THE APPROACH TO NUCLEAR STATISTICAL EQUILIBRIUM

Abstract

The transformation of a region composed initially of ²⁸Si to nuclei in the vicinity of the iron peak, which is thought to take place in the late stages of evolution of some stars, is considered in detail. In order to follow these nuclear transformations, a nuclear reaction network is established providing suitable reaction links connecting neighboring nuclei. A method of solution of the network equations is outlined. Thermonuclear reaction rates for all neutron, proton, and alpha-particle reactions involving the nuclei in this network have been determined from a consideration of the statistical properties of nuclei. The evolution of this silicon region has been followed in time for two cases: T = 3 × 10⁹ °K, ρ = 10⁶ g cm⁻³ and T = 5 × 10⁹ °K, ρ = 10⁷ g cm⁻³. While both the observed solar and meteoritic abundances display a broad peak in the vicinity of iron, centered on ⁵⁶Fe, in these calculations ⁵⁴Fe is found to be the most abundant isotope in this mass range. Beta decays required to change the peak to ⁵⁶Fe are very slow. As the transformation 2 ²⁸Si → ⁵⁴Fe + 2p is endothermic by ~1.3 MeV, these results suggest that the silicon-to-iron conversion may not comprise an exothermic nuclear burning stage of stellar evolution.