Can COSI detect $\gamma$-ray lines from rare isotopes produced in the astrophysical intermediate neutron-capture process?

We investigate the nuclear $\gamma$-ray line emission from rare isotopes produced in the astrophysical intermediate neutron-capture process ($i$ process) and assess the prospects of observing these emissions with $\gamma$-ray telescopes. The astrophysical sites of the $i$ process remain uncertain, but two candidates with predicted rapid mass ejections at metallicities of stars in the solar neighborhood are post-asymptotic giant branch (post-AGB) stars, such as Sakurai's object (V4334 Sagittarii), and rapidly-accreting white dwarfs (RAWDs). Detailed 1D and 3D simulations indicate that the convective-reactive fluid dynamics responsible for $i$-process nucleosynthesis can lead to violent, non-radial outbursts resulting in mass ejections of $i$-process products. We calculate ejected yields of rare isotopes whose radioactive decays may produce detectable $\gamma$-ray lines, particularly in the 0.5-2 MeV range, focusing on $^{22}$Na, $^{89}$Sr, and $^{95}$Zr. We estimate the formation rates of these sources and the likelihood of detecting their $\gamma$-ray emissions within 1000 parsecs of the Sun. The probability of observing $i$-process emission lines during COSI's operational period is up to $\approx 1\%$, rising to $11\%$ for $^{89}$Sr if observed within a few days. Due to the long lifetime and large production of $^{22}$Na from proton-capture reactions its detection is more likely, with a probability of $\approx 5\%$. Future space missions could increase the observation probability to several tens of percent. Detection of long-lived neutron-rich isotopes such as $^{137}$Cs would provide the first direct $\gamma$-ray signature of intermediate neutron-density nucleosynthesis, distinguishing the $i$ process from classical s- and r-process pathways. (abridged)