Constraints on key $^{17}$O($α,γ$)$^{21}$Ne resonances and impact on the weak s-process

The efficiency of the slow neutron-capture process in massive stars is strongly influenced by neutron-capture reactions on light elements. At low metallicity, $^{16}$O is an important neutron absorber, but the effectiveness of $^{16}$O as a light-element neutron poison is modified by competition between subsequent $^{17}$O$(\alpha,n)^{20}$Ne and $^{17}$O$(\alpha,\gamma)^{21}$Ne reactions. The strengths of key $^{17}$O$(\alpha,\gamma)^{21}$Ne resonances within the Gamow window for core helium burning in massive stars are not well constrained by experiment. This work presents more precise measurements of resonances in the energy range $E_{c.m.} = 612 - 1319$ keV. We extract resonance strengths of $\omega\gamma_{638} = 4.85\pm0.79$ $\mu$eV, $\omega\gamma_{721} = 13.0^{+3.3}_{-2.4}$ $\mu$eV, $\omega\gamma_{814} = 7.72\pm0.55$ meV and $\omega\gamma_{1318} = 136\pm 13$ meV, for resonances at $E_{c.m.} =$ 638, 721, 814 and 1318 keV, respectively. We also report an upper limit for the 612 keV resonance of $\omega\gamma