STELLAR NEUTRON CAPTURE ON PROMETHIUM: IMPLICATIONS FOR THEs-PROCESS NEUTRON DENSITY

R. Reifarth, C. Arlandini, M. Heil, and F. Kappeler

ForschungszentrumKarlsruhe, Institut fur Kernphysik, Postfach 3640, D-76021Karlsruhe, Germany

P. V. Sedyshev

Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 14980Dubna,MoscowRegion, Russia

A.Mengoni

Ente Nazionale per le Nuove Tecnologie, l’Energia, e l’Ambiente (ENEA), Applied Physics Division, Via Don Fiammelli 2, I-40129 Bologna, Italy

M. Herman

International Atomic Energy Agency Nuclear Data Section,Wagramerstrasse 5, A-1400 Vienna, Austria

T. Rauscher

Departement fur Physik undAstronomie, Universitat Basel, CH-4056 Basel, Switzerland

R. Gallino

Istituto di Fisica Generale, Universita di Torino and Sezione INFN di Torino, I-10125 Torino, Italy

and

C. Travaglio

Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Strasse 1, D-85748Garching, Germany;and Istituto Nazionale di Astrofisica (INAF), Osservatorio Astronomico di Torino, Strada Osservatorio,

20, I-10025 Pino Torinese (To), ItalyReceived 2002May 31; accepted 2002 September 16

ABSTRACT

The unstable isotope 147Pm represents an important branch point in the s-process reaction path. This paperreports on the successful determination of the stellar (n, �) cross section via the activation technique. Theexperiment was difficult because the relatively short 147Pm half-life of 2.62 yr enforced the sample mass to berestricted to 28 ng or 1014 atoms only. By means of a modular, high-efficiency Ge Clover array the lowinduced activity could be identified in spite of considerable backgrounds from various impurities. Bothpartial cross sections feeding the 5.37 day ground state and the 41.3 day isomer in 148Pm were determinedindependently, yielding a total (n, �) cross section of 709� 100 mbarn at a thermal energy of kT ¼ 30 keV.The (n, �) cross sections of the additional branch point isotopes 147Nd and 148Pm as well as the effect ofthermally excited states were obtained by detailed statistical model calculations. The present results allowedconsiderably refined analyses of the s-process branchings at A ¼ 147=148, which are probing the neutrondensity in the He-burning shell of low-mass asymptotic giant branch stars.

Subject headings:methods: laboratory — nuclear reactions, nucleosynthesis, abundances — stars: late-type

1. THE s-PROCESS BRANCHINGS AT A ¼ 147=148

Nucleosynthesis by slow neutron capture (s-process) isknown to contribute about half of the isotopic abundancesin the mass region between Fe and Bi. Because of the com-parably low neutron densities, neutron capture times areslower than the average �-decay times. Accordingly, thereaction path of the s-process follows the stability valley,and the evolving abundances are determined by the respec-tive (n, �) cross sections. At some points, however, the reac-tion path hits sufficiently long-lived isotopes, where neutroncapture can compete with �-decay. This competition resultsin branchings of the reaction path, which proved particu-larly useful, since the resulting isotopic patterns carry directinformation on the physical conditions during the s-process,i.e., neutron density, temperature, and pressure.

The present study is focused on an improved analysis ofthe branchings in the Nd-Pm-Sm region. By measuring thecross section of one of the radioactive branch point nuclei,the nuclear physics uncertainties can be reduced to the levelwhere they no longer dominate the problem. Accordingly, it

is expected that the analysis of this branching will eventuallyreflect the underlying stellar physics.

The Nd-Pm-Sm branchings sketched in Figure 1 are ofparticular interest for constraining the s-process neutrondensity. Their overall strength is well defined by the two s-only isotopes, 148Sm and 150Sm, which are both shieldedagainst �-decays from the r-process region by their Nd iso-bars. Because of its location at the closure of the branching,150Sm belongs to the few s-only nuclei that are exposed tothe full reaction flow. The reliable analysis of the branchingsin Figure 1 benefits from the fact that the relative abundan-ces of the rare earth elements (REEs) are known to betterthan 2% because of their chemical similarity (Anders &Grevesse 1989). The resulting abundance ratio of 148Sm and150Sm is affected by three branchings of the neutron capturechain as a result of competition of neutron capture and �-decay at the unstable isotopes 147Nd, 147Pm, and 148Pm. Forthe interpretation of these branchings it is important to notethat the three �-decay rates are practically independent oftemperature and electron density (Takahashi & Yokoi1987; Lesko et al. 1989) and that the stellar neutron capture

The Astrophysical Journal, 582:1251–1262, 2003 January 10

# 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.

1251

cross sections for the involved stable isotopes have beenaccurately measured by time-of-flight (TOF) experiments(Wisshak et al. 1993, 1998b; Wisshak, Voss, & Kappeler1998a) and partly by activation (Toukan et al. 1995). A setof recommended values for the Maxwellian-averaged crosssections for these isotopes has recently been suggested (Baoet al. 2000).

The remaining nuclear physics uncertainties lie evidentlyin the cross sections of the branch point isotopes, for whichonly theoretical values existed so far. While the short half-lives of 147Nd (t1=2 ¼ 10:98 days) and 148Pm (t1=2 ¼ 5:37days) are prohibitive for measuring their (n, �) cross sectionswith present techniques, the activation method was success-fully applied to an experimental determination of the neu-tron capture cross section of 147Pm (t1=2 ¼ 2:62 yr).

The result of this measurement was important for directuse in analyzing these branchings, but also to adjust theparameter systematics for statistical model calculations inthe mass region 140 � A � 150, which are complicated bythe transition from spherical to deformed nuclei. This infor-mation allowed the cross section data of the unstable iso-topes to be considerably improved. In this context, the effectof temperature on the (n, �) rates due to the thermal popula-tion of low-lying excited states in the hot stellar photon bathwas reexamined as well.

Themeasurement of the stellar (n, �) cross section of 147Pmvia the activation method by irradiation in a quasi-stellarneutron spectrum at the Karlsruhe Van de Graaff acceleratoris described in x 2. Data analysis and a discussion of theresults are presented in xx 3 and 4. The database for analyzingthe s-process branchings at A ¼ 147=148 was completed bystatistical model calculations (x 5) and used for an updateddiscussion of the astrophysical consequences in x 6.

2. CROSS SECTION MEASUREMENTS

2.1. ExperimentalMethod

A detailed description of the activation method forobtaining stellar (n, �) cross sections and the experimental

setup can be found in the literature (Beer & Kappeler 1980;Toukan et al. 1995). The essential features consist of twosteps: irradiation of a 147Pm sample in a quasi-stellar neu-tron spectrum and counting the induced 148Pm activity byhigh-resolution Ge detectors.

The quasi-stellar neutron spectrum was obtained by bom-barding a thick metallic Li target with protons of 1912 keV,slightly above the reaction threshold at 1881 keV. The7Li(p, n)7Be reaction then yields a continuous energy distri-bution with a high-energy cutoff at En ¼ 106 keV. Theproduced neutrons are emitted in a forward cone of 120�

opening angle. The angle-integrated spectrum closelyresembles a Maxwellian distribution for kT ¼ 25 keV ther-mal energy, almost exactly the shape required to determinethe stellar cross section.

