i-process nucleosynthesis and mass retention efficiency in He-shell flash evolution of rapidly accreting white dwarfs

Based on stellar evolution simulations, we demonstrate that rapidly accreting white dwarfs in close binary systems are an astrophysical site for the intermediate neutron-capture process. During recurrent and very strong He-shell flashes in the stable H-burning accretion regime H-rich material enters the He-shell flash convection zone. $^{12}$C(p,$\gamma)^{13}$N reactions release enough energy to potentially impact convection, and i process is activated through the $^{13}$C($\alpha$,n)$^{16}$O reaction. The H-ingestion flash may not cause a split of the convection zone as it was seen in simulations of He-shell flashes in post-AGB and low-Z AGB stars. We estimate that for the production of first-peak heavy elements this site can be of similar importance for galactic chemical evolution as the s-process production by low-mass AGB stars. The He-shell flashes result in the expansion and, ultimately, ejection of the accreted and then i-process enriched material, via super-Eddington luminosity winds or Roche-lobe overflow. The white dwarf models do not retain any significant amount of the accreted mass, with a He retention efficiency of $\leq 10\%$ depending on mass and convective boundary mixing assumptions. This makes the evolutionary path of such systems to supernova Ia explosion highly unlikely.