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1.3 The Local Abundance Distribution

Figure 1.4

Fig. 1.4. The ``local galactic'' abundance distribution of nuclear physics, normalised to 106 28Si atoms, adapted from Cameron (1982).

Fig. 1.4 shows the ``local galactic'' abundances of isobars, based on a combination of elemental and isotopic determinations in the Solar System with data from nearby stars and emission nebulae. These are sometimes referred to as ``cosmic abundances'', but because there are significant variations among stars and between and across galaxies this term is best avoided. The curve shows a number of features that give clues to the origin of the various elements:


Hydrogen is by far the most abundant element, followed fairly closely by helium. This is mainly formed in the Big Bang, with some topping up of the primordial helium abundance (Yp appeq 0.24) by subsequent H-burning in stars (Y appeq 0.28 here and now). Only a small fraction (Z appeq 0.02) of material in the ISM and in newly formed stars has been subjected to high enough temperatures and densities to burn helium.


The fragile nuclei Li, Be and B are very scarce, being destroyed in the harsh environment of stellar interiors although some of them may also be created there. (The lithium abundance comes from measurements in meteorites; it is still lower in the solar photosphere because of destruction by mixing with hotter layers below.) On the other hand, they are much more abundant in primary cosmic rays as a result of alpha - alpha fusion and spallation reactions between p, alpha and (mainly) CNO nuclei at high energies. The latter may also account for the production of some of these species in the ISM. Some 7Li (about 10 per cent) also comes from the Big Bang.


Although still more fragile than Li, Be and B, deuterium is vastly more abundant (comparable to Si and 5). D is virtually completely destroyed in gas recycled through stars and there are no plausible mechanisms for creating it there in such quantities, but it is nicely accounted for by the Big Bang. The observed abundance is a lower limit to the primordial abundance. The light helium isotope 3He is the main product when deuterium is destroyed and can also be freshly produced in stars. It has comparable abundance to D and some is made in the Big Bang, but in this case the interpretation of the observed abundance is more complicated.


Nuclei from carbon to calcium show a fairly regular downward progression modulated by odd:even and shell effects in nuclei which affect their binding energy (see Chapter 2). These arise from successive stages in stellar evolution when the exhaustion of one fuel is followed by gravitational contraction and heating enabling the previous ashes to ``burn''. The onset of carbon burning, which leads to Mg and nearby elements, is accompanied by a drastic acceleration of stellar evolution due to neutrino emission. This occurs because at the high densities and temperatures required for such burning, much of the energy released comes out in the form of neutrinos which directly escape from the interior of the star, relative to photons for which it takes of the order of 106 yrs for their energy to reach the surface. It is this rapid loss of energy that speeds up the stellar evolution (cf. Chapter 5).


The iron-group elements show an approximation to nuclear statistical equilibrium at a temperature of several x 109 K or several tenths of an MeV leading to the iron peak, This was referred to by B2FH as the ``e-process'' referring to thermodynamic equilibrium. Because the neutrinos escape, complete thermodynamic equilibrium does not apply here, but one has an approach to statistical equilibrium in which forward and reverse nuclear reactions balance. The iron peak is thought to result from explosive nucleosynthesis which may occur in one or other of two typical situations. One of these involves the shock that emerges from the core of a massive star that has collapsed into a neutron star; heat from the shock ignites the overlying silicon and oxygen layers in a Type II (or related) supernova outburst. Another possible cause is the sudden ignition of carbon in a white dwarf that has accreted enough material from a companion to bring it over the Chandrasekhar mass limit (supernova Type Ia). In either case, the quasi-equilibrium is frozen at a distribution characteristic of the highest temperature reached in the shock before the material is cooled by expansion, but the initial neutron-proton ratio is another important parameter. Calculations and observations both indicate that the dominant product is actually 56Ni, the ``doubly magic'' most stable nucleus with equal numbers of protons and neutrons, which later decays into 56Fe.


Once iron-group elements have been produced, all nuclear binding energy has been extracted and further gravitational contraction merely leads to photodisintegration of nuclei with a catastrophic consumption of energy. This is one of several mechanisms that either drive or accelerate core collapse. By contrast, the SN Ia explosion of a white dwarf simply leads to disintegration of the entire star. Consequently charged-particle reactions do not lead to significant nucleosynthesis beyond the iron group and the majority of heavier nuclei result from neutron captures. One or more such captures on a seed nucleus (in practice mostly 56Fe) lead to the production of a beta-unstable nucleus (e.g. 59Fe) and the eventual outcome then depends on the relative time-scales for neutron addition and beta-decay. In the slow or s-process, neutrons are added so slowly that most unstable nuclei have time to undergo beta-decay and nuclei are built up along the stability valley in Fig. 1.2 up to 209Bi, whereafter alpha-decay terminates the process. In the rapid or r-process, the opposite is the case and many neutrons are added under conditions of very high temperature and neutron density, building unstable nuclei up to the point where (n, gamma) captures are balanced by (gamma, n) photodisintegrations leading to a kind of statistical equilibrium modified by (relatively slow) beta-decays. Eventually (e.g. after a SN explosion), the neutron supply is switched off and the products then undergo a further series of beta-decays ending up at the nearest stable isobar, which will be on the neutron-rich side of the beta-stability valley (Fig. 1.5). Some species have contributions from both r- and s-processes, while others are pure r (if by-passed by the s-process) or pure s (if shielded by a more neutron-rich stable isobar); the actinides (U, Th etc.) are pure r-process products. A few species on the proton-rich side of the stability valley are not produced by neutron captures at all and are attributed to what B2FH called the ``p-process''; these all have very low abundances and are believed to arise predominantly from (gamma, n) photodisintegrations of neighbouring 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 (cf. 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.

Figure 1.5

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 beta-decay lifetimes for unstable ones. 116Sn is an s-only isotope, shielded from the r-process by 116Cd. After D.D. Clayton, WA. Fowler, TE. Hull & B.A. Zimmerman, Ann. Phys., 12, 331, ©1961 by Academic Press, Inc. Courtesy Don Clayton.

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