.1 ...
2966 3130 3045 2888 3230 3048
0.8 1.3 1.1 3.3 2.8 0.5
6.4 6.4 6.4 6.4 6.4 6.4
Lua
Source of Uncertainty
Au
Counting statistics................................................ Gold cross section................................................ Number of sample atoms..................................... Uncertainty due to tw , tm , tb ................................ -ray intensity per 100 decays ............................ Correction factor K ............................................ Detector efficiency ...............................................
0.7 2.5
