The impact of (n,γ) reaction rate uncertainties of unstable isotopes on the i-process nucleosynthesis of the elements from Ba to W

The abundances of neutron (n)-capture elements in the carbon-enhanced metal-poor (CEMP)-r/s stars agree with predictions of intermediate n-density nucleosynthesis, at N_n ~ 10¹³-10¹⁵ cm^-3, in rapidly accreting white dwarfs (RAWDs). We have performed Monte Carlo simulations of this intermediate-process (i-process) nucleosynthesis to determine the impact of (n,γ) reaction rate uncertainties of 164 unstable isotopes, from ¹³¹I to ¹⁸⁹Hf, on the predicted abundances of 18 elements from Ba to W. The impact study is based on two representative one-zone models with constant values of N_n = 3.16 × 10¹⁴ and 3.16 × 10¹³ cm^-3 and on a multizone model based on a realistic stellar evolution simulation of He-shell convection entraining H in a RAWD model with [Fe/H] = -2.6. For each of the selected elements, we have identified up to two (n,γ) reactions having the strongest correlations between their rate variations constrained by Hauser-Feshbach computations and the predicted abundances, with the Pearson product-moment correlation coefficients |r_P| > 0.15. We find that the discrepancies between the predicted and observed abundances of Ba and Pr in the CEMP-i star CS 31062-050 are significantly diminished if the rate of ¹³⁷Cs(n,γ)¹³⁸Cs is reduced and the rates of ¹⁴¹Ba(n,γ)¹⁴²Ba or ¹⁴¹La(n,γ)¹⁴²La increased. The uncertainties of temperature-dependent β-decay rates of the same unstable isotopes have a negligible effect on the predicted abundances. One-zone Monte Carlo simulations can be used instead of computationally time-consuming multizone Monte Carlo simulations in reaction rate uncertainty studies if they use comparable values of N_n. We discuss the key challenges that RAWD simulations of i process for CEMP-i stars meet by contrasting them with recently published low-Z asymptotic giant branch (AGB) i process.