The r-process

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. 

For purposes of comparison with stellar abundances, it is useful to have the relative contributions of s- and r-processes to the various elements (as opposed to nuclides) in the Solar System, because in most cases only element abundances without isotopic ratios are available from stellar spectroscopy. At the same time, elements formed in one process may often be expected to vary by similar factors in the course of stellar and Galactic evolution, but to be found in differing ratios to elements formed in another process. Relative contributions are listed for some key elements in Table 6.3. 

Such neutron densities are presumably associated with very high temperatures, leading to reverse (y, n) reactions. At each Z, neutrons are added up to a so-called waiting point (which defines the r-process path) in the waiting-point approximation , (n, y) and (y, n) reactions balance, so that for given Z, there is a Saha-type equilibrium 

From time to time, a -decay occurs, increasing Z by 1 unit this leads to an increase in Q (corresponding to the increased distance above the neutron drip line) and consequently to further neutron captures until Q is again reduced to the appropriate value and a further fi-decay occurs. At the magic numbers, this leads to a vertical zig-zag track, paralleling the rise in the neutron drip line. Along this track, 

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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). 

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. 

A pre-supernova model of a 9Mq star is taken from Nomoto [3], which forms a 1.38 Mq O-Ne-Mg core. We link this core to a one-dimensional implicit La-grangian hydrodynamic code with Newtonian gravity. The equation of state of nuclear matter (EOS) is taken from Shen et al. [4]. We find that a very weak explosion results, where no r-processing is expected. In order to examine the possible operation of the r-process in the explosion of this model, we artificially obtain an explosion with a typical energy of 1051 ergs by application of a multiplicative factor (= 1.6) to the shock-heating term in the energy equation. 

We selected three stars with [Fe/H] < — 3, which were known to have [Ba/Fe] — 1, typical for their metallicities, and estimate Eu abundance using Subaru HDS. As shown in Fig. 1, our data add the lowest detections of Eu, at [Fe/H] < —3. The three stars and most others are located between the 50% confidence lines for this case. However, if Eu comes from more massive stars, these stars are located outside the 90% confidence region. We suggest, therefore, the r-process site is most likely to be SNe from low-mass progenitors such as 8 — 10M0 stars. 

Fig. 1. (left panel) [Eu/Fe] as a function of [Fe/H]. Gray-scale indicates predicted distribution of stellar fraction. The r-process site is assumed to be SNe of 8 — IOMq. The average stellar distributions are indicated by thick-solid lines with the 50% (solid lines) and 90% confidence intervals (thin-solid lines). The current observational data are given by large circles, with other previous data (small circles). 

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. 

Fig. 1.5. Paths of the r-, s- and p-processes in the neighbourhood of the tin isotopes. Numbers in the boxes give mass numbers and percentage abundance of the isotope for stable species, and /9-decay lifetimes for unstable ones. 116Sn is an s-only isotope, shielded from the r-process by 116Cd. After Clayton et al. (1961). Copyright by Academic Press, Inc. Courtesy Don Clayton.

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. 

The r-process path is terminated by (neutron-induced or yd-delayed) fission near A max = 270, feeding matter back into the process at around Amax/2, followed by recycling as long as the neutron supply lasts, assuming sufficient seed nuclei to start the process off. The number of heavy nuclei is thus doubled at each cycle, which could take place in a period of a few seconds, yd-delayed fission also occurs after freeze-out, when the yd-decay leaves nuclei with A > 256 or so with an excessive positive charge (see Eq. 2.90). 

The site of the r-process is also not clear, but it seems that the conditions needed to reproduce Solar-System r-process abundances may hold in the hot bubble caused by neutrino winds in the immediate surroundings of a nascent neutron star in the early stages of a supernova explosion (see Fig. 6.10). Circumstantial evidence from Galactic chemical evolution supports an origin in low-mass Type II supernovae, maybe around 10 M (Mathews, Bazan Cowan 1992 Pagel Tautvaisiene 1995). Another possibility is the neutrino-driven wind from a neutron star formed by the accretion-induced collapse of a white dwarf in a binary system (Woosley Baron 1992) leading to a silent supernova (Nomoto 1986). In stars with extreme metal-deficiency, the heavy elements sometimes display an abundance pattern characteristic of the r-process with little or no contribution from the s-process, and the... 

Fig. 6.10. Results of a dynamical calculation of the r-process in the hot neutrino bubble inside a 20 Mq supernova (continuous curve) compared to the observed Solar-System abundance distribution (filled circles). After Woosley etal. (1994). Courtesy Brad Meyer.

Modern dynamical calculations of the r-process are described by Cowan, Thielemann and Truran (1991ab), Takahashi, Witti and Janka (1994) and Woosley et al. (1994). Chen el al. (1995), Langanke and Wiescher (2001), Thielemann et al. (2001) and Kratz (2001) discuss the nuclear physics issues. Goriely and Arnould (2001) discuss the estimation of yields and their uncertainties. 

Fig. 8.35. According to their calculations, the efficiency of the s-process increases sharply as the metallicity decreases to about 0.1 solar, but thereafter decreases rapidly at still lower metallicities because of shortage of iron seeds and a relatively high amount of neutron poisons such as C, N and O. Thus below [Fe/H] = — 1 or so, heavy nuclei like Ba are predominantly due to the r-process and are assumed to track europium.

For Solar-System actinides, given a set of production ratios / , / p calculated from the theory of the r-process, one can use meteoritic abundance measurements to derive the observed quantities... 

Fig. 10.5. Logarithmic differential Th/Eu ratios plotted against stellar age. The crosses represent the average of two UMP r-process-rich stars CS 22892-052 and HD 115444 (Westin et al. 2000), and a third one BD +17° 3248 (Cowan et al. 2002) which are a kind of Rosetta stone for the r-process, assuming an age of 13 1 Gyr. Curves show predictions from various models discussed in the text.

The resulting dependences of [Th/Eu] on stellar age are shown in Fig. 10.5, together with a selection of observational data from del Peloso et al. for disk stars Westin et al. (2000) for two of the r-process enriched ultra-metal-poor (UMP) halo stars and Cowan et al. (2002) for a third one. The range among disk stars is little more than can be expected from uncertainties in the determination, while the UMP stars show more or less the expected deficiency. For BD +17 0 3248, Cowan et al. used theoretical production ratios for Th relative to Eu, Ir and Pt, based on certain nuclear models, to deduce a Galactic-model-independent age of 13.8 4 Gyr, which happens to fit our two production-ratio-independent model curves simple inflow and modFowler T = 15 quite nicely, but the error bars are large so that what we have is more a test of consistency than an independent chronometer. 

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