Revista Mexicana de Física 40, Suplemento 1 (1994) 237-249

Heavy element production during stellar heliumburning

F. KAPPELER, K. GUBER, K. WISSIIAK AND F. Voss

K ernforschungszentrum Karlsruhe, [nslilut für K ernphysikPoslfach 3640, D-76021 Kar/sruhe, Federal Repub/ic of Germany

Received 6 January 1994; accepted 19 May 1994

ABSTRACT. The elements heavier than iron are efficiently produced in the so-called s-process thatoccurs during stellar helium burning. The currently discussed scenarios refer to massive stars inthe mass range 15 < M/M0 < 30 as well as to low mass stars with 1 < M/M0 < 3. Therelevant features oC these sites are presented with emphasis on the nuclear physics inCormationrequired for quantitative nucleosynthcsis models. The experimental techniques for determining thecorresponding oeutron capture rates are outlined at the example of the stable samarium isotopes.Eventually, the analysis of the related s-process branching yields an estimate for the mean neutrondensity for helium shell burning in low mass stars.

RESUMEN.Los elementos mis pesados que el Hierro son eficientemente producidos en los asillamados procesos-s que ocurren durante el quemado del Helio estelar. Los argumentos común-mente discutidos se refieren a las estrellas masivas en el rango de 15 < M/M0 < 30 comotambién a las estrellas de masa pequeña con 1 < M/M0 < 23. Las características impor-tantes de estos tamaños se presentan con énfasis en la información de la física nuclear requeridapara modelos cuantitativos de nuclcosíntcsis. Las técnicas experimentales para determinar la tazade la captura de neutrones correspondiente son esbozadas en el ejemplo de los isótopos esta-bles de samario. Eventualmente los análisis de bifurcación de los procesos-s dan una estimaciónde la densidad de neutrones medida para la capa de Helio quemado en las estrella.., de masapequeña.

PACS: 25.40.Lw; 28.20.Fc; 97.1O.Cv

1. NEUTRON CAPTURE NUCLEOSYNTIIESIS

In astrophysical scenarios, the heavy elements can only be produced by neutron capturereactions and subsequent beta decays. Fusion of charged particles no longer contributesin this mass range, since beyond A ~ 60, the Coulomb barriers are becoming too highand the binding energies per nucleon are decreasing. For explaining the observed abun-dance distribution between iron and the actinides [1]' essentially three processes must beinvoked as illustrated in Fig. J. The dominating mechanisms are the slow and the rapidneutron capture processes (s- ami r-process). which both account for approximately 50%of the abundances in the mass range A > 60. A minor part of the resulting abundancedistribution is modified by the p-process at very high temperatures, which accounts forthe rare proton rieh nuc1ei.The s-process associated with stellar helium burning is characterized by relatively low

neutron densities. This implies neutron capture times of the order of several months,

237

238 F. KAI'PELER ET AL.

'o'

regían ofr-process synthesis,decay of r-processmaterial índtcatedby orrows

ZrySr ORbo

"-"-

"-

"- ,-----

O

s-processbranchings 1 ó1NI. NSe. ~Kr,...lAl!:::: AO

KrBrSeAss

\s-processsynthesispoth inVOllE'Y ofbeta slobillty

200

seed fars-process

ZnCu

NI OCoFe

Is6Fe

"'"MASS NUMBER

FIGUHE 1. An illustration oC the neutron capture proccsscs rcsponsiblc for the formation oí thenuc1ei between iron and the actinides. The observed abundancc distribution in the ¡oset showscharacteristic twin peaks. These result froro the nuclear properties al magic ncutron numbers undertypical g- ami r-process conditionsl an obvious examplc for the intimate corrclation betwecn theobserved abundances and the physical conditions during nucleosynthesis.

