Role of ($\alpha$,n) reactions under $r$-process conditions in neutrino-driven winds revisited

Abstract

Background: The astrophysical $r$-process occurs in an explosive astrophysical event under extremely neutron-rich conditions, leading to (n,$\gamma$)-($\gamma$,n) equilibrium along isotopic chains which peaks around neutron separation energies of a few MeV. Nuclei with larger $Z$ are usually produced by ${\beta }^{-}$-decay, but under certain conditions also $\alpha$-induced reactions may become relevant for the production of nuclei with $Z+2$. Purpose: The uncertainties of the reaction rates of these $\alpha$-induced reactions are discussed within the statistical model. As an example, $\alpha$-induced ($\alpha$,n) and $(\alpha$,$x$n) reaction cross sections for the neutron-rich ${}^{86}$Se nucleus are studied in detail. Method: In a first step, the relevance of ($\alpha$,n) and $(\alpha$,$x$n) reactions is analyzed. Next the uncertainties are determined from a variation of the $\alpha$-nucleus potential which is the all-dominant parameter for the astrophysical $Z\to Z+2$ reaction rate. Results: It is found that the $r$-process flow towards nuclei with larger $Z$ is essentially influenced only by the $\alpha$-nucleus potential whereas the other ingredients of the statistical model play a very minor role. This finding is based on the fact that the flow towards larger $Z$ depends on the sum over all ($\alpha$,$x$n) cross sections which is practically identical to the total $\alpha$-induced reaction cross section. Conclusions: $\alpha$-nucleus potentials play an important role under certain $r$-process conditions because the flow towards larger $Z$ depends sensitively on the total $\alpha$-induced reaction cross section. The uncertainty of the reaction rate is about a factor of two to three at higher temperatures and exceeds one order of magnitude at very low temperatures.

7 pages, 3 figures, Phys. Rev. C, accepted for publication

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• Uncertainty of the astrophysical ${}^{17,18}$O($\alpha$,n)${}^{20,21}$Ne reaction rates and the applicability of the statistical model for nuclei with $A\lesssim 20$
• Measurements of the ${}^{96}$Zr($\alpha$,n)${}^{99}$Mo cross section for astrophysics and applications
• Cross sections at sub-Coulomb energies: full optical model vs.\ barrier transmission for ${}^{40}$Ca + $\alpha$
• Measurement of $\beta$-particles to determine cross sections relevant to the weak r-process
• Bayesian Analysis of the ${}^{86}$Sr$(\alpha ,\alpha )$ Reaction to Constrain the ${}^{86}$Sr$(\alpha ,n)$ Cross Section at Astrophysical Energies