The s-process

Even though in the example of a 3M0 star of Langer et al. (1999) the star evolves close to rigid rotation on the main sequence, the extreme expansion of the hydrogen-rich envelope and the compactness of the C/O-core on the AGB create an enormous shear at the core-envelope interface. While this remains without drastic consequences as long as active nuclear shell sources separate both regions well in terms of entropy, this is different during the thermal pulses where both nuclear shell sources are periodically switched off. 

By applying the concept of rotationally induced mixing as it has been developed for massive stars during the last years without alteration to a 3 Mq TP-AGB model sequence, Langer et al. (1999) obtained conditions which appear favourable for the development of the s-process, i.e. a 13C-rich layer which produces a considerable neutron flux later-on. 

The maximum 13C abundance and its distribution in the 3 M model is, at first, similar to that found due to diffusive convective overshooting by Herwig et al (1997). However, the rotational mixing spreads the 13C peak out before the neutrons are produced (cf. Fig. 13), which is not the case in the models of Herwig et al (1997). At the present time one can not discriminate which of these scenarios would agree better with empirical constraints. However, we want to stress that both mechanisms of 13C production, rotation and overshooting, do not exclude each other, and that it is possible that they act simultaneously in AGB stars. 

Finally, we want to emphasise that, although stars of less than 1.3 M lose 99% of their angular momentum due to a magnetic wind during their main sequence evolution, it can not be excluded that the proposed mechanism of 13C-production due to differential 

However, as pointed out by Rayet Hashimoto (2000), the metallicity dependence of the weak s-process production is not yet well understood — which may hamper an understanding of observed s-abundances in metal poor stars — due to nuclear physics and stellar structure uncertainties (cf. also Baraffe Takahashi 1993). 

A significant clue to the order of magnitude of neutron fluxes, temperatures and densities relevant to the s-process comes from the outcome of branchings, such as 

More detailed considerations (Kappeler, Beer Wisshak 1989) lead to a temperature range of up to 4 x 108K and neutron densities up to about 10s cm-3. 

Electron-density effects on fi-decay lifetimes also enable the total density to be placed in the range 2500 to 13 000 gm cm-3 all these parameters are characteristic of helium shell-burning zones as expected. 

The classical analysis of the s-process assumes a simple chain starting from 56Fe as the seed. The independent variable is the neutron irradiation , exposure or fiuence  

in a steady state, dNi/dt = 0, one has aN = const., which actually holds over considerable ranges of mass number (thus being usable as a local approximation), but not globally (except if r — oo) in particular, it breaks down near the magic numbers (see Fig. 6.3). 

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J. S. Spevack, The Concentration of Deuterium by the S-Process, ReportM-393, Columbia University, War Research Department, New York, Dec. 3,1942. 

Because of the long time scale involved in the s-process, unstable nuclides formed by (n.y) reactions have time to decay subsequently by decay (electron emission). The crucial factor in determining the relative abundance of elements... 

During the red giant phase of stellar evolution, free neutrons are generated by reactions such as C(a,n) and Ne(a,n) Mg. (The (ot,n) notation signifies a nuclear reaction where an alpha particle combines with the first nucleus and a neutron is ejected to form the second nucleus.) The neutrons, having no charge, can interact with nuclei of any mass at the existing temperatures and can in principle build up the elements to Bi, the heaviest stable element. The steady source of neutrons in the interiors of stable, evolved stars produces what is known as the "s process," the buildup of heavy elements by the slow interaction with a low flux of neutrons. The more rapid "r process" occurs in... 

Fig. 2-3 Schematic showing the path of the s process. The isotopes Xe, Xe, and Ce are beyond the reach of s process nucleosynthesis and are only produced by the r process.

Because the path of the s process is blocked by isotopes that undergo rapid beta decay, it cannot produce neutron-rich isotopes or elements beyond Bi, the heaviest stable element. These elements can be created by the r process, which is believed to occur in cataclysmic stellar explosions such as supemovae. In the r process the neutron flux is so high that the interaction hme between nuclei and neutrons is shorter that the beta decay lifetime of the isotopes of interest. The s process chain stops at the first unstable isotope of an element because there is time for the isotope to decay, forming a new element. In the r process, the reaction rate with neutrons is shorter than beta decay times and very neutron-rich and highly unstable isotopes are created that ultimately beta decay to form stable elements. The paths of the r process are shown in Fig. 2-3. The r process can produce neutron-rich isotopes such as Xe and Xe that cannot be reached in the s process chain (Fig. 2-3). 

Although the half-life of "Tc in steller interiors is remarkably decreased, a substantial amount of the isotope ean survive the s-process. Observations have revealed that more than 50 stars contain technetium in their outer envelope. According to other calculations, the production of neutrons in the competitive processes of neutron capture and / -decay is even more enhanced at such high temperatures, and this fact almost compensates for the depletion of "Tc [41]. 

Nowadays it is widely accepted that the 13C(a, n)160 reaction is the main source or neutrons of the s-process in AGB stars. Comparison between the s-element abundance patterns found in AGB stars of different classes and metallicity with theoretical predictions show a nice agreement (see e.g. Busso et al. 2001 and references therein). This comparison would indicate also that, at a given stellar metallicity, a dispersion in the quantity of 13C burnt may exists as one would expect, on the other hand. In fact, s-element patterns for individual stars can be fitted assuming that the amount of 13C burnt ranges from 10 7 to almost 10-5 Mq. However, the large error bar in the abundances precludes to put more... 

