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

Abstract

The abundances of n-capture elements in the CEMP-r/s stars agree with predictions of intermediate n-density nucleosynthesis, at $N_{\mathrm{n}}\sim 10^{13}$-$10^{15}{\mathrm{cm}}^{-3}$, in rapidly-accreting white dwarfs (RAWDs). We have performed Monte-Carlo simulations of this i-process nucleosynthesis to determine the impact of (n,$\gamma$) reaction rate uncertainties of 164 unstable isotopes, from ${}^{131}$I to ${}^{189}$Hf, 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 $N_{\mathrm{n}}=3.16\times 10^{14}{\mathrm{cm}}^{-3}$ and $N_{\mathrm{n}}=3.16\times 10^{13}{\mathrm{cm}}^{-3}$ and on a multi-zone 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,$\gamma$) 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 discrepancies between the predicted and observed abundances of Ba and Pr in the CEMP-i star CS31062-050 are significantly diminished if the rate of ${}^{137}$Cs(n,$\gamma {)}^{138}$Cs is reduced and the rates of ${}^{141}$Ba(n,$\gamma {)}^{142}$Ba or ${}^{141}$La(n,$\gamma {)}^{142}$La increased. The uncertainties of temperature-dependent $\beta$-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 multi-zone Monte-Carlo simulations in reaction rate uncertainty studies if they use comparable values of $N_{\mathrm{n}}$ (abridged).

15 pages, 16 figures, 3 tables, accepted for publication in MNRAS

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