The samples were sandwiched between gold foils andplaced directly on the lithium target. The simultaneous acti-vation of the gold foils provides a convenient tool formeasuring the neutron flux, since both the stellar neutroncapture cross section of 197Au (Ratynski & Kappeler 1988)and the parameters of the 198Au decay (Auble 1983) areaccurately known.

After activation, the �-rays from the 148Pm decay werecounted with a high-purity (HP) Ge spectrometer consistingof two fourfold Clover detectors in close geometry.

2.2. Relevant �-Decay Channels

147Pm decays almost exclusively to the 7/2� ground stateof 147Sm with an endpoint energy E� ¼ 224:5 keV. It exhib-its only a very weak �-channel, where the strongest transi-tion at 121.22 keV occurs with a relative intensity of0.00285%. Since all other �-transitions are at least a factorof 104 weaker, the specific activity of the sample is expectedto be sufficiently low not to obscure the weak induced 148Pmactivities.

Neutron capture on 147Pm produces comparable quanti-ties of 148Pm nuclei in the 1� ground state (t1=2 ¼ 5:370days) and in the 137.9 keV 6� isomeric state (t1=2 ¼ 41:29days). The subsequent �� decays to 148Sm are accomplishedthrough several cascades, the most important beingsketched in Figure 2. These cascades are an important

Nd 146 11d 148 150

Pm 1.2y

Sm 149 150148

r-process

p-process

s-process path

s-process path

147

5.2d

Fig. 1.—s-process path between Nd and Sm partly bypassing 148Sm as aresult of the branchings at A ¼ 147=148. The second s-only isotope, 150Sm,experiences the full reaction flow. An additional, very small branching to149Pm has been omitted for better readability of the figure but was consid-ered in all branching analyses. The half-lives of the branching points reflectthe stellar values (Takahashi &Yokoi 1987).

Fig. 2.—Main decay channels for 148gPm and 148mPm. All energies aregiven in units of keV.

1252 REIFARTH ET AL. Vol. 582

advantage for identifying the weak induced 148Pm activityvia the coincidence technique. Recording the signals fromthe Ge spectrometer event by event allowed the experimen-tal data to be analyzed in a very flexible way off-line.

2.3. Sample Preparation

A 147Pm solution in 5 ml HCl (0.1 M) with a total activityof 4 MBq was supplied by AEA Technology. The measure-ment of this solution with a 40 cm3 HP Ge detector con-firmed the specified 147Pm activity but revealed also animpurity of 0.0015% 146Pm. Although no other radioactivecontaminations were detected, the promethium solutionwas known to contain also an Nd impurity of 100 mgliter�1.

In order to handle the minute amount of 120 ng 147Pm,enriched 147Sm (98.27%) was used as a carrier since it wouldnot disturb the later activation. A total of 4 mg of 147Sm2O3

were dissolved with two drops of concentrated HCl. Themixture with the Pm solution was reduced to �4 millilitersand then dried in a quartz vial, leaving a green-white depositof samarium chloride. When heated in air the chlorides ofthe REEs progressively dehydrate and convert to oxide, thetemperature for complete conversion depending on therespective element. Although quite different estimates werereported for Sm (Gmelin 1993), a temperature of 900�C wasfound to be a safe choice (Wisshak et al. 1993).

After heating, a fraction of the Pm/Sm sample was mixedwith 10 mg of fine graphite powder and pressed at 20 kNinto a pellet 6 mm in diameter and 0.4 mm in thickness. Thepellet was then enclosed in a flat graphite cylinder with 0.3mm thick walls. The canned sample was centered on a stan-dard sample holder consisting of a 0.03 mm thick Kaptonfoil stretched over a 3 mm thick Al ring with 36 mm innerand 40 mm outer diameter.

The sample mass was determined from the 147Pm activityusing the 121 keV transition. The efficiency of the 40 cm3

HP Ge detector used for this measurement was determinedvia the 122 keV transition of a calibrated 57Co source. Thecorresponding self-absorption correction was found to be1% with negligible uncertainty, and the decay parameterswere adopted from the literature (der Mateosian & Peker1992; Table 1). The resulting activity of 982� 41 kBq corre-sponds to ð1:17� 0:05Þ � 1014 atoms or 28:7� 1:2 ng.

2.4. Activation at the Van de Graaff Accelerator

The sample was sandwiched between two gold foils with 6mm diameter and 0.03 mm thickness, which were mountedin the same way on Kapton foils and Al rings as the 147Pmsample. During and between the activations, the sample waskept in an argon atmosphere to avoid possible waterabsorption. The sample sandwich was placed on top of theneutron-producing target, a metallic Li layer 6 mm in diam-eter evaporated on a water-cooled 1.5 mm thick copperbacking. The cooling water flows in a ring outside the neu-tron cone. The setup sketched in Figure 3 includes also a6Li-glass monitor located about 1 m from the target, whichserves a twofold purpose. Before the activation, the detectoris used to select the proper proton energy (Ep ¼ 1912 keV)corresponding to a maximum neutron energy of En ¼ 106keV. In this step, the accelerator is operated in pulsed modefor a TOF measurement of the neutron energy. During theirradiation, the detector measures the neutron yield in timesteps of 99 s for the later determination of the correctionfactor fb (see below).

Two activations were carried out (see Table 2). The firstwas finished after only 60 hr as a result of an acceleratorproblem, but the second lasted for 12 days or about twohalf-lives of 148gPm. For the first activation a single targetconsisting of a 30 lm thick lithium layer was used. Duringthe second activation this was replaced by targets that wereobtained by pressing a metallic 0.38 mm thick lithium foilonto the backing. This technique resulted in a somewhathigher neutron flux and a more stable neutron yield. Goldfoils and Li targets were changed every 2 days.

3. DATA ANALYSIS

3.1. Determination of the Neutron Flux

The induced 198Au activity was measured with the 40 cm3

HP Ge detector. The net counts in the 412 keV line of the

TABLE 1

Adopted Decay Parameters

Product Nucleus

Half-Lifea

(days)

E�

(keV)

I�b

(%)

147Pma...................... 2.6234 � 0.0002c 121.22 (2.85 � 0.11)� 10�3

148gPmb .................... 5.370 � 0.009 550.27 22.0 � 0.6

914.85 11.5 � 0.3148mPmb.................... 41.29 � 0.11 550.27 94.5 � 1.1

629.97 88.6 � 0.7

725.70 32.7 � 0.5

915.33 17.1 � 0.3

1013.8 20.2 � 0.3198Aud ...................... 2.696 � 0.002 411.8 95.5 � 0.1

a derMateosian & Peker 1992.b Peker 1990.c In units of years instead of days.d Auble 1983.

147PmLi - target

Cuproton-beam neutron cone

Au

neutronmonitor

Fig. 3.—Sketch of the activation setup at the Van de Graaffaccelerator.