much longer than typical beta decay half-lives. Thercfore, in the N-Z-plane of Fig. 1 thes-process path follows the stability valley as indicated by the solid líne. The developings-abnndances are deterlllined by the respective (n, 1) croS" scctions averaged over thestellar neutron spectrulll, snch that isotopes with small cross sections are built up to largeabundances. This holds in particular for nuclei with closed Ileutron shells N = 50, 82,and 126, giving rise to the sharp s-process lllaxillla in the abundance distribution aroundA = 88, 140, and 208.The r-process counterparts of these lllaxillla are caused by the effect of neutron shell

closure on the beta decay half-líves. Since the r-process occurs during stellar explosions(presumably in supernovae) on time scales of a few seconds, neutron captures are muchfaster thall beta decays. This drives the r-process path off the stabilíty valley to wherethe neutroll separation energies are only ~ 2 MeV. At these points, (n,1) and ("(, n)reactions are in equilibrium, and the reaction flow has to wait for beta decay to the nexthigher elemellt. Accordillgly, the r-process abundallces are proportiollal to the half-líves ofthese waiting point nuclei. This means that abundance peak s accUfnulate again at magicnClltron Ilumhcrs, but at lowcr mass numbers comparcd thc relatcd s-process maxima.The separatioll of the abundance peaks indicates the intersection of the r-process pathwith thc magic Ileutron lluIllbers.

HEAVY ELEMENT PRODUCTION DURING STELLAR. . . 239

The following discussion is restricted to the s-process, which is more easily accessibleto laboratory experiments as well as to stellar models and astronomical observations [2].Attempts to describe the r-process are hampered by the large uncertainties in the nuelearphysics data far from stability, but also -and perhaps more severely- by the problemsrelated to a detailed modelling of the stellar explosion [3]. These difficulties are bestillustrated by the fact that the site of the r-process has not been reliably identified bynow [4].From the aboye, it is obvious that most isotopes received abundance contributions

from both, the s- and the r-process. But as indicated in Fig. 1, there are stable isotopes(marked r) that are not reached by the s-process because of their short-lived neighbors.Consequently, this species is of pure r-process origino In turn, these nuelei shield theirstable isobars against the r-process, so that there is an ensemble of s-only nuelei as well.The existence of these two groups is of vital importance for nueleosynthesis, since thecredibility of any model depends on how well the abundances of these particular nueleican be reproduced. The currently favored stellar s-process scenarios are introduced in 32.A second observation from Fig. 1 has significant impact on the role of the s-process

with respect to stellar models: At sorne points, the neutron capture chain encountersisotopes with long beta decay half-lives that are comparable to the neutron capture times.The resulting competition between beta decay and neutro n capture causes the s-processpath to split, e.g. at 63Ni, 79Se, and 85Kr, leading to abundance patterns that reflect thephysical conditions of the stellar plasma. The nuelear physics data required for detaileds-process calculations are addressed in 33, and in 34, the analyses of s-process branchingsare discussed.

2. S-PROCESS SCENARIOS

2.1. The c1assical s-process

This first attempt for a quantitative description of the s-process dates back to the fun-damental paper by Burbidge el al.[5], and was later improved mainly by Seeger el al. [6].In this approach it is empirically assumed that a certain fraction G of the observed 56Feabundan ce was irradiated by an exponential distribution of neutron exposures. An an-alytical solution can be obtained if a possible time dependence of the rates for neutroncapture, ),n = nn (a)vT, and for beta decay, ),fJ = In2/tl/2, is neglected. In other words, itis assumed that temperature and neutron density are constant. Then, the characteristics-process quantity, stellar cross section times s-abundance, can be given by the simpleexpression

G NO A ( 1)-1(a)(A) . N,(A) = . 56 TI 1+ -( -).

70 i=56 70 C1 !

Apart from the two parameters G and ro (which are adjusted by fitting the abundancesof the s-only nuelei), the only remaining input for the expression of (a). N, are the stellar(n, ,) cross sections (a). (For further details see Re!. [2]).

