Nuclear reaction rate

The nuclear reaction rates and their uncertainties (at the time) are described in detail by... 

In principle these should be predictable from theory, but in practice there are many grey areas such as the effects of rotation, convective mixing, mass loss, the mechanism of stellar explosions, nuclear reaction rates such as 12C(a, y)160, the evolution of close binaries and the corresponding mass limits between which various things happen for differing initial chemical compositions. Figure 5.14 shows a version of what may happen in single stars with different initial masses and two metallicities, Z Z and Z Z /20. 

Reaction probabilities have been extensively measured in many laboratories all round the world, and in particular at the California Institute of Technology under the guidance of William Fowler. But whenever experimental data is lacking, nuclear reaction rates can be estimated theoretically. In this way, reaction rates have been fully tabulated as a function of temperature, ready to be integrated into numerical codes for stars or the Big Bang, and made available to the whole astrophysical community. 

The model Sun tells all. We may read off its temperature, density, chemical composition, luminosity and nuclear reaction rates at any depth and any stage of its evolution, from the youthful Sun, to its current middle age and forthcoming old age. The day-star has become limpid and with it every other star. 

We have to deal with two distinct sets of problems concerning (a) nuclear reaction rates, and (b) the mathematical treatment of convection. However, their effects are combined in the result. As an example, combined nuclear and convective uncertainties affect the size of the carbon - - oxygen core resulting from helium fusion as well as the ratio of carbon to oxygen within it. From there, they influence the ratio of the ashes of these elements and the mass of the iron core, which is a determining factor in the explosion. 

Figure 2-12 Nuclear reaction rates d[ He]/dtbyPPI and PPII chains as a function of temperature. The rmit of temperature is megakelvins (MK). The unit of the reaction rate is somewhat arhitraiy. The highest temf)erature in this calculation is 15.6 MK, roughly corresponding to the center temperature of the Srm. The concentrations of species used in the calculation of the reaction rates are the modeled species concentrations in the standard solar model (Bahcall, 1989).

Figure 2-12 Nuclear reaction rates, PP I chain versus PP II chain 155...

Stanfield S., Truran J. W., Wiescher M. C., and Sparks W. M. (1998) Evolutionary sequences for Nova V1974 Cygni using new nuclear reaction rates and opacities. Mon. Not. Roy. Astron. Soc. 296, 502-522. 

The primordial abundances of D, 3He, and 7Li(7Be) are rate limited, depending sensitively on the competition between the nuclear reactions rates and the universal expansion rate. As a result, these nuclides are potential baryometers since their abundances are sensitive to the universal density of nucleons. As the universe expands, the nucleon density decreases so it is useful to compare the nucleon density to that of the CMB photons r) = n /n7. Since this ratio will turn out to be very small, it is convenient to introduce... 

A nuclear reaction rate rxy between two kinds of particles is defined as... 

The amount of leO produced by a massive star depends strongly on a) the mass of the C/O-core at the time of iron core collapse and b) the C/O-ratio established in the C/O-core at core-He exhaustion. Both factors can be influenced in various ways. While the C/O-core mass is a strong function of the He-core mass and of the convection model, the C/O-ratio of core-He burning is sensitive to the 12C(a, y)160 nuclear reaction rate and — again — the employed convection model. While we postpone the discussion of the dependence of the 16 O yield on stellar wind mass loss to later, let us in the following compare the results of models where mass loss is unimportant. 

The C/O ratios in the most metal-poor galaxies are consistent with the predictions for massive star nucleosynthesis by Weaver Woosley (1993 hereafter WW93) for their best estimate of the 12C(a,7)160 nuclear reaction rate factor. On the other hand, the amount of contamination by C from intermediate mass stars is poorly known in these galaxies. 

The rate of the reaction is modulated by controlling the number and energy of the neutrons allowed to stay in the uranium filled core of the reactor. Control rods are used to modulate the nuclear reaction rate. Control rods are made from an element (cadmium metal is often used) that strongly adsorbs neutrons. The rods are installed in channels in the reactor. When the rods are fully inserted in the reactor, so many neutrons are adsorbed that little reaction can occur. As the rods are withdrawn, more and more neutrons can react and the reactions begin. The reaction rate is controlled by the depth and number of rods inserted in the reactor. 