TABLE 2

Parameters and Neutron Fluxes for the Two Irradiations

Parameter Activation 1 Activation 2

Irradiation time (days) .............. 2.50 12.36

Integral neutron flux ................. 4.7� 1014 3.9� 1015

Average flux (s�1)...................... 2.4� 109 3.5� 109

Decay corrections:

f Aub ........................................ 0.756 0.329

f148gPmb .................................... 0.866 0.525

f148mPmb .................................... 0.981 0.909

No. 2, 2003 STELLAR NEUTRON CAPTURE ON PROMETHIUM 1253

198Au decay can be expressed as

Z� ¼ N��I�tlivetm

K�fwfm ; ð1Þ

where N denotes the total number of activated nuclei at theend of irradiation, �� ¼ ð1:99� 0:04Þ � 10�5 is the efficiencyof the Ge detector for the geometry used (M. Schumann1998, private communication), I� ¼ 0:9558� 0:0012 is therelative intensity for the 412 keV line (Chunmei 1995), andtlive/tm is the dead-time correction. K�, the correction for �-ray self-absorption in the 30 lm thick gold foils, could beneglected. The time factors fw ¼ e��tw and fm ¼ 1� e��tm

account for the fraction of nuclei that decay during the wait-ing time between irradiation and measurement and duringthe measurement itself and are discussed elsewhere (Beer &Kappeler 1980); � is the decay constant of the respectiveproduct nucleus. Pile-up and summing corrections could beneglected in this measurement as a result of the 76 mm dis-tance between sample and detector and the comparablysmall detector efficiency.

The total number of activated nuclei,N, is given by

N ¼ �totN0�Aufb ; ð2Þ

where �tot ¼R�ðtÞdt is the time-integrated neutron flux,

N0 is the number of gold atoms, and �Au ¼ 648� 10 mbarn(Ratynski & Kappeler 1988) is the spectrum-averaged neu-tron capture cross section. The time factor fb corrects for thedecay during activation, including the effects due to a timevariation of the neutron flux (for a definition see Beer &Kappeler 1980). Since the neutron flux is determined by thegold foils on both sides of the sample, corrections for targetgeometry as well as for neutron scattering and self-shieldingare accounted for by averaging the neutron fluxes obtainedfrom the two gold foils.

The total flux uncertainty was determined by quadraticsummation of the various systematic errors, since the influ-ence of the counting statistics in measuring the activity ofthe gold foils was negligible. Apart from the above effects, a7% uncertainty was allowed to account for the flux at theposition of the Pm sample corresponding to a 0.5 mm uncer-tainty in the position of the Pm sample relative to the goldfoils. This correction was derived from the linear decrease ofthe induced activity with distance from the neutron target,which was found by activation of a stack of five gold foils(Fig. 4). The mass of the gold foils was determined with neg-ligibly small uncertainties.

3.2. The �-Spectrometer

The induced activity was measured with two Clover-typeHP Ge detectors facing each other in close geometry. TheClover detectors (Eurisys Mesures) are an assembly of fourindependent n-type Ge crystals in a four-leaf clover arrange-ment with 0.2 mm gaps in between. The originally cylindri-cal crystals with 50 mm diameter and 70 mm length areshaped as shown in Figure 5, leaving an active volume ofabout 145 cm3 per crystal. The crystals are held from therear through a steel rod of 1 mm diameter and about 35 mmlength and are enclosed in a cryostat with a 1 mm thick alu-minum window 5mm in front.

The individual Ge crystals have a resolution of typically2.0 keV at 1.33 MeV. At 122 keV, the peak-to-Comptonratio is �45. The detector can be operated either in singlemode by considering the signals from each crystal independ-

ently or in calorimetric mode, when coincident signals fromdifferent crystals are added off-line. In this way Compton-scattered events can be restored in the sum spectrum if thescattered photon is detected in one of the neighboring crys-tals, resulting in a significantly higher photopeak efficiency.

The detector signals were recorded on PC using the dataacquisition system MPA-WIN (FAST Comtec). In order tolimit the count rate per crystal to �1 kHz, where the systemwas still operating reliably, single events were suppressed bya hardware veto. This veto was created by requesting a coin-cidence between any of the crystals within a fixed time win-dow of about 30 ns (optimized with a 22Na source). Therespective energy signals were processed in the usual way byspectroscopy amplifiers and analog-to-digital converters(ADCs) with fixed conversion times of 800 ns. The datawere stored event by event for off-line analysis. A thresholdlevel of 35 keV was set for each ADC. Data acquisition wasorganized in separate runs of 12 hr. This allows us to reducethe interference between the decay of ground state and iso-mer in 148Pm because of their different half-lives.

3.3. �-Ray Efficiencies of the Clover Detector

In view of the low count rates expected for the activationof the small 147Pm sample, the two Clover detectors werearranged face to face with a distance of only 3mm. The sam-ple was exactly centered in the gap by means of a special

1 2 3 4 5 6DISTANCE FROM Li-TARGET (mm)

0.4

0.6

0.8

1

NE

UT

RO

N F

LU

X (

norm

aliz

ed a

t 1.5

mm

)

5 mm10 mm

Fig. 4.—Neutron flux vs. distance from the target measured byactivation of a stack of gold foils. The linear dependence holds for gold foils5 and 10mm in diameter.

70 mm 70 mm

91 mm 91 mm

82 mm

sample

35 mm

13 mm

Fig. 5.—Schematic view of the HP Ge spectrometer consisting of twoClover-type detectors in close geometry.

1254 REIFARTH ET AL. Vol. 582

holder. For this very close geometry the total and peak effi-ciencies of the Clover system were determined in the rangefrom 50 to 1200 keV using a set of calibrated sources. Meas-urements were performed at 59 (241Am), 88 (109Cd), 662(137Cs), 835 (54Mn), and 1115 keV (65Zn). For the last twosources, the cascade summation effect with X-rays had to beconsidered and was calculated with the code CASC (Jaag1993). Typical uncertainties of the measured efficiencies are2% including all statistical and systematic effects.

The measurements were supplemented by a Monte Carloanalysis made with the GEANT code (Apostolakis 19931).The geometry of the system, including the source holder,was carefully simulated in the calculations. The resultingefficiencies are plotted in Figure 6. The lower curve corre-sponds to the average photopeak efficiency, and the uppercurve shows the efficiency for the calorimetric mode, whencoincident events in the other seven crystals are considered.The efficiencies of the individual crystals do not differ bymore than �1%. The advantage of the calorimetric modefor the detection efficiency is evident: the ratio of the photo-peak efficiency in calorimetric mode and for a single crystal,�addðEÞ=

P�iðEÞ, increases from �1 at 50 keV (where most

Compton-scattered photons fall below the detection thresh-old) to�2 near 1.5MeV.

The results obtained in the GEANT simulations (solidlines) are slightly higher than the experimental values as aresult of uncertainties of the internal detector geometry, inparticular with respect to the dimensions of the metal rodinside the crystals (Eurisys Mesures 1991, private communi-cation). However, these differences are small at energiesabove 100 keV. Therefore, the cross section analysis wascompletely based on �-ray lines in the energy range above100 keV.

