Annu. Rev. Astron. Astrophys. 1994. 32: 153-90 Copyright © 1994 by Annual Reviews. All rights reserved

4.2. s-Process Sites

To obtain a good fit of the N curve to the solar system s-process abundance distribution, three distinct exponential distributions of neutron exposures may be necessary (Clayton & Rassbach 1967, Clayton & Ward 1974). One exposure, with ₀ 0.30 mb^-1, produces most of the nuclei in the mass range 90 < A < 204. This is the main component. Another exposure, with ₀ 0.06 mb^-1 contributes to the A 90 s-nuclei abundances. This weak component is required in order to explain the N curve around A ~ 90. These two components indicate that two separate sites contributed to the abundance of solar s-nuclei. Finally, a strong component, with ₀ 7.0 mb^-1, may be necessary to explain the abundances of the A = 204 - 209 nuclei. One possible explanation of this component is that the distribution of exposures in the main component is not exactly exponential, but rather is higher than exponential at larger. There is probably no need for a separate site for the strong component of the s-process.

The weak s-process component likely comes from He burning in the cores of massive stars ( 15M) (Truran & Iben 1977, Lamb et al 1977), where the temperature is high enough for the ²²Ne(, n)²⁵Mg reaction to produce a substantial amount of neutrons. These stars also have strong winds that eject this material into the interstellar medium. Recent work has confirmed the plausibility of this site (Arnett & Thielemann 1985, Busso & Gallino 1985, Prantzos et al 1987, Langer et al 1989, Raiteri et al 1991a, Baraffe et al 1992). Uncertainties in the ²²Ne(, n)²⁵Mg and ²²Ne(, ) ²⁶Mg reaction rates prevent us from predicting the neutron exposure in these models to high accuracy. Recent results on these rates may indicate that the s-process is somewhat more robust in this site than previously thought (e.g. Baraffe & El Eid 1994). This may complicate the separation of the A 90 s-nuclei into those coming from the weak and main components.

Some s-processing may also occur in core carbon burning or shell helium burning in massive stars. This has been studied by Arcoragi et al (1991) and Raiteri et al (1991b). The results indicate that this processing does not contribute in a significant way to the weak component.

The main component of the s-process is likely to occur in the helium-burning shell in asymptotic giant branch (AGB) stars (Weigert 1966, Schwarzchild & Harm 1967, Ulrich 1973). The structure of such a star is an inert carbon-oxygen core, on top of which lies a convective helium-burning shell. On top of this helium-burning shell is the hydrogen-rich envelope, which itself is convective. The original idea was that the convective helium shell might reach out far enough into the hydrogen-rich envelope that protons and ¹²C (the result of helium burning) could mix and produce ¹³C, as discussed in Section 4.1. The ¹³C would then be the source of neutrons for the s-process. [The current picture is that convection does not provide the mixing, but that protons reach down into the carbon-rich shell by diffusion or semiconvection (see below).]

An attractive feature of this model is the fact that the helium burning occurs in pulses. Between pulses, hydrogen burns quiescently in a thin shell. Once the supply of helium from the hydrogen burning builds up. a helium-burning pulse occurs. The energy liberated expands the star and shuts off the hydrogen burning. After the pulse has occurred, the star settles down again and begins hydrogen-shell burning anew. Pulses last of order tens of years while the interpulse periods are of order thousands of years. The significance for the s-process is that there is an overlap of mass zones experiencing successive helium-burning pulses. Ulrich (1973) was able to show that the mixing and burning sequence could naturally give rise to an exponential distribution of neutron exposures. Alternating overlap of convection zones can carry the newly produced s-nuclei into the envelope (the so-called "third dredge up"). These nuclei would then find their way into the interstellar medium via winds or by the ejection of the atmosphere in a planetary nebula phase.

This nice model for the s-process suffered a setback when Iben showed that an entropy barrier prohibited mixing of protons into the helium shell (Iben 1975a, b, 1976). It was then proposed instead that ²²Ne(, n)²⁵Mg be the source (e.g. Iben & Renzini 1983). The helium core grows by accreting the ashes of the hydrogen-burning shell. The products of CNO burning are ⁴He and ¹⁴N in that shell, which combine to give ²²Ne early in helium burning, as discussed in Section 4.1. The ²²Ne(, n)²⁵Mg reaction then drives the s-process. The pulse and mixing that occurs gives an exponential distribution of neutron exposures. This model has some difficulties, however. Basically, the shell flashes in most AGB stars are not hot enough to liberate most of the ²²Ne neutrons, and the massive ABG stars that are hot enough are too rare. This has led workers to consider alternative neutron sources in low-mass AGB stars (M < 3M).

In low-mass AGB stars, the temperature is too low in the helium-burning shell for the ²²Ne(, n)²⁵Mg reaction to be the major source of neutrons. Iben & Renzini (1982) argued, however, that, despite the entropy barrier to convection, semiconvection or diffusion could cause the mixing of protons with ¹²C in the interpulse period. This produces pockets of ¹³C atop the He zones which can liberate neutrons during convective ingestion by the next pulse. Recent work indicates that this is a promising site for the s-process (Gallino et al 1988; Boothroyd & Sackmann 1988a, b, c, d; Hollowell & Iben 1988; Kappeler et al 1990). In particular, these models seem to give a good fit to the main component of the solar N curve (e.g. Kappeler et al 1990). We must note that these s-process calculations are post-processing calculations, which means that the neutron density is a parameterized quantity. Even more serious is the lack of a demonstrated occurrence of the needed ¹³C-rich pocket, which is therefore taken on faith at the present time. It remains to be seen whether the good agreement with the solar s-process abundances will hold up when the s-process calculations are directly coupled to complete stellar models. Such coupled calculations may be available in the not-too-distant future. It will also be important to include the effects of energy generation by all the nuclear reactions on the stellar structure (Bazan & Lattanzio 1993).