240 F. l(APPELER ET AL.

10'

•wUZ

10'ex:OZ::Jw-ex: "'O lá'~lO 11 ~.:J o #$

zU; t " ~ ¿-: 0~~.,'. ,O,O; T"~ . 0'~

10'f- ~ •. i"•.t::>U.íJW EUl-

Ul 1rfUlOa:U

60 90 120 150 180 210

MASS NUMBERFIGURE 2. The characteristic product of cross section times s~process abundance plotted as afunction of mass number [7J.The solid line was obtained via the classical model, and the symbolsdenote the empirical products for the s-only nuclei. Sorne important branchings of the neutroncapture chain are indicated as well.

Given the very schematic nature of this elassical approach, it was surprising to see thatit provides for an excellent description of the s-process abundances. In fact, the agreementbetween observed and calculated abundances beca me the better the more the input datawere improved. The present status is illustrated in Fig. 2, which shows the calculated(0'). N, values (solid line) compared to the corresponding empirical products of the s-onlynuelei (symbols) in the mass regio n between A = 56 and 209 [7]. The error bars of theempirical points reflect the uncertainties of the abundances and of the respective crosssections. One finds that equilibrium in the neutron capture flow was obtained betweenmagic neutron numbers, where the (0') . N,-curve is almost constant. The small crosssections of the neutron magic nuelei act as bottlenecks for the capture flow, resulting inthe distinct steps, e.g. at A = 140 and 208.The global parameters, G and TO, that determine the overall shape of the (O')N,-curve,

represent a first constraint for the stellar s-process site with respect to the required seedabundance and total neutron exposure. It is found that 0.04% of the observed 56Fe abun-dance are a sufficient seed, and that on average about 15 neutrons are captured by eachseed nueleus. These numbers refer to the main s-process component given by the so lidline in Fig. 2. For A < 90, this line falls below the empirical points, and these discrepanciesrequire an additional, the so-called weak, component. In terms of stellar sites, the maincomponent can be attributed to helium shell burning in low mass stars [8-11], whereas theweak component is due to core helium burning in massive stars [12-14, 15 and rcferencestherein).

HEAVY ELEMENT PRODUCTION DURING STELLAR... 241

The excellent agreement between the empirical points and the data obtained with theclassical model provides sorne confidence that at least the s-abllndances can be reliablydescribed by this schematic approach. In fact, those s-only nuclei that are not affected bybranchings, are reproduced by the model with a mean square deviation of only 3% [71.

2.2. Helium shell buming in AGB-stars

Most of their life, stars are qllietly burning their central hydrogen inventory. The stellarstrllcture during that phase is characterized by the equilibrium between the gravitationalpressure exerted by the outer layers and the radiation pressure created by the energyproduction in the interior, a situation that can be described, for example, by the standardsolar model 116]. After hydrogen exhaustion in the central region, stellar evollltion speedsup and becomes much more violento While hydrogen burning continlles in a shell aroundthe center, the inert helillm core is no longer prodllcing the energy to maintain the ra-diation pressure. Therefore, it shrinks and heats up by the released gravitational energylIntil He bllrning is ignited at temperatures in excess of ~ 150 million K. The high centraltemperatures cause the stars to expand and to cool on the outside -they are becomingRed Giants.This stage of evolution is schematically sketched in Fig. 3 for a star during its Red