3.4. Response to �-Cascades in the Decay of 148Pm

Inspection of the �-ray spectra taken after irradiationshowed that the induced 148Pm activity could not easily beidentified. All single lines from the decay of the isomer andthe ground state of 148Pm were completely obscured bydominant backgrounds originating from the initial 146Pm

contamination and from activation of the Nd impurities inthe sample. Because of the long counting time, backgroundsfrom natural radioactivities were not negligible either.Therefore, the coincident detection of cascade transitions inthe decay of 148Pm was instrumental for reducing the overallbackground, making use of the high efficiency and the eight-fold granularity of the Clover array.

The first step for a detailed quantitative description of theresponse of the Ge Clover array to the radiation emitted inthe decay of isomer and ground state of 148Pm was to calcu-late complete cascades consisting of electrons and �-rays.According to the decay scheme, the probabilities for feedingthe nuclear states in 148Sm were chosen case by case, and theelectron energies were then randomly selected from theFermi distribution (Schopper 1966). The subsequent decayof the excited states in 148Sm was described by allowing thedecay branchings to be followed using a Monte Carlo tech-nique. The resulting �-cascades were evaluated includingthe respective conversion ratios. In this way, 105 decays ofisomer and ground state were characterized separately.

For each of these ensembles, the response of the Cloverarray was calculated. The efficiency of these GEANT simu-lations was enhanced by repeating each decay pattern 10times but with statistically modified angular distributions.The simulated spectrum for the isomer 148mPm is shown inFigure 7. This spectrum is far too complex for evaluatingthe so-called cascade corrections by theMonte Carlo techni-que used for single Ge detectors, e.g., by means of the codeCASC. These corrections, which account for the coincidentregistration of signals from the same cascade, resulting inthe loss of events due to summing-in our summing-outeffects, are particularly crucial for �-counting with large Gedetector arrays. Obviously, the comprehensive GEANTsimulation is essential for retrieving the full information

1 Available at http://www.cern.ch.

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

γ-ENERGY (keV)

8

10-1

2

4

6

8

100E

FFIC

IEN

CY

experiment 8 x single crystalexperiment calorimeter

GEANT simulation 8 x single crystalGEANT simulation calorimeter

Fig. 6.—Photopeak efficiency of the Clover system. The lower datapoints refer to single crystals, the upper to the calorimetric mode.Measuredvalues are indicated by filled symbols, GEANT simulations by dashedlines.

Fig. 7.—GEANT simulation of the decay of 148mPm with the Cloversystem operated in calorimetric mode. The complex response illustrates theneed for a detailed simulation, since cascade corrections for summing-inand summing-out effects can no longer be handled with codes for single Gedetectors.

No. 2, 2003 STELLAR NEUTRON CAPTURE ON PROMETHIUM 1255

from the spectra and for keeping control of these complexcascade corrections simultaneously.

3.5. Determination of the Partial Cross Sections

In view of the critical background situation the analysiswas focused on the strongest �-ray cascades in the decay of148Pm.

The best suited cascade in the decay of 148gPm starts fromthe 1� state at Ex ¼ 1465:1 keV, which is fed with 33.3%probability (Fig. 2). This cascade consists of a 914.9 keV E2transition followed by a 550.3 keV E2 transition to theground state and represents 11% of the total ground statedecays. At the sum energy of this cascade the background isdominated by coincident events due to Compton scatteringof the 1461 keV line from the decay of 40K. This backgroundwas discriminated in the following way.

The cascade gammas (550 and 915 keV) were searched forby the condition that the sum of coincident signals wouldreproduce the respective energy within�0.5 keV. The corre-sponding background was defined by repeating this proce-dure with slightly different energy combinations. Forexample, the 550 keV window was shifted in steps of 1 keVover the energy range from 545 to 555 keV while keeping the915 keV window fixed. Repeating this scan by moving the915 keV window, all energy combinations from (545, 910)up to (555, 920) were covered as plotted in Figure 8. Thenumber of true events was determined by a two-dimensionalGaussian fit, whereas the background was treated by a con-stant component and a Gaussian fit for the 1461 keV line.The FWHMs of the �-ray lines were adopted from themeasured resolution.

The decay of the isomer 148mPm could be characterized bythree cascades consisting of the combinations (550.3 and725.7 keV), (630.0 and 725.7 keV), and (630.0 and 414.1keV) as indicated in Figure 2. These combinations werechosen because of their favorable overall detection effi-ciency (Table 3).

The evolution of the abundances of 148gPm and 148mPmduring the irradiation ofN0 atoms of 147Pm in a neutron flux�(t) is described by the differential equations

dNgðtÞdt

¼ ��gNgðtÞ þ �g�ðtÞN0 þ ��mN

mðtÞ ; ð3Þ

dNmðtÞdt

¼ ��mNmðtÞ þ �m�ðtÞN0 ; ð4Þ

where Ng and Nm denote the produced number of 148Pmatoms in the ground state and isomer, respectively. Theadditional feeding by internal transitions is considered bythe last term in equation (3), � being the decay probabilityto the ground state. The activation time was divided intointervals Dti ¼ 99 s for which the neutron flux�i can be con-sidered to be constant. Then, the equations can be solved bynumerical integration, and one obtains the produced abun-dances at the end of the irradiation as

Ngact ¼ �gN0Dt

"Xni¼1

�ie�ðn�iÞ�gDt

þ � 1�Xni¼1

�ie�ðn�iÞ�mDt

!#; ð5Þ

Nmact ¼ �mN0Dt

Xni¼1

�ie�ðn�iÞ�mDt : ð6Þ

After a certain short waiting time tw, the activity is mea-sured for a time t. Since � is only 4.6% and since the half-lifeof the isomer is almost 8 times longer than that of theground state, the correction for internal transitions is verysmall and has been omitted in the following equations. Thenumber of decays during the measurement is

DNg;m ¼ Ng;mact e

��g;mtw 1� e��g;mt� �

; ð7Þ

which relates to the observed count rateZ� by

Z� ¼ DNI���tlivetm

K�C�P� ; ð8Þ

in analogy to equation (1), except that the correction factorsC� and P� for coincident detection of cascade transitionsand pile-up can no longer be neglected because of the highercounting efficiency of the Clover array.

The self-absorption correction K� ¼Q

Ki� ¼Q

½ 1� e�lidið Þ=lidi� accounts for the various constituents iof the sample, di and li being the respective thicknesses andthe photon attenuation coefficients. The latter were adoptedfrom the current version of XCOM, a database available

0

5

10

15

20

CO

UN

TS

Fig. 8.—�-ray spectrum of coincident events from the activated 147Pmsample. The spectrum was obtained by off-line analysis of the data takenwith the Ge Clover array. Events due to cascades from the decay of 148gPmconsisting of the 915 and 550 keV transitions are concentrated in the center,clearly separated from the overall background and from Compton-scattered events of the 1461 keV line from 40K, which appear as thediagonal band in the lower left part.

TABLE 3

�-Ray Cascades Used in Data Analysis, Detection Efficiencies,

and Number of Recorded Events

Decay

�-Cascades

(keV)

Absolute Detection

Efficiencya

(%)

Number of

Events

148gPm............... 550, 915 0.51 235148mPm .............. 550, 726 0.76 240

630, 726 0.68 258

630, 414 0.37 120

a Including decay intensities.

