Nuclear Astrophysics I

In certain isotopes, the probability of direct transition between the ground state and the isomeric metastable is very low. When the ground and isomeric state do not equilibrate in an astrophysical plasma, the isomer is termed an “astromer” (ApJS. 252.1 (2020): 2) and abundance predictions from reaction network calculations differ from those in which internal equilibration of the nucleus is assumed. In this work, we adopt a directed graph (digraph) treatment to understand the internal equilibration rates of astromers. Gupta and Meyer (Phys. Rev. C, 64(2):025805, 2001) presented an approach to include the isomers as two separate species in a reaction network with rates of transition between them and between them and the rest of the species in the network. In our approach, we abstract the isotope to a directed graph, and by employing the matrix-tree and matrix-forest theorem (as given in arXiv:2309.05827, 2023), we calculate abundances and internal transition rates as the ratio of the weights of spanning branchings. These results give a new computational treatment of isomerization rates in nuclei and generalize the Gupta-Meyer approach, thereby allowing application to other similar systems.