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

The anomalous abundances of n-capture elements in the CEMP-r/s stars agree in many instances very well with simulation predictions of intermediate n-density nucleosynthesis, $N_\mathrm{n}\sim 10^{13}$ - $10^{15} \mathrm{cm}^{-3}$, in rapidly-accreting white dwarfs (RAWDs). We have performed Monte-Carlo simulations of this i-process nucleosynthesis in order to determine the impact of (n,$\gamma$) reaction rate uncertainties of 164 unstable isotopes, from $^{131}$I to $^{189}$Hf, on the prediction of abundances of 18 elements from Ba to W. The impact study is based on two representative one-zone models with constant values of $N_\mathrm{n} = 3.16\times 10^{14}\ \mathrm{cm}^{-3}$ and $N_\mathrm{n} = 3.16\times 10^{13}\ \mathrm{cm}^{-3}$ and on a multi-zone simulation based on a realistic stellar evolution model 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,$\gamma$) 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 $|r_\mathrm{P}| > 0.15$. We find that the possible discrepancies between the predicted and observed abundances of Ba and Pr in the CEMP-r/s star CS31062-050 could be significantly diminished if the rate of the reaction $^{137}$Cs(n,$\gamma)^{138}$Cs were reduced and the rates of $^{141}$Ba(n,$\gamma)^{142}$Ba or $^{141}$La(n,$\gamma)^{142}$La increased. (abridged)