Decay properties of ${}^{22}\mathrm{N}\mathrm{e}+\alpha$ resonances and their impact on $s$-process nucleosynthesis

The astrophysical $s$-process is one of the two main processes forming elements heavier than iron. A key outstanding uncertainty surrounding $s$-process nucleosynthesis is the neutron flux generated by the ${}^{22}\mathrm{N}\mathrm{e}(\alpha ,n){}^{25}\mathrm{M}\mathrm{g}$ reaction during the He-core and C-shell burning phases of massive stars. This reaction, as well as the competing ${}^{22}\mathrm{N}\mathrm{e}(\alpha ,\gamma ){}^{26}\mathrm{M}\mathrm{g}$ reaction, is not well constrained in the important temperature regime from ${\sim} 0.2$--$0.4$~GK, owing to uncertainties in the nuclear properties of resonances lying within the Gamow window. To address these uncertainties, we have performed a new measurement of the ${}^{22}$\mathrm{N}\mathrm{e}$({}^{6}$\mathrm{L}\mathrm{i}$, d){}^{26}$\mathrm{M}\mathrm{g}$$ reaction in inverse kinematics, detecting the outgoing deuterons and ${}^{25,26}\mathrm{M}\mathrm{g}$ recoils in coincidence. We have established a new $n\mathrm{/}\gamma$ decay branching ratio of $1.14(26)$ for the key $E_x=11.32$ MeV resonance in ${}^{26}\mathrm{M}\mathrm{g}$, which results in a new $(\alpha ,n)$ strength for this resonance of $42(11)\mu$eV when combined with the well-established $(\alpha ,\gamma )$ strength of this resonance. We have also determined new upper limits on the $\alpha$ partial widths of neutron-unbound resonances at $E_x=11.112,$ $11.163$, $11.169$, and $11.171$ MeV. Monte-Carlo calculations of the stellar ${}^{22}$\mathrm{N}\mathrm{e}$(\alpha, n){}^{25}$\mathrm{M}\mathrm{g}$$and${}^{22}$\mathrm{N}\mathrm{e}$(\alpha, \gamma){}^{26}$\mathrm{M}\mathrm{g}$$ rates, which incorporate these results, indicate that both rates are substantially lower than previously thought in the temperature range from $\sim 0.2$–$0.4$~GK.