Nuclear statistical equilibrium

The a-process Could the low [a/Fe] and low [Y/Eu] ratios in dSph stars be related by the a-process The a-process (or a-rich freeze out) occurs when a neutron-rich, a-rich gas is out of nuclear statistical equilibrium and is thought to be important in the formation of 44Ca (Woosley Weaver 1995), 48Ti (Naka-... 

Fig. 4.2. Evolution of light-element abundances with temperature, for rj io = 3.16. The dashed curves give the nuclear statistical equilibrium abundances for 4He, 3He, 3H(t) and 2D(d) respectively the dotted curve for 2D allows for the diminishing number of free neutrons. After Smith, Kawano and Malaney (1993). Courtesy Michael Smith.

As a partial summary, in normal C3 V inclusions material from the neutron-rich nuclear statistical equilibrium nucleosynthetic process is in excess relative to the average solar system composition, as well as an O-rich component. Nevertheless, the exact composition of this material is somewhat blurred by secondary processes (nebular or interstellar) as the observations show no strict interelement correlation (Jungck et al. 1984 Birck and Lugmair 1988). 

As for Allende s inclusions, variable contributions of a component produced in neutron-rich nuclear statistical equilibrium best explains the Ti- Ca data. Some parts of the solar nebula were depleted in these isotopes as deficits are also seen. There are several possibilities for explaining the variations in Ti. 1) The neutron-rich component itself may be heterogeneous and incorporate locally less neutron-rich statistical equilibrium products (Hartmann et al. 1985). 2) Ti may result from another process like explosive Si or He burning (Clayton 1988). This component would be associated with the neutron-rich component but not completely homogenized. In all cases, carriers are solid grains which may have behaved differently than the gaseous nebula during the formation of the solar system. A minimum number of components may be calculated to account for the Ca and Ti isotopic data, which number up to 3 (Ireland 1990) but to be conservative at the 5ct level, clearly resolved effects are present only on 3 isotopes ( Ca, Ti, Ti). 

Chromium. The isotopic heterogeneity is limited to this isotope which can be compared with the normal refractory inclusions of Allende. Both Cr dehcits and excesses are formd ranging from -7.6 e to +210 e (Fig. 8b). The fractions showing the highest enrichment in Cr with no correlated effects in Cr, Cr, Cr points towards a nucleosynthetic component, which is 99% pure in Cr. This component is probably the same as the component found in the CV3 inclusions, and which is produced in a neutron-rich nuclear statistical equilibrium in presupemova massive stars. 

Figure 8. Figure (a) after Clayton et al. (1976, 1977). The scales are as in Figure 1. The O isotopic compositions of the different meteorite classes are represented ordinary chondrites (H, L, LL), enstatite chondrites (EFl, EL), differentiated meteorites (eucrites, lAB irons, SNCs) and some components of the carbonaceous chondrites. As the different areas do not overlap, a classification of the meteorites can be drawn based on O isotopes. Cr (b) and Mo (c) isotope compositions obtained by stepwise dissolution of the Cl carbonaceous chondrite Orgueil (Rotaru et al. 1992 Dauphas et al. 2002), are plotted as deviations relative to the terrestrial composition in 8 units. Isotopes are labeled according to their primary nucleosynthetic sources. ExpSi is for explosive Si burning and n-eq is for neutron-rich nuclear statistical equilibrium. The open squares represent a HNOj 4 N leachate at room temperature. The filled square correspond to the dissolution of the main silicate phase in a HCl-EIF mix. The M pattern for Mo in the silicates is similar to the s-process component found in micron-size SiC presolar grains as shown in Figure 7.

Most of the Cr found in the solar system is produced in presupemova neutron-poor nuclear statistical equilibrium as Mn which then decays to Cr (Hainebach et al. 1974 Hartmann et al. 1985). The first evidence for the presence of Mn in the early solar system... 

Another important reaction chain for future phases, including the final nuclear statistical equilibrium (see below), is one which enhances the neutron content... 

Any attempt to understand the conditions in which iron and its kin were created, and identify the astrophysical site of their birth, must focus on the idea of nuclear statistical equilibrium. The situation is the exact nuclear analogy of the ionisation equilibrium occurring in hot gases. 

Fig. A3.1. Binding energy per nucleon in symmetric nuclei (Z = N) and asymmetric nuclei (0.86 < Z/N < 0.88). Ni is the most tightly bound nucleus with an equal number of protons and neutrons, whilst Fe is the strongest nucleus with Z/N = 0.87. Nuclear statistical equilibrium favours Fe if the ratio of neutrons to protons is 0.87 in the mixture undergoing nucleosynthesis. In fact nature seems to have chosen to build iron group nuclei in a crucible with Z = N.