Giant phase when it has already exhallsted its central helium. Energy is produced in anarrow double shell on top of an inert core consisting of 12C and 160. The inset showsthat hydrogen bllrning at the bottom of the deeply convective envelope produces helillmthat accumulates in a thin layer arollnd the coreo As soon as this layer exceeds a criticalmass, helium burning is ignited, leading to a highly lInstable sitllation because of thelarge assodated energy production. As a reslllt, strong convective motions cause practi-cally instantaneous mixing in the helium burning layer, and eventually freshly synthesizedmatter is dredged up to the surface. It is important to note that helium burning lasts foronly abollt 500 yr, while it takes about 2 x 105 yr for hydrogen burning to replenish theconsumed helium. These helium burning episodes can repeat up to about 20 times. Asa consequence of the comparably short time scale and the strong impact of convection,stellar models for the Red Giant phase are very difficult to qllantify and often have toresort to uncertain approximations [8,91.An alternative way for gaining insight in that state of stellar evolution is to investigate

the abundance pattern in the vario liS s-process branchings, which still carry the informa-tion about the physical conditions at which they were formed (34). Nelltrons are liberatedduring helium burning by side reactions, Le. by 13C(a, n)160 and to a smaller fraction by22Ne(a, n)25Mg.

2.3. eore helium buming in massive stars

Towards the end of core helium burning in massive stars the temperatures become suffi-ciently high for neutron production via the 22Ne(a, n)25Mg reaction. The resulting neutrondensity is comparably weak and lasts for about 3 x 104 yr, resulting in the modest neutronexposure of the weak s-process component. This scenario is discussed in the followingcontribution [171.

242 F. KAI'I'ELER ET AL.

FIGURE 3. Sehematie sketch of the stellar strueture during the heHumshell burning phase in !owmass stars. Energy is produced in a narro\\' zone on tap oC the inert core consisting essentially oí12C ami 160. The envelope is deeply convective, so that freshly synthesized rnattcr is transportedto the surfacc. Helium burning occurs in repeated flashes, which renders the assodated s-processdifficu!t to mode!.

3. LABORATORY STUDIES

This section contains a brief discussion of those quantities which determine the s-processabundance patterns: the stellar (n, /,) cross seelions and ,8-decay rates. The charged par-ticle reactions during helium burning, and in particular the neutron producing (a, n)reactions are the subject of the following contribution [171.

3.1. Neutron capture cross sections

3.1.1. The I<arlsruhe 4". DaF2 detector

The best signature for the identification of neutron capture events is the total energy ofthe gamma cascade by which the product nucleus deexcites to its ground state. Hence,the accurate measurement of (n, /,) cross sections should use a detector that opera tes asa calorimeter with good energy resolution. In the gamma spectrum of such a detector, allcapture events would fall in a line at the neutron separation energy (typically between5 and 10 MeV), well separated from the gamma-ray backgrounds that are inevitably inneutron experiments.These arguments point to a 4". detector of high efficiency, made of a scintillator with

reasonably good time and energy resolution. In addition, this detector should be insensitiveto scattered neutrons, since -on average- the scattering cross sections are about 10times larger than the capture cross sections. The combination of these aspects is bestcovered by a 4". detector of DaF2. Most important is the weak neutron sensitivity of thatscintillator, which keeps the background from scattered neutrons at a manageable level.

HEAVYELEMENTPRODUCTIONDURINGSTELLAR.. . 243

collimatedneutronbeam

==re=_

sample

I--~ flight path 17,m

pul sedprotonbeam

4rr BaF2 detector neutron [ollimator

FIGUHE4. The I\aris<uhe 411" ilaF2 detectoc.

The concept of the Karlsruhe 411" BaF2 detector and the way it is operated is sketchedin Fig. 4, showing the setup at the accelerator. The detector is indicated schematicallyby a computer simulation. which presents only the spherical BaF2 shell (15 cm thicknessand 20 cm inner diameter) consisting of 42 individual BaF2 crystals, and the supportingstructure. All other details are omitted for the sake of elarity.Neutrons are produced by means of a pulsed Van de Graaff accelerator (repetition rate

