Astrophysical sites of the intermediate neutron-capture (i) process

The i-process operates at neutron densities $n_n \sim 10^{13} \text{ to } 10^{16}\,\mathrm{cm}^{-3}$, between the s-process ($\sim 10^{7} \text{ to } 10^{10}\,\mathrm{cm}^{-3}$) and the r-process ($> 10^{20}\,\mathrm{cm}^{-3}$), and is invoked for carbon-enhanced metal-poor stars with mixed s and r signatures, Sakurai's object and some presolar grains. Identify which candidate sites (proton ingestion into helium-flash convective zones of low-metallicity AGB and super-AGB stars, rapidly accreting white dwarfs, helium shells of massive stars) produce the observed $[\mathrm{Ba}/\mathrm{La}]$, $[\mathrm{La}/\mathrm{Eu}]$ and $[\mathrm{Ba}/\mathrm{Eu}]$ ratios, and with what neutron exposure, given the large uncertainties in neutron-capture rates on unstable nuclei near $A \sim 130 \text{ to } 140$.

Multidimensional hydrodynamic models of proton ingestion that yield the neutron exposure without free parameters, combined with measured or constrained capture rates on the key unstable isotopes, reproducing the abundance patterns of i-process stars.