1256 REIFARTH ET AL. Vol. 582

from the American National Institute of Standards.2 Sincethese corrections were always less than 1%, the relateduncertainties were negligible.

Eventually, the experimental cross section in the quasi-stellar spectrum is

h�iPm25 keV ¼ NPmact

NAuact

NAu0

NPm0

f Aub

f Pmb

h�iAu25keV ; ð9Þ

where Nact is the number of activated nuclei, N0 is the num-ber of target nuclei in the sample, and fb is the correctionfactor for the fraction of activated nuclei that decayed dur-ing activation. This factor is given by

fb ¼P

i �ðtiÞe��ðtirr�tiÞPi �ðtiÞ

;

where tirr is the total irradiation time, � is the decay con-stant, and�(ti) is the neutron flux history.

4. RESULTS AND DISCUSSION

4.1. Experimental Cross Sections and Uncertainties

The experimental cross sections for the quasi-stellar spec-trum approximating the thermal distribution for kT ¼ 25keV are listed in Table 4 together with the correspondinguncertainties. The partial cross section to the isomer repre-sents the weighted average of the analyses performed viathe three relevant �-cascades emitted in the isomer decay(Table 3).

Combination of the partial results yields a total crosssection of

h�ð147PmÞi25 keV ¼ 777� 109 mbarn ;

which is clearly smaller and at least a factor of 2 more accu-rate than the results of statistical model calculations (seebelow).

The overall uncertainties are dominated by systematiceffects. The larger uncertainties of the partial cross sectionto the ground state are partly due to less reliable line inten-sities, partly because the ground state cascade had to be cor-rected for an interfering component from the isomer decay.The various contributions have already been discussedalong with the measurements and the data analysis and aresummarized in Table 5. Obviously, the need for coincidentdetection of �-cascades led to limitations in counting statis-tics, in particular for the weaker lines of the ground statedecay. Comparably large systematic uncertainties were dueto the flux measurement (7%), to the line intensities for theground state decay (6.5%), and in particular to the complex

GEANT simulations of the cascade efficiencies. All othercontributions had little impact on the overall uncertainties.

4.2. TheMaxwellian-averaged Cross Section at 30 keV

The resulting cross sections are finally corrected for thedifference of the experimental spectrum from an idealMaxwell-Boltzmann distribution and extrapolated to thestandard thermal energy of 30 keV traditionally usedfor s-process compilations. The determination of theMaxwellian-averaged cross sections (MACSs) is accom-plished by considering the energy dependence of the 197Auand 147Pm cross sections. The corresponding corrections aresmall and contribute a systematic uncertainty of only 2%despite the fact that the slope of the 147Pm cross section hadto be adopted from statistical model calculations.

With the stellar gold cross section of 582� 9 mbarn for athermal energy of kT ¼ 30 keV (Ratynski & Kappeler1988), the partial cross sections are

h�gð147PmÞi30 keV ¼ 313� 60 mbarn ; ð10Þh�mð147PmÞi30 keV ¼ 395� 55 mbarn ; ð11Þ

and add to a total stellar (n, �) cross section of

h�ð147PmÞi30 keV ¼ 709� 100 mbarn : ð12Þ

5. STATISTICAL MODEL CALCULATIONS

5.1. Codes and Techniques

Neutron capture cross section calculations for 147Pm,148Pm, and 149Pm have been performed in the framework of

2 See http://www.nist.gov.

TABLE 4

Measured Neutron Capture Cross Sections of the147

Pm(n, �) Reaction

Uncertainties

(%)

Reaction

MACS at kT ¼ 25 keV

(mbarn) Statistical Systematic Total

147Pm(n, �)148gPm............... 344 6 17 18147Pm(n, �)148mPm.............. 433 4 13 14147Pm(n, �)148Pm................ 777 4 15 14

TABLE 5

Compilation of Uncertainties

Uncertainty

(%)

Source of Uncertainty147Pm(n, �)148gPm 147Pm(n, �)148mPm

Gold cross section .................... 1.5 1.5

Neutron fluxmeasurement....... 7 7

Sample mass ............................ 4 4

Time factors, fb, fw, fm............... �1 �1

Measured detector efficiency,

��;casc ....................................

3.0 3.7

Line intensity, I�;casc ................. 6.2 1.6

GEANT simulations of

cascade efficiency..................

13 9.6

Absorption,K�......................... �1 �1

Counting statistics ................... 6.5 4.0

Total uncertainty.................. 18 14

No. 2, 2003 STELLAR NEUTRON CAPTURE ON PROMETHIUM 1257

the Hauser-Feshbach statistical model (HFSM) theory ofnuclear reactions. For the mass and energy range consid-ered here, the assumption of the compound nucleus reactionmechanism, on which the HFSM is based, is fully justified.Three different sets of calculations using the same HFSMtheory but different parameterizations have been consid-ered. The first set (HFSM-1) is based on the NON-SMOKER code (Rauscher & Thielemann 1998). A secondset of calculations (HFSM-2) is based on the EMPIRE-IIcode (M. Herman 2003, unpublished). The third set of cal-culations (HFSM-3) is based on a code developed at ENEA(A. Mengoni 2003, unpublished). The basic expression forthe neutron capture cross section in HFSM is the following:

��;�ðE�Þ ¼�

k2�

Xj

T�T�ðjÞP T

W�;�ðjÞ :

The neutron transmission coefficients T� for all the states inthe entrance channel� as well as in the exit channel � are cal-culated as solutions of the two-body Schrodinger equationfor a complex optical potential. Different optical modelparameter (OMP) sets have been used in the reportedHFSMcalculations. For energies under consideration here, the exitchannel can be either elastic and inelastic neutron emission(� ¼ n and n0) or capture (� ¼ �). For excited target states,superelastic neutron emission channels have been includedin HFSM-1 and HFSM-3. The T�( j) transmission coeffi-cients for each � transition j have been calculated using giantdipole resonance (GDR) parameters. Experimentally knowndiscrete nuclear levels have been used at low excitation ener-gies (Rauscher & Thielemann 2001). For transitions leadingto states above the known discrete levels, the nuclear leveldensity, (E), is needed. A constant-temperature model fit,matched to the Fermi gas model with pairing correlationsand corrected for shell inhomogeneities at excitation ener-gies close to the neutron binding energy, has been adoptedfor the calculation of (E). Finally, the level width fluctua-tion correction factor, W�;�, has been calculated usingdifferent approaches. The parameterizations adopted in thethree sets of calculations are listed in Table 6.

5.2. Stellar Enhancement Factors andAdopted Cross Sections

The different parameterizations of the HFSM theory leadto different results in the cross sections of the promethiumisotopes. In particular, for 147Pm, the nucleus of majorconcern here, the calculated MACS at 30 keV variesfrom 923 to 1280 mbarn, significantly higher than the709� 100mbarn found experimentally. However, the ratiosof these results, 148Pm/147Pm and 149Pm/147Pm, are consis-tent within 8% for the three sets of calculations. In combina-tion with the measured value of 147Pm, this provides areliable estimate of the reaction rates for 148Pm and 149Pm,where no experimental information is available.