In situations where the abundances of individual elements or nuclides are important (e.g. nuclear reaction rates), relative abundances by mass will be given as x, where i is either the atomic number, or denotes the nuclide in some other distinct way. Values for the Sun are given in Table 1 errors on the last digits are shown in parentheses. Table 2 provides constants used throughout the text and enables many equations to be evaluated. 

Part II deals with explosive nucleosynthesis that plays a critical role in cosmochemistry. The lectures by Kamales Kar provide essential background material on weak-interaction rates for stellar evolution, supernovae and r-process nucleosynthesis. He also discusses in detail the solar neutrino problem. Massive stars, their evolution and nuclear reaction rates from the point of view of astronomers and nuclear physicists are discussed by Alak Ray. His lectures also describe the various stages of hydrostatic nuclear fuel burning with illustrative examples of how the reactions are computed. He also discussed core-collapse (thermonuclear vs. core-collapse) and supernovae in brief. The lectures by Marcel Arnould address the phenomena of evolution of massive stars and the concomitant non-explosive and explosive nucleosynthesis. He highlights a number of important problems that are yet unresolved but crucial for our understanding of Galactic chemical evolution. The p-process nucleosynthesis attributed to the production of proton-rich elements, a topic of great importance but yet less explored is also discussed in his lectures. 

Table 3.13 gives effective cross sections for thermal neutrons and other nuclear properties of the materials in the core of this reactor. These effective cross sections have been calculated by the procedure recommended by Westcott, which has been outlined in Chap. 2, from data provided by Westcott [W3] and Critoph [Cl]. To obtain appropriate nuclear reaction rates, these effective cross sections are to be multiplied by the thermal-neutron flux, wmb. where Hub is density of neutrons in the Maxwell-Boltzmann part of the spectrum and C is the average speed of the Maxwell-Boltzmann neutrons. 

There is little sensitivity here to the actual nuclear reaction rates, which are important in determining the other left-over abundances D and He at the level of a few times 10 by number relative to H, and Li/H at the level of about... 

In addition to the above tools, we are developing other tools related to Galactic chemical evolution. These include a Nuclear Reactions Tool, a Nuclear Network Tool, and a Stellar Ejecta Tool. The Nuclear Reactions Tool will help users calculate nuclear reaction rates and help organize, view, and sort many of the common parameters need for these calculations. The Nuclear Network Tool will provide an easy way to evolve a system of species through time for a given environment s temperature and pressure. The features of the Stellar Ejecta Tool are designed to help a user understand the isotopic anomalies found in primitive meteorites or presolar grains. The Stellar Ejecta Tool will provide an easy way to view the isotopic abundance of a star s ejecta, run a nuclear decay network on this material, and then mix it with a second distribution of isotopic abundances. In this way it can simulate systems such as a late injection of material into the early solar nebula. When these tools are released, we will announce them over the Webnucleo mail list (see below). 

The nuclear reaction rates (cross section) for the reactions specified in Fig. 12.4 are well determined, also at the interaction energies relevant to primordial nucleosynthesis, which are comparatively low by nuclear physics standards. Thus, once the initial conditions are determined, the evolution of the different species with time and the final abundances can be calculated with high accuracy. The only open parameter in the standard Big Bang nucleosynthesis model is 77. Since the baryon density is proportional to rj and the reaction rates are density dependent, the final abundances will also depend on the choice of 77. 

A detailed introduction to stellar evolution is given in the following hooks Clayton (1984), Hansen and Kawaler (1994), Kippenhahn and Weigert (1994), PhiDips (1994), Tayler (1994). Books and reviews discussing stellar nucleosynthesis are RoUs and Rodney (1988), Arnett (1996), Thielemann et al. (2001h). Tables of nuclear reaction rates and cross sections can be found in Rauscher and Thielemann (2000). 

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