250 kH" average beam current 2 ILA, pulse width 0.7 ns) via the 7Li(p, n)7Be reaction.The collimated neutro n beam hits the sample in the centre of the detector at a f1ight pathof 77 cm. Up to S samples can be used in the measurements, all mounted on a verticalladder. One position is occupied by a gold sample for determination of the neutro n flux,while an empty sample position and a scattering sample are routinely used for backgrounddetennination. The samples are cyeled into the measuring position in intervals of about10 min that are defined by integrating the beam current on target. Additional neutronmonitors are used to check for equal neutron exposure per sample and to collect data forthe correction of backgrounds due to scattered neutrons.The csscntial fcatures of the detector are: a resolution in gamma-ray energy ranging

from 14% at 662 keV to 6% at 6.13 MeV, a time resolution of 500 ps, and an overallefficiency for capture events of abont 96%. For a detailed description of the detector anda typical measurement see \Visshak el al. [lS,19].With this new detector, (n, ')') cross sections can be determined with an accuracy of

1 to 2%. Reccntly, it was used for a precise measurement of the cross sections of thes-only samarium isotopes [19]' which define the branchings at A = 147, 14S, 149 (lj4).This experiment has becn performed on highly enriched samarium oxide samples in theneutron energy range from 3 to 225 keV. The efficiency for capture events was evaluatedby mcallS of the cxpcriulCutal pulse hcight spcctra showll in Fig. 5. 1\1ost of the cvcnts are,indced, recorded in a line at the neutron separation energy, but there is also a tail towardslower energies. This tail corresponds to events where not all gamma-rays of the cascade

244 F. KAPPELER ET AL.

OOO 2' 8. 1 MeV 5.9 MeV~ 1nSm "SSm16"" Threshold--l 8 2.5 MeVW OZ Counts/2

Zcr: 16

"9Sm 8.0 MeV 150Sm 5.6 MeVI 8U I

O Counls-2.5crW 32CL 152Sm 5.9 MeV

2'(j) 16 191Au 6.5 MeVf- 8Z I::J OOU O 20 'O 60 80 100 120 O 20 'O 60 SO 100 120

CHANNEL NUMBERFIGURE 5. Sum energy spectra used for determination of the detector efficiency.

could be detected, mainly due to losses through the openings for the neutron beam andthe sample changer. The relateel systematic uncertainty of 0.7% is the major contributionto the overall uncertainty.The stellar cross sections were obtained by folding the elifferential data, atEn), with

the stellar neutron spectra for various temperatures. The Maxwellian averages for the"standard" thermal energy of kT = 30 keV exhibit uncertainties of ~ 1%, 4 limes smallerthan reported for lhe best previous elata [20]. The precision of lhe presenl results providesfor a new quality thal is indispensable in the astrophysical discussion of the branchingsat A = 147-149 (see 34).

3.1.2. The activation technique

The activation technique represents an alternalive method for the determination of stellar(n,,) rates. Compareel to the lechniques using the eleleclion of the prompt capture ,-rays,lhis methoel offers lhe aelvanlages of higher sensitivity (which means that much smallercross sections can be measureel reliably -an important aspect for the investigation ofraelioactive isotopes on the s~process path), anel of selectivily (which means lhat isotopemixtures can be stuelieel via the characleristic ,-ray energies of the respective decay proel-uds). Howcvcr, it is rcstrictcd to thosc cases, wherc neutro n capture produces an unstablenueleus, and it yielels lhe stellar rale only for two thermal energies at kT = 25 anel52 keV.This methoel is based on the fact that quasi-stellar neutron spectra can be produceel

in lhe laboratory via the 7Li(p, n)7I3e and the 3H(p, n)3He reactions [21-231. With thefirst reaction, the proper neulron speclrnm is obtained by bombareling thick metalliclithiuIl1 targets wilh protons of 1912 keV, only 31 keV aboye lhe reaction threshold. Theresulling neutrons exhibit a conlinuous energy distribulion with a high-energy cutoff al

HEAVY ELEMENT PRODUCTION DURING STELLAR.. . 245

En = 106 keY and a maximum emlSSlOn angle of 60°. The angle-integrated spectrumcorresponds closely to a Maxwell-Boltzmann distribution for kT = 25 keY. Hence, thereaction rate measured in such a spectrum yields immediately the proper stellar crosssection. The second reaction can be applied analoguously. The 197Au(n, 1) cross sectioncan be used as a standard in both caBes.Recent applications of this technique can be found in the literature [24,25).

