Analytic Solutions for s-Process and i-Process Nucleosynthesis and Neutron Bursts

The s process, the i process, and neutron bursts are neutron-capture processes in which the temperature is typically too low to allow for photo-disintegration reactions. Nuclei are only produced by neutron-capture reactions and beta decays, and the network flow among the heavy nuclei is strictly one in which a nuclide transmutes into another nuclide with greater mass or charge. In such a case, the reaction network can be represented as a directed acyclic graph. We provide solutions to such networks in the case of constant temperature and neutron density. These solutions require sums over paths between pairs of species in the network, and we briefly discuss how such sums could be implemented. Our solutions will provide insights into nucleosynthesis relevant for isotopic abundances in meteoritic presolar grains and elemental abundances in extremely metal-poor stars.