Monte Carlo rate uncertainty of the $^{8}$Li(n,$γ$)$^{9}$Li reaction within $R$-matrix framework

Abstract

The $^{8}$Li$(n,γ)^{9}$Li reaction is considered significant for the synthesis of nuclei beyond the $A=8$ stability gap in inhomogeneous big-bang nucleosynthesis models, as well as in $r$-process nucleosynthesis scenarios. However, direct measurement of this reaction is precluded by the short half-life of $^{8}$Li and the absence of a neutron target. Consequently, existing reaction rate estimates based on indirect experimental methods and theoretical calculations differ by orders of magnitude. In the present work, the $^{8}$Li(n,$γ$)$^{9}$Li neutron-capture cross section and the corresponding thermonuclear reaction rate are evaluated within a phenomenological $R$-matrix framework, including both non-resonant direct capture (DC) and resonant capture through the $5/2^{-}$ state at $E_{x} = 4.30$~MeV. The uncertainties associated with the $R$-matrix input parameters are propagated using Monte Carlo sampling, while the sensitivity to the channel radius is treated as an $R$-matrix model uncertainty. The effective total uncertainties in the calculated cross sections and reaction rates are obtained by adding these two uncertainty contributions in quadrature. We obtain a total capture rate of $983.9^{+410.9}_{-261.5}~\mathrm{cm^{3}\,mol^{-1}\,s^{-1}}$ at $T = 1$~GK, with DC dominating at low temperatures ($T=0.01-0.4$~GK) and the $5/2^{-}$ resonance at higher temperatures ($T=0.5-5$~GK). The present results are consistent with the upper limit of Kobayashi et al.~\cite{Kobayashi2003}, which previous theoretical predictions exceed by factors of 3-50.