We know today that nuclear statistical equilibrium in a neutron-poor environment (p/n = 1.01), dominated by nickel-56 rather than iron-56, gives a good overall explanation of the abundance table in the neighbourhood of the iron peak. This is a natural consequence of high-temperature combustion. The corresponding combustion times are... 

Ca) (iii) the nuclear statistical equilibrium peak at the position of Fe and (iv) the abundance peaks in the region past iron at the neutron closed shell positions (zirconium, barium, and lead), confirming the occurrence of processes of neutron-capture synthesis. The solar system abundance patterns associated specifically with the slow (s-process) and fast (r-process) processes of neutron capture synthesis are shown in Figure 2. 

A representative nucleosynthesis calculation for such a type la supernova event is shown in Figure 6. Note particularly the region of mass fraction between — 0.2M and 0.8M , which is dominated by the presence of Ni, is in nuclear statistical equilibrium. It is this nickel mass that is responsible—as a consequence of the decay of Ni through Co to Fe—for the bulk of the luminosity of type la supemovae at maximum... 

Table 1. The 25 most abundant nuclei, and the processes which formed them. Here, NSE refers to nuclear statistical equilibrium (cf. Clayton, 1968) which occurs in explosive burning at high temperature, producing iron group nuclei. ...

It was first seen that (n, 7) -> (7, n) equilibrium is obtained at T> 2 x 109 K and N > 102° cm-3 [37]. Later network calculations get the equilibrium at neutron density of 102° cm-3 for temperatures 2 x 109 K and at a density of 1028 cm 3 for half the temperature. One also notes that at temperatures greater than 6 x 109 K Nuclear Statistical Equilibrium (NSE) is achieved where the forward strong and electromagnetic reactions are balanced by their reverse reactions. 

Co(ti/2 = 18 hr) are produced in explosive, incomplete Si burning as well as in normal freezeout of nuclear statistical equilibrium, in the inner ejecta of core collapse supernovae. However, no evidence of the 5.9 keV line emission from Mn could be found in 400 ks of Chandra ACIS data and the upper limit to the mean flux was < 3 x 10-7 cm-2s-1. Rauscher et al. [148] calculated the ejected mass of A = 55 radioactive nuclei to be 7.7 x 10 4 M for 20M models of which most was 55 Co. If only about half this mass of55Fe were ejected, the reduced flux would be consistent with the observed upper limit. On the other hand, even if the total mass inside were as much as 1 x 10-3 M , but the 55 Fe abundance was zero outside the radial velocity shells at 1500 kms-1, the line flux would be still consistent with data, as at late times the emerging flux depends sensitively on the presence of 55Fe in the outer zones. 

In associating the r-process with supernova explosions, several attempts to go beyond the canonical and MER models have been made by taking into account some evolution of the characteristics of the sites of the r-process during its development. These models are coined dynamical (DYR) in the following in order to remind of the time variations of the thermodynamic state of the r-process environment (see [24] for references). These models do not rely on any specific explosion scenario. They just assume that a material that is initially hot enough for allowing a nuclear statistical equilibrium (NSE) to be achieved expands and cools in a prescribed way on some selected timescale. This evolution is fully parameterized. 

The elements of the iron peak group provide information on the late evolution of massive stars by nuclear statistical equilibrium processes. Any isotopic anomalies found in these elements would reflect variations in the quasi-equilibrium conditions of stellar interiors, provided that the isotopic... 

Figure 4 shows the isotopic anomalies of the iron peak elements predicted by the multi-zone mixing model as compared with the average excesses as observed in Ca-Al-rich inclusions. The match between the two data sets is impressive, except for Fe and Zn. In the case of Fe no significant anomalies have been measured, but the multi-zone mixing model only predicts a Fe excess of approximately 1 part in 10", which is at the limit of present mass spectrometric capability. In the case of Zn, the excess in Zn is approximately an order of magnitude less than that expected. This can be explained in terms of the volatility of Zn with respect to the other iron peak elements, as it would be the last of these elements to condense from the expelled stellar material. The correlation between anomalies in neutron-rich isotopes in the iron peak elements can therefore be explained in terms of the nuclear statistical equilibrium processes, which took place at a late stage in the evolution of massive stars. 

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