The Equilibrium Distribution of Nuclides in Matter at High Temperatures

• Published in: Monthly notices of the Royal Astronomical Society 1965-01, Vol.129 (1), p.104-104
• Main Authors: Clifford, F. E., Tayler, R. J.
• Format: Article
• Language: English
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/129.1.104

At temperatures between 109 and 1010 °K and at suitable densities, nuclear reactions may become so profuse that approximate statistical equilibrium is set up between the concentrations of the different nuclides. Current theories of stellar evolution suggest that this equilibrium can be set up in stars and the resulting e-process elements may be distributed through space by a stellar catastrophe such as a supernova explosion. Complete statistical equilibrium between all the types of particles which occur in a star cannot be set up because the neutrinos, which occur in all β-decay reactions, have an effectively infinite mean free path. However, nuclear and electromagnetic interactions occur much more rapidly than β-decays and in a short time the nuclei and photons comes almost into equilibrium while the total numbers of protons and neutrons in the system are essentially constant. Subsequently β-decay reactions gradually change the relative proportions of protons and neutrons and, although the neutrino losses prevent true equilibrium, it is possible that the β-decays and inverse β-decays come into balance and that the ratio of the total number of protons to the total number of neutrons tends to a limiting value. In this paper calculations are reported for the whole range of values of the physical parameters which are thought to be important, at least in stellar interiors. Nuclidic abundances have been found as a function of three parameters: the density, the temperature and the ratio of the total number of protons to the total number of neutrons. In all, results have been obtained for 333 sets of values of the three parameters and detailed nuclidic abundances, before and after β-decay, are tabulated for 96 of these cases. The accuracy of the calculation is limited by the uncertainties of nuclear data. A detailed discussion is given of the possible size of errors arising from these uncertainties. It is also pointed out that, if the properties of only a few nuclides are shown to be seriously in error, it is a relatively simple matter to modify the tabulated results so that they are still solutions of the equilibrium equations but now refer to different values of the density and the ratio of total number of protons to total numbers of neutrons.