Internal equilibration of a nucleus with metastable states:: 26Al as an example -: art. no. 025805

In many isotopes important to nucleosynthesis theory there exists a low-lying metastable state whose deexcitation to the ground state is strongly inhibited by a large angular momentum difference. In a stellar plasma, the equilibration of the ground and metastable states of such nuclei proceeds primarily via indirect transitions that involve upper-lying levels. We present a mathematical technique to follow these multistep transitions. Under the crucial assumption that the abundances of the upper-lying levels are in a steady-state abundance distribution. our method abstracts away all the higher-lying excited states allowing the isotope in question to be represented as a two-state system with transitions between these two states. The two states are properly not the ground and metastable states themselves but rather two ensembles of states. one tied to the ground state and one tied to the metastable state. We show how to compute effective rates into and out of these ensembles and between them. as well as how to identify the dominant pathways. This allows such nuclei to be treated in a simple, straightforward, and accurate fashion in nucleosynthesis networks. The specific example of Al-26, including its effective beta-decay lifetime, is considered in detail.