Taking the average between the results of the three sets ofcalculations, we have obtained �ð148Þ=�ð147Þ ¼ 1:43 and�ð149Þ=�ð147Þ ¼ 1:02, for the MACS at kT ¼ 30 keV. Theadopted neutron capture cross sections for 148Pm and 149Pmhave been, therefore, derived by multiplying the experimen-tal cross section for 147Pm by these factors, respectively.Based on the differences between the calculated ratios, anuncertainty of 10%was assigned to this normalization.

The resulting cross sections, which were eventuallyadopted for the discussion of the astrophysical implications,are given in Table 7. The stellar enhancement factors (SEFs)have been calculated considering thermal populations of thefirst five excited states in each target nucleus. For the tem-peratures considered here, kT up to 100 keV, this has beenverified to be sufficient to include all significant contribu-tions to the stellar rates. A complete list of the cross sectionsused in the following branching analysis is given in Table 8.

6. PROBING THE s-PROCESS NEUTRON DENSITY

6.1. The Classical s-Process

Until recently, the phenomenological picture of the s-process (Burbidge et al. 1957; Seeger, Fowler, & Clayton1965) provided an appealing analytic solution based on theassumption of a steady s-process with constant temperatureand neutron density. The set of differential equations

TABLE 6

Parameterization Used in the HFSM Calculations and Capture Cross Section Ratiosaat kT ¼ 30 keV

QuantitybHFSM-1

NON-SMOKER

HFSM-2

EMPIRE-II

HFSM-3

ENEACode

Tn.................................... Microscopic OMPc Wilmore-Hodgson OMPd Moldauer OMPe

T�.................................... GDR from droplet model,f

parameterized widths,g

modified low-energy behaviorh

Experimental GDR, own systematics Experimental GDR, own systematics

(E ) ................................ Shifted Fermi gas, microscopic corrections,

constant-temperature formula at

low excitation energiesi

BCS+Fermi gas with shell corrections

and collective effects,

fitted to discrete levels

Fermi gas, pairing, shell corrections

W .................................... Tepel, Hoffmann, &Weidenmuller (1974) Hofmann et al. (1975) Lynn (1968)

�(148Pm)/�(147Pm) .......... 1.48 1.49 1.33

�(149Pm)/�(147Pm) .......... 0.90 1.08 1.08

a Values refer toMACS for the ground states.b For definition see text.c Jeukenne, Lejeune, &Mahaux 1977.d Wilmore &Hodgson 1964.e Moldauer 1964.f Meyers et al. 1977.g Thielemann&Arnould 1983.h Rauscher & Thielemann 2000.i Rauscher, Thielemann, &Kratz 1997.

1258 REIFARTH ET AL. Vol. 582

describing the neutron capture chain could be solved(Clayton 1968) by adopting an exponential distribution ofneutron exposures

ð�Þ ¼GN56

�0

exp � �

�0

� �:

This Ansatz allowed for a simple analytical solution for theproduct of s abundance and stellar cross section, whichcharacterizes the unbranched reaction flow:

�iNis ¼

GN56

�0

Yij¼56

1þ �j�0� ��1

h i�1

:

In this way, the solar system h�iNs curve could be success-fully reproduced with the fit of only two parameters, thefraction G of the solar iron abundance N56

required as aseed and the mean neutron exposure �0 (Kappeler, Beer, &Wisshak 1989).

The justification for the choice of (�) seemed to appearas the natural consequence of repeated He shell flashes dur-ing the asymptotic giant branch (AGB) phase. The expo-

nential distribution was shown to follow simply from thepartial overlap of subsequent thermal pulses (Ulrich 1973).Following this classical concept, s-process calculations havebeen performed by means of the network code NETZ (Jaag1991), which yields a complete description of the s-processbranchings.

A branching in the neutron capture path occurs when anunstable nucleus is encountered that exhibits comparableneutron capture and �-decay rates. The description of theresulting reaction flow is determined by several parameters.In the classical picture, the (constant) neutron density nngoverns the capture branch, whereas temperature T andelectron density ne may affect the stellar �-decay rate andhence the �-branch. Once the neutron density is established,this value can be used to fit the effective temperature inbranchings where the �-decay rates are strongly tempera-ture dependent. In a similar way, an estimate for the elec-tron density can be derived from branchings where therespective decay rate is sensitive to the electron density(Takahashi & Yokoi 1987; Kappeler et al. 1990).

The strength of a branching can be expressed in terms ofthe rate for �-decay and neutron capture of the branch pointnucleus as well as by the h�iNs values of the involved iso-topes,

f� ¼ ��

�� þ �n� h�iNsð Þbranched

h�iNsð Þunbranched:

As illustrated in Figure 1, the effective strength of the com-bined branchings at A ¼ 147=148 can be expressed by thebranched and unbranched s-only isotopes 148Sm and 150Sm,respectively. In this case one has h�iNs ¼ h�iN. Since theisotopic ratio is well defined and the branching factor couldbe accurately determined by a measurement of the crosssection ratio (Wisshak et al. 1993), one findsf eff� ¼ 0:870� 0:009.

Since the �-decay rates of the branch point nuclei 147Nd,147Pm, and 148Pm are practically independent of tempera-ture and electron density during the s-process (Takahashi &Yokoi 1987), the expression can be solved for �n ¼ nnh�ivT ,choosing the neutron density nn such as to reproduce 148Smand 150Sm in solar proportions. An important informationin this respect was provided by Lesko et al. (1989), who

TABLE 7

Calculated Maxwellian-averaged Cross Sections and Stellar

Enhancement Factors (SEFs)

147Pm 148Pm 149Pm

Thermal Energy

(keV)

h�i(mbarn) SEF

h�i(mbarn) SEF

h�i(mbarn) SEF

5............................. 2257 1.00 3365 1.00 2356 1.00

8............................. 1602 1.00 2381 1.00 1660 1.00

10........................... 1373 1.00 2035 1.00 1417 1.00

15........................... 1055 1.00 1550 1.00 1081 1.00

20........................... 887 1.00 1292 1.01 906 1.00

25........................... 782 0.99 1129 1.03 798 1.00

30........................... 709 0.99 1014 1.05 723 0.99

40........................... 613 0.98 865 1.12 626 0.98

50........................... 553 0.97 771 1.19 563 0.97

60........................... 503 0.96 707 1.26 517 0.95

80........................... 455 0.94 643 1.37 448 0.92

100 ......................... 418 0.93 579 1.46 399 0.89

TABLE 8

Adopted Cross Sections and Stellar Enhancement Factors for the Nd-Pm-Sm Regiona

kT ¼ 10 keV kT ¼ 25 keV kT ¼ 30 keV

Target Nucleus

h�i(mbarn) SEF

h�i(mbarn) SEF

h�i(mbarn) SEF

146Nd ............................... 147.1�3.8 1.00 98.0�1.3 1.00 91.2�1.0 1.00147Nd ............................... 1236�204 1.00 623�103 0.98 544�90 0.97148Nd ............................... 266�7 1.00 159�2 1.00 147�2 1.00147Pm ............................... 1373�192b 1.00 782�110b 0.99 709�100c 0.99148Pm ............................... 2035�352b 1.00 1129�195b 1.03 1014�175b 1.05149Pm ............................... 1417�245b 1.00 798�138b 1.00 723�125b 0.99147Sm ............................... 1963�43 1.00 1085�12 1.00 973�10 1.00148Sm ............................... 415�9 1.00 259�3 1.00 241�2 1.00149Sm ............................... 4017�83 0.98 2059�21 0.94 1820�17 0.94150Sm ............................... 742�16 1.00 455�5 1.00 422�4 1.00

a FromBao et al. 2000 unless stated differently.b This work, calculated results, normalized to experimental 147Pm value at kT ¼ 30 keV.c This work, experimental 147Pm.

