We present photoionization cross sections for bromine and rubidium ions (including Br2+, Rb2+, Rb4+, Rb5+, and Rb6+) calculated with the R-matrix method. These calculations are part of a larger program to determine atomic data for low-charge Br and Rb ions in order to accurately derive the abundances of these elements in astrophysical nebulae. The orbital wavefunctions are an important ingredient to photoionization calculations. To determine these, we utilized the AUTOSTRUCTURE atomic structure code, which uses the configuration interaction approximation. The scaling parameters to the radial wavefunctions were optimized on the first ~10 term energies in LS coupling, in order to best reproduce experimental energies and ionization potentials from NIST. The R-matrix calculations were first carried out in LS coupling using a suite of FORTRAN routines from the UK-APAP group. To test the veracity of these results, we compared them against experimental photoionization cross section measurements conducted at the Advanced Light Source synchrotron radiation facility at Lawrence Berkeley National Laboratory in California. Once good agreement between the LS and experimental cross sections was found, the fully relativistic level-resolved cross section was calculated with the Breit-Pauli R-Matrix code. Overall, we find good agreement between our theoretical and experimental photoionization cross sections, typically to within 25-30% for direct photoionization. The experimental resonance structures are also reproduced well by our calculations. Our results provide key ingredients for modeling the ionization equilibrium of Br and Rb in astrophysical nebulae, which will enable accurate nebular abundance determinations of these elements for the first time. The atomic data will be applied to modeling planetary nebulae (ionized ejecta marking the death of 1-8 solar mass stars), which may be enriched in Br and Rb by neutron-capture nucleosynthesis in their progenitor stars. We gratefully acknowledge support from NSF award AST-1412928

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