Fig. la shows the abundance ratio [Ba/Fe] for this sample as a function of [C/Fe]. Thirty stars (77% of the sample) have [Ba/Fe] > +0.7, while the others have [Ba/Fe] < 0.0. There is a clear gap in the Ba abundances between the two groups, suggesting at least two different origins of the carbon excesses. Ba-enhanced stars The Ba-enhanced stars exhibit a correlation between the Ba and C abundance ratios (Fig. la). This fact suggests that carbon was enriched in the same site as Ba. The Ba excesses in these objects presumably originated from the s-process, rather than the r-process, because (1) nine stars in this group for which detailed abundance analysis is available clearly show abundance patterns associated with the s-process [2], and (2) there is no evidence of an r-process excess in the other 21 objects. Hence, the carbon enrichment in these objects most likely arises from Asymptotic Giant Branch (AGB) stars, which are also the source of the s-process elements. 

Since most (if not all) low-metallicity objects that are currently observed in the halo are not in the AGB phase, material enriched in carbon and the s-process elements is assumed to have accreted from the companion AGB stars, which have already evolved to faint white dwarfs, to the surface of the surviving companion. This scenario is the same as that applied to classical CH stars [4], Unfortunately, long-term radial velocity monitoring has been obtained for only a limited number of objects a clear binarity signature has been established for six objects in our sample to date. However, there exists additional support for the mass-accretion scenario for the Ba-rich CEMP stars. Fig. lb shows [C/H] as a function of luminosity roughly estimated from the effective temperature... 

The data available so far show no evidence for a dependence of the s-process efficiency (traced by [Pb/Ba]) from metallicity (see Figure 1, left panel). Conversely, the state-of the art models (e.g. Busso et al. 2001) predict that, as the number of seed nuclei decreases with decreasing metallicity, the path of the s-process shifts more toward the third peak (e.g. Pb) with respect to the second peak (e.g. Ba). Thus an increase of [Pb/Ba] is expected as the metallicity lowers. 

Variations in star formation history should be imprinted on the s- and r-process ratios as well, however their interpretation can be more complicated because of uncertainties in their exact sources (and thus yields). Y and Ba trace the first and second peak in neutron magic number, respectively, and can be used to examine r-process yields in very metal-poor stars. However, they also have a significant contribution from the s-process in AGB stars, which dominates their production with increasing metallicity. Since AGB s-process yields are thought... 

AGB stars constitute excellent laboratories to test the theory of stellar evolution and nucleosynthesis. Their particular internal structure allows two important processes to occur in them. First is the so-called 3(,ldredge-up (3DUP), a mixing mechanism in which the convective envelope penetrates the interior of the star after each thermal instability in the He-shell (thermal pulse, TP). The other is the activation of the s-process synthesis from alpha captures on 13C or/and 22Ne nuclei that generate the necessary neutrons which are subsequently captured by iron-peak nuclei. The repeated operation of TPs and the 3DUP episodes enriches the stellar envelope in newly synthesized elements and transforms the star into a carbon star, if the quantity of carbon added into the envelope is sufficient to increase the C/O ratio above unity. In that way, the atmosphere becomes enriched with the ashes of the above nucleosynthesis processes which can then be detected spectroscopically. 

Stars of mass greater than 1.4 solar masses have thermonuclear reactions that generate heavier elements (see Table 4.3) and ultimately stars of approximately 20 solar masses are capable of generating the most stable nucleus by fusion processes, Fe. The formation of Fe terminates all fusion processes within the star. Heavier elements must be formed in other processes, usually by neutron capture. The ejection of neutrons during a supernova allows neutron capture events to increase the number of neutrons in an atomic nucleus. Two variations on this process result in the production of all elements above Fe. A summary of nucleosynthesis processes is summarised in Table 4.4. Slow neutron capture - the s-process - occurs during the collapse of the Fe core of heavy stars and produces some higher mass elements, however fast or rapid neutron capture - the r-process - occurs during the supernova event and is responsible for the production of the majority of heavy nuclei. 

Neutron capture processes give rise to the so-called magic-number peaks in the abundance curve, corresponding to closed shells with 50, 82 or 126 neutrons (see Chapter 2). In the case of the s-process, the closed shells lead to low neutron-capture cross-sections and hence to abundance peaks in the neighbourhood of Sr, Ba and Pb (see Fig. 1.4), since such nuclei will predominate after exposure to a chain of neutron captures. In the r-process, radioactive progenitors with closed shells are more stable and hence more abundant than their neighbours and their subsequent decay leads to the peaks around Ge, Xe and Pt on the low-A side of the corresponding s-process peak. 

Fig. 6.1. Part of the s-process path, showing some s-only nuclei (marked s ) and some branchings between n-capture and p -decay (shaded boxes), which give an idea of relevant neutron densities and temperatures. After Kappeler, Beer and Wisshak (1989). Copyright by IOP Publishing Ltd. Courtesy Franz Kappeler.

Planetary nebulae are often even more rich in carbon than cool carbon stars, and those classified by M. Peimbert as Type I are rich in nitrogen, indicating effects of hot-bottom burning in intermediate-mass progenitor stars. The s-process elements are not normally detectable in PN or their central stars, but a remarkable case is that of FG Sagittae, the central star of a fossil planetary nebula, which has cooled in the course of the twentieth century from around 25 000 K to around 5000 K at constant bolometric luminosity. This star suddenly showed an enhancement of s-process elements in its atmosphere between 1965 and 1972 (see Jeffrey Schoenberner 2006, and references therein). 

A separate neutron capture process is needed for neutron-rich nuclides by-passed by the s-process and for species above 209Bi. A possible path for this rapid or r-process is shown in Fig. 6.9. 

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