No. 2, 2003 STELLAR NEUTRON CAPTURE ON PROMETHIUM 1259

showed that ground state and isomer in 148Pm are thermallyequilibrated at the temperature of the s-process. At thispoint previous analyses obtained an estimate of nn ¼ð4:1� 0:6Þ � 108 cm�3 (Wisshak et al. 1993; Toukan et al.1995) using theoretically calculated cross sections for thebranch point isotopes (147Nd: 550� 150 mbarn; 147Pm:985� 250 mbarn; 148Pm: 1410� 350 mbarn). Adopting theresult of Wisshak et al. (1993) for the �N-ratio(0:870� 0:009) and using the recommended cross sectionsof Bao et al. (2000) (147Nd: 544� 90 mbarn; 147Pm:1290� 470 mbarn; 148Pm: 2970� 500 mbarn), oneobtains a significantly lower neutron density ofnn ¼ ð2:7þ0:38

�0:30Þ� 108 cm�3.The present results, the measured value of 147Pm, and the

normalized, theoretical value for 148Pm provide a majorimprovement for the analysis of this branching. Since bothcross sections are smaller compared to the data used in allprevious analyses, the reproduction of 148Sm and 150Smabundances requires now a correspondingly higher neutrondensity of

nn ¼ 4:94þ0:60�0:50

� �� 108 cm�3 :

If compared to the result of independent analyses for thebranchings at 192Ir [nn ¼ ð7þ0:5

�0:2Þ � 107 cm�3; Koehler et al.2002] and at 185W [nn ¼ ð3:5þ1:7

�1:1Þ � 108 cm�3; Kappeler etal. 1991], it turns out that the classical approach does notprovide a consistent solution for the neutron density, in con-trast to the fact that this represents one of the basic assump-tions for this model. This inconsistency confirms once morethat the s-process mechanism must include a dynamic com-ponent as pointed out by Arlandini et al. (1999).

6.2. Possible p-Process Corrections

At this level of accuracy the �N-ratio of the s-only iso-topes 148Sm and 150Sm may be possibly affected by small p-process contributions. Before quantitative p-process modelswere available, p-process corrections were based on empiri-cal estimates deduced from abundance trends of nearby p-only nuclei. In this way, the p contributions to 148Sm and150Sm are 1.1% and 1.7%, respectively, leading to a marginaleffect on the neutron density. The p-process correctionsobtained from realistic model calculations (Rayet, Prantzos,& Arnould 1990; Prantzos et al. 1990; Howard, Meyer, &Woosley 1991; M. Rayet et al. 2002, private communica-tion) indicate even smaller corrections of 0.7% and 0.3% for148Sm and 150Sm, respectively. In view of the presentlyremaining uncertainty, the impact of the p-process can,therefore, be neglected.

6.3. Thermally Pulsing AGB Stars

In agreement with observations, the main s-processcomponent is commonly ascribed to He shell burning inthermally pulsing stars on the asymptotic giant branch (TP-AGB stars) with masses between 1.5 and 3 M (Gallino etal. 1988; Hollowell & Iben 1988; Kappeler et al. 1990). Inthese stars the neutron supply results from the interplay ofthe dominant 13C(�, n)16O reaction and a comparably weakcontribution from the 22Ne(�, n)25Mg reaction. The spectraof these stars show an excess of s-process elements but donot exhibit the Mg excess expected if 22Ne(�, n)25Mg werethe main source of neutrons (Smith & Lambert 1990). Onthe other hand, the small amount of 13C produced by the

preceding CNO cycle could not account for the neutronexposure required to produce the observed s-process yields.It is therefore necessary to postulate the presence of a tiny13C-enriched layer (a few times 10�3 M). This

13C pocket isproduced by the penetration of protons from the convectiveenvelope into the He shell at the end of a thermal instability.Subsequently the temperature increases and 13C is producedby the reaction sequence 12C(p, �)13N(�+)13C.

The consumption of all the 13C in the pocket duringthe interpulse time of a few times 104 yr provides a rela-tively high neutron exposure at comparably low tempera-tures (kT ’ 8 keV) and neutron densities (nn � 107

cm�3). When this s-process–enriched layer is engulfedinto the next convective instability, a sufficiently hightemperature is reached at the bottom of the He-burningzone (Tb � 3� 108 K) to marginally activate the 22Nesource. This short burst of �5 yr reaches peak neutrondensities of nn � 1010 cm�3. Although this second burstrepresents only a few percent of the total neutron expo-sure, it suffices to determine the final abundance patternof the s-process branchings. In particular, the timedependence of this second burst is defining the freezeoutof the final abundances. Accordingly, the s-processbranchings represent sensitive model tests.

Transport of the freshly synthesized material from the Heshell to the stellar surface, the so-called third dredge-up(TDU; Straniero et al. 1997), is considered by a self-consis-tent mixing mechanism. Unless otherwise specified the sabundances reported in the following refer to the composi-tion of the TDU material integrated over the whole AGBphase and ejected by stellar winds. This composition repre-sents the s-process enrichment of the interstellar medium bythe particular model star and has to be considered in com-parison with the s-process enhancements of chemicallypeculiar red giants (Smith & Lambert 1990; Lambert et al.1995; Busso, Gallino, & Wasserburg 1999; Busso et al.2001).

AGB stars in the mass range 1:5 � M=M � 3 exhibitfairly similar physical conditions with respect to s-processnucleosynthesis, at least for metallicities down to 1

3 solar(Gallino et al. 1998). Accordingly, such Galactic diskstars can be considered as suitable sites for reproducingthe main s component. This is confirmed by observationsof MS and S stars in the solar neighborhood (Smith &Lambert 1990; Busso et al. 1992). Although the s abun-dances in these stars exhibit a certain spread, the averageis remarkably well represented by the solar s distribution(Busso et al. 1999). In particular, it is found that themain s component is best reproduced by the averagedresults obtained with stellar models for 1.5 and 3 Mstars with 50% of the solar metallicity (Arlandini et al.1999). Therefore, this approach was adopted in the fol-lowing unless otherwise specified.

