Observational signatures and constraints on the intermediate neutron-capture psrocess. The case of the carbon-enhanced metal-poor star TYC 6044-714-1 (RAVE J094921.8-161722)

Observational abundances of carbon enhanced metal-Poor (CEMP) stars with patterns in between those produced by the rapid (r) and slow (s) nucleosynthesis processes ( CEMP-rs stars) are currently invoked as evidence of synthesis via the intermediate (i) process in the early AGB evolutionary phase of metal-poor low-mass stars. Nevertheless, discriminating between r+s- and i-process hypotheses requires high-precision abundances obtained through advanced spectral modelling techniques. Theoretical models of the i-process have become more robust, incorporating refined stellar modelling and nuclear reaction physics, providing ranges of probable elemental abundances and isotopic ratio predictions to be confronted with observational determinations. We performed a new analysis of a high-resolution and high-signal-to-noise UVES spectrum of TYC 6044-714-1, one of the best-studied CEMP-rs stars. We derived accurate effective temperature ( and highly precise atmospheric parameters, element abundances, and isotopic ratios using state-of-the-art one-dimensional non-local thermodynamic equilibrium (1D non-LTE) and three-dimensional non-LTE (3D non-LTE) spectral line modelling. Using the latest AGB nucleosynthesis models computed with the FuNS evolutionary code, we assessed the possibility of the i-process to act aside the s-process. We find that TYC 6044-714-1 was likely born as a normal in situ halo star about 13 Gyr ago, pre-enriched by the r process through a standard Galactic chemical-evolution pathway. Among the explored scenarios, the s$+r model provides the best overall reproduction of the observed heavy-element abundance pattern and Ba isotopic ratios, yielding excellent agreement across all three s-process peaks. While i+s+$r models with increasing overshooting efficiency improve the fit for specific elements -- particularly Nb and those between the first and second neutron-capture peaks -- they do not consistently reproduce the full abundance pattern. Although the i+s+r models achieve statistical fits comparable to the s+r case, they require extreme and physically implausible conditions, and predict s-process Ba fractions inconsistent with those inferred from isotopic ratios of the 4934 Å resonance line. We therefore conclude that the pure s+r scenario is the most plausible explanation.