Atomic Data Calculations for Au I - III and Exploration in the Application of Collisional-Radiative Theory to Laboratory and Neutron Star Merger Plasmas

Neutron binary star mergers have long been proposed as sufficiently neutron rich environments that could support the synthesis of rapid neutron capture elements (r-process) elements such as gold. However, the literature reveals that beyond neutral and singly ionised systems, there is an incompleteness of atomic data for the remaining ion stages of importance for mergers. In this work we report on relativistic atomic structure calculations for Au~I-III using the GRASP$^0$ codes. Comparisons to calculations using the Flexible Atomic Code suggest uncertainties on average of 9.2\%, 5.7\%, and 3.8\% for Au~I-III level energies. Agreement around $\sim$50\% is achieved between our computed $A$ values and those in the literature, where available. Using the GRASP$^0$ structure of Au~I, we calculated electron impact excitation rates coefficients and use a collisional-radiative model to explore the excitation dynamics and line ratio diagnostics possible in NSM environments. We find that proper accounting of metastable populations is critical for extracting useful information from UV-VIS line ratio diagnostics of Au~I. As a test of our data, we applied our electron impact data to study a gold hollow cathode spectrum in the literature and diagnosed the plasma conditions as $T_\textrm{e} = 3.1\pm1.2$~eV and $n_\textrm{e} = 2.7^{+1.3}_{-0.9}\times10^{13}$~cm$^{-3}$.