We note however that the use of the solar s abundances asa constraint for s-process studies has to be made with cau-tion, since the s-process is not a unique event but rather theresult of a complex Galactic evolution mechanism. In par-ticular, the s-process production varies strongly for TP-AGB stars with different metallicity (Busso et al. 1999).Therefore, the description of the main s component fromthe Sr/Y/Zr region up to Pb and Bi must account for theincreasing metallicity during galactic evolution by integra-tion of the s abundances from different generations of AGBstars (Travaglio et al. 1999, 2001).

1260 REIFARTH ET AL. Vol. 582

6.4. The A ¼ 147=148 Branching in AGB Stars

In the stellar model outlined in the previous section, themild neutron densities of the 13C(�, n)16O source are not suf-ficient for the reaction flow to bypass 148Sm. Only in the sec-ond burst, when neutron densities up to 1010 cm�3 arereached, is 148Sm bypassed and even strongly depleted(Fig. 9). However, during the final decline of the neutrondensity, the branchings to 148Sm are restored, and eventu-ally the final value is established during the freezeout of theabundance pattern.

Hence, in the stellar model the neutron density deter-mines this branching in two ways: via the peak neutron den-sity and, more importantly, via the freezeout of the neutronsupply. The first point explains why stars of different mass,which differ slightly in their peak temperatures and corre-spondingly in their peak neutron densities, produce smallbut noticeable differences in the Sm abundances. On theother hand, the decline of the neutron density and conse-quently the freezeout conditions are independent of themodel star in the considered range of stellar mass andmetal-licity, resulting in 148Sm/150Sm ratios that are fairly con-stant after all.

With the new cross sections, these models reproduce theobserved abundance ratio to better than 1%. If the overallabundance distribution is normalized on a grid of s-only iso-topes, which are not affected by branchings and for whichthe cross sections are well defined (as described by Arlandiniet al. 1999), the corresponding production factors for 148Smand 150Sm are 1.023 and 1.014, respectively, well compatiblewith the uncertainty of the cross section ratio of the two iso-topes. With the recommended Pm cross sections of Bao etal. (2000), the same model yields an abundance ratio of148Sm and 150Sm, which differs from the solar value by 2.3%(see also the previous analysis by Arlandini et al. 1999).

In earlier branching analyses, it was pointed out (Cosner,Iben, & Truran 1980; Kappeler et al. 1982) that the effectiveparameters obtained by the classical analysis have to be con-sidered as local features, which, therefore, could be com-pared to the freezeout conditions obtained by the stellarmodels. The moment in which the isotopic abundance of thepartially bypassed s isotope reaches 90% of its final valuecan be defined as an intuitive criterion for freezeout. Themore complex criterion proposed by Cosner et al. (1980)was also considered, but with negligible differences. Accord-

ing to Figure 9, the neutron density at freezeout obtainedwith the present stellar model is �1� 108 cm�3. This valueis considerably lower than the phenomenological estimateand reflects the time dependence of the more complex stellarmodel.

The final abundance pattern at the end of the He shellflash is affected by the 22Ne(�, n)25Mg rate, which deter-mines the neutron density and the corresponding exposure.This influence is illustrated in Table 9 by adopting differentchoices for this critical reaction rate. One finds that even rel-atively small changes, well within present uncertainties, arecausing a noticeable effect (compare the second and thirdcolumns, for example).

7. SUMMARY

The stellar (n, �) cross section of the unstable isotope147Pm has been successfully measured with an overall

0.01 0.1 1 10TIME DURING HE-SHELL FLASH (y)

10-8

10-7

AB

UN

DA

NC

E B

Y M

ASS

107

108

109

1010

1011

1012

NE

UT

RO

N D

EN

SIT

Y (

cm-3

)

148Sm

150Sm

nn

Fig. 9.—Evolution of neutron density (right scale) and of the abund-ances of 148Sm and 150Sm in fractions of mass during the 22Ne neutronrelease in a typical advanced pulse (pulse 15 of the standard AGB model).The timescale starts at the moment when the bottom temperature reaches2:5� 108 K. The arrow indicates the freezeout of the 148Sm abundanceaccording to the criterionXfreeze ¼ 0:9Xfinal.

TABLE 9

Stellar Model Production of148

Sm and150

Sm for Different Choices of the

22Ne(�, n)25Mg Rate

Parameter Zeroa Lowb Standardc Kappeler et al. 1994d

148Sme ......................................... 1110.0 1014.7 1021.1 1030.1150Sme ......................................... 941.9 985.9 1012.3 1031.0

Mean factorf ............................... 969.1 984.0 998.5 1012.6

Standard deviationg (%) .............. 6.7 4.8 2.7 2.9

a Assuming that the 22Ne(�, n)25Mg rate equals zero.b Lower limit of Kappeler et al. 1994 times 7, equivalent to Jaeger et al. 2001.c Lower limit of Kappeler et al. 1994.d Kappeler et al. 1994, without contribution from resonance at 633 keV.e Enhancement factor in the s-process material cumulatively mixed with the envelope by all

TDU episodes.f Mean enhancement factor of the normalization isotopes 100Ru, 110Cd, 124Te, 150Sm, and

160Dy characterizing the entire s-process abundance distribution.g Standard deviation from the mean enhancement factor.

No. 2, 2003 STELLAR NEUTRON CAPTURE ON PROMETHIUM 1261

uncertainty of 12%. This experiment demonstrates the sensi-tivity in determining (n, �) cross sections of unstable iso-topes by combining the activation method with coincidencetechniques for detecting the induced activity. In the presentcase, the method was essentially limited by sample impur-ities and could, in principle, be further improved.

The present result is at least a factor of 2 more accuratethan careful statistical model calculations. Accordingly, ithas a significant impact on the theoretical assessment of theother branch point isotopes 147Nd and 148Pm. In particular,the uncertainty of the important 148Pm cross section couldbe reliably reduced to 15%, since it could be shown in threeindependent HFSM calculations that the cross section ratioto 147Pm was stable within�8%.

The classical analysis of the s-process branchings atA ¼ 147=148 yields a neutron density, which confirms pre-vious results reported for this branching (Toukan et al.1995), but is in conflict with recent studies of the branchingsat A ¼ 185 (Kappeler et al. 1991) and A ¼ 191=192(Koehler et al. 2002). This inconsistency underlines thedifficulty of the classical model in describing the abundance

patterns of the s-process branchings reliably (Arlandini etal. 1999;Wisshak et al. 2000). On the other hand, the s-proc-ess models related to the He-burning zones of TP-AGB starsallow the abundance pattern of the Nd/Pm/Sm isotopes tobe well reproduced. This emphasizes the importance of thedecline of the neutron density predicted in these models,which leads to a stepwise freezeout of the abundanceaccording to the particular cross section situation in eachbranching.

We would like to thank G. Rupp for his invaluable helpin all technical questions as well as D. Roller, E.-P.Knaetsch, and W. Seith for the excellent beam conditionsduring the irradiations at the Van de Graaff accelerator.This work was supported by the ItalianMURST-Cofin2000Project ‘‘ Stellar Observables of Cosmological Relevance.’’R. R and M. H. are grateful for support by CERN. T. R.acknowledges support by a PROFIL Fellowship from theSwiss National Science Foundation (grants 2124-055832.98and 2000-61822.00).

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