3.2. Weak interaction rates

The competition between neutron capture and beta decay at s-process branchings requiresthe consideration of thermal effects on the beta decay rates at stellar conditions. Thatisotopes, which are exposed to the high temperatures and densities in a He burning plasma,may experience a dramatic enhancement of their decay rate, will be illustrated at theexample of the branch point isotope 79Se. Such temperature-dependent branchings areimportant, since their abundance pattern can be considered aB a thermometer for thes-process site.The inset in Fig. 6 illustrates the mechanism responsible for the enhancement uf the

{3--rate of 79Se under stellar conditions. The decay of the ground state is unique firstforbidden with a terrestrial half-life of about 6.5 x 104 yr. The first excited state is a3.9 min isomer at 96 keY, which decays by internal transitions but can also undergoallowed beta decay. From log jt systematics one expects a half-life of about 20 d for thisdecay branch. The intense photon bath in the stellar plaBma gives rise to thermally inducedtransitions, resulting in a finite population probability of low lying excited nuclear states.At typical s-process temperatures, the isomer in 79Se is populated to ~ 1%, correspondingto an effective stellar half-life of about 2000 d -an enhancement by a factor 104 comparedto the terrestrial value.The most important nuclear physics parameter in this problem is the log jt value for

the isomer in 79Se. Since theoretical estimates were too uncertain, this quantity WaBde-termined experimentally by producing 79mSe via activation with thennal neutrons [26).With the experimentallog jt value of 4.70~g:6g for the beta decay brancll of the isomer,the temperature dependence of the effective stellar half-life of 79Se was rccalculated withthe formalism of TakahaBhi and Yokoi [27).The resulting half-life is plotted in Fig. 6 with the error band according to the experi-

mental range of log j t values. This figure indicates also a remaining ambiguity in the half-life of the ground state: While only an upper limit of 6.5 x 104 yr is known experimentally,a lower limit of 1700 yr would also be consistent with the log jt systematics for unique firstforbidden transitions. At temperatures aboye 200 x 106 K, however, the effective half-lifeis completely insensitive to this ambiguity. This leads to the rather strange consequencethat, at present, the stellar half-life of 79Se is much betterknown than the terrestrial one!

4. BRANCIIlNGS IN TlIE S-PROCESS PATlI

In addition to the parameters G and TO, which were deduced from the overall shape ofthe (a)N,-curve, analyses of the abundance patterns in the various branchings can be

246 F. KAPPELEH ET AL.

,,'

.•lO10'

10-' o , ,ternptr¡turt IlOIK 1

""s.1/2"

TV2= E3191min

712.

n-

"Sr

FIGURE 6. Stellar half-life of 79Se as a function of temperature. The error band reHects the un-ccrtainty oí the expcrimentallog Ji valuc. Thc dashed Hne rcfers to thc cstimated lower bound forthe ground state decay [261.

expected to yield more detailed information on the stellar s-process site. The strengthof such a branching is preserved in the respective abundance pattern and can be used todetermine inforlllation on the physical conditions during the s-process. As an example,Fig. 7 shows the s-process f10w in the mass region between neodymium and samariulll,with the possible branchings at 147Nd and 147-149Pm. Note that 148Sm and 150Sm areshielded against the r-proceos by their isobars in neodymiulll. As the result of a significantbranching at A = 147-149, the (a)N,-value of 150Smwill, therefore, be always larger tha~that of 148Sm.The strength of a branching can be expressed in terms of the rates for beta decay and

neutro n capture of the branch point nuclei as well as by the (a)N,-values of the involveds-only isotopes,

Inserting the equations for the decay rates this expression can be solved for the neutrondensity. JI -for simplicity~ only the branching at 148Pm is considered, one obtains

1- f~ 1 In2nn=---. . .f~ vT(a)H8I'm t;/2(148l'm)

This cquation demonstrates the input data that are important for reHable branchinganalyscs.

