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The intermediate neutron capture process. VI. Proton ingestion and i-process in rotating magnetic asymptotic giant branch stars

The intermediate neutron-capture process (i-process) can occur during proton ingestion events (PIEs), which may take place in the early evolutionary phases of asymptotic giant branch (AGB) stars. We investigate the impact of rotational and magnetic mixing on i-process nucleosynthesis in low-metallicity, low-mass AGB stars. We computed AGB models with [Fe/H] = $-2.5$ and $-1.7$ and initial masses of 1 and 1.5 $M_{\odot}$ using the STAREVOL code, including a network of 1160 nuclei coupled to transport equations. Rotating models incorporate a calibrated Tayler-Spruit (TS) dynamo to account for core rotation rates inferred from asteroseismic observations of solar-metallicity sub-giants and giants. Initial rotation velocities of 0, 30, and 90 km s$^{-1}$ were considered, along with varying assumptions for magnetic mixing. We find that rotation without magnetic fields strongly suppresses the i-process due to the production of primary $^{14}$N, which is subsequently converted into $^{22}$Ne $-$ a potent neutron poison during the PIE. Including magnetic fields via the TS dynamo restores the models close to their non-rotating counterparts: strong core-envelope coupling suppresses shear mixing and prevents primary $^{14}$N synthesis, yielding i-process nucleosynthesis similar to non-rotating models. We also find that rotational mixing during the AGB phase is insufficient to affect the occurrence of PIEs. Proton ingestion event-driven nucleosynthesis proceeds similarly in asteroseismic-calibrated magnetic rotating AGB stars and non-rotating stars, producing identical abundance patterns.