The competing $^{22}$Ne($alpha,gamma$)$^{26}$Mg and $^{22}$Ne($alpha,n$)$^{25}$Mg reactions control the production of neutrons for the weak $s$-process in massive and AGB stars. In both systems, the ratio between the corresponding reaction rates strongly impacts the total neutron budget and strongly influences the final nucleosynthesis. The $^{22}$Ne($alpha,gamma$)$^{26}$Mg and $^{22}$Ne($alpha,n$)$^{25}$Mg reaction rates was re-evaluated by using newly available information on $^{26}$Mg given by various recent experimental studies. Evaluations of The evaluated $^{22}$Ne($alpha,gamma$)$^{26}$Mg reaction rate remains substantially similar to that of Longland {it et al.} but, including recent results from Texas A&M, the $^{22}$Ne($alpha,n$)$^{25}$Mg reaction rate is lower at a range of astrophysically important temperatures. Stellar models computed with NEWTON and MESA predict decreased production of the weak branch $s$-process due to the decreased efficiency of $^{22}$Ne as a neutron source. Using the new reaction rates in the MESA model results in $^{96}$Zr/$^{94}$Zr and $^{135}$Ba/$^{136}$Ba ratios in much better agreement with the measured ratios from presolar SiC grains.
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