HEAVY EI.EMENT 1'1l0llUCTION DUIUNG STELLAIl.. . 247

Sm

PmNd

r-PROCESS

FIGUHE 7. The s-proccss flow bctwcen ncodymium ami samarium.

o The first terln depends on the cross sections for the s-only nuclei, which define thebranching factor f¡J. Since the neutron density is required to ~ 10%, the branchingfactor, ami, hence, the cross sections for the s-only nuclei need to be known to about1% in mauy cases. While conventiona! techniqnes are limited to uncertainties > 4%,the new 4" l3aF2 detector allows now to reach the requircd accuracy.

o The second ter m contains the stellar cross seetions of the radioactivc brand! pointisotopes. Since there are practically no measurements for the unstable brand! pointnudei, only calculated cross sections are availahle at present. l3ut even the most care-fui statistical model calculations are limited to uncertainties of 20-30%, not sufficientfor deducing the entire information contained in the abundance patterns. For sorneof these short-lived nuc1ci, experimental cross section studies aiming at a 5 to 10%uncertainty were recently suggested [28,291.

o The last terln denotes the stellar decay rate of the branch point isotope. While thereis no difference between the stellar ami the terrestrial rate for some of the brand!points, a variety of examples exhibit sometimes drastical changes under the hightemperatures aud densities of the stellar plasma. For the branchings at A = 147-149,thcsc effects are of millor importallcC [29].

Since the rclevant beta decay rates in Fig. 7 are not significantly affected by tem-perature, the branchings at A=147-149 can be used for obtaining an improved estimateof the s-process neutron density. Compared to the previous result of Winters el al. [201(J¡J = 0.92:l: 0.04), the measurement with the 4" l3aF2 detector yields a considerably moreprecise value, f¡J = 0.870:l: 0.009, with a 4 times smaller uncertainty [191.This branchingfactor implics a neutron density of "" = (3.8:l: 0.6) x 108 cm-3, in agreement with thepreviously estimated (3.4 :l: 1.1) x 108 cm-3 [7J.Along the s-process path there are ahout 15 to 20 significant branchings, which can be

studied with respect to the physical cOllditiolls at the stellar site. In a first step, the neutron

248 F. KAPPELER ET AL.

density must be obtained from those branchings which are not affected by temperature.\Vith this information, the effective branching factor of the remaining examples can bederived and the mean stellar decay rates be determined. Eventually, the dependence ofthese rates on temperature andfor electron density can then be used to estimate thes-process temperature and mass density [7].The present status of branching analyses is characterized by the neutron density from

the branchings of Fig. 7, Un = (3.8:!: 0.6) X 108 cm-3, and a mean temperature, T, =(3.1 :!: 0.6) x 108 K. A !irst attempt to determine the mass density in the s-process wascarried out by Beer et al. ¡3D] by analyzing a small branching to 163Ho. Their value,p, = (8:!: 5) x 103 gcm-J, is in reasonable agreement with stellar models for hclium shellburning ¡8,9].So far, the results from the different branchings are still consistent with each other.

This means that they still satisfy the assumption of the classical approach, that neutrondensity and temperature are constant during the s-process. In contrast, the stellar modelssuggest these parameters to vary strongly with time. Consequently, the freeze-out behaviorat the end of each neutron exposure may well cause a distortion of the abundance patternpredicted by the classical approach. Since these effects are still obscured by the presentuncertainties of the input data, future efforts have to concentrate on improving the relevantcross sections and beta decay rates, which characterize the various branchings.

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19.20.21.22.23.24.25.26.27.28.

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30.

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