Thermalization of long-lived nuclear isomeric states under stellar conditions

We examine the various paths and mechanisms by which the isomeric states of nuclei that are formed during nucleosynthesis are brought into statistical thermal equilibrium with their ground states. Simple two- and three-level systems which can be solved algebraically are initially studied. and a more generalized technique is presented for numericaLly studying the approach to internal thermal equilibrium of the ground and isometric states in many key nuclei with special emphasis on 26Al. In particular, regimes characterized by specified time scales and temperatures are studied in which (i) the ground state and the isomer may be taken to be in a thermal mixture, or (ii) the ground state and the isomer must be treated as separate nuclear species. The thermal equilibrium time scales are calculated as a function of stellar temperature for given initial rates at which the isomer and the ground state are populated by their source reaction. By separating the internal details of production and equilibration, these time scales can then be compared to the leakage rates out of the nucleus due to beta decay and any other nuclear destruction rates for a given astrophysical environment