Abstract The reaction rates of $^{22}$Ne($\alpha$, n)$^{25}$Mg and its competing channel $^{22}$Ne($\alpha$, $\gamma$)$^{26}$Mg control the production of neutron flux for weak $s-$process nucleosynthesis in low mass AGB stars and in massive stars with $M\geq 10M_\odot$. The temperature range of interest for these reactions lies between $0.2- 0.4$ GK. However, the rates of these reactions are poorly constrained at these temperatures due to uncertainties in the nuclear properties of a number of resonance states in the compound nucleus $^{26}$Mg, lying within the Gamow window. The present work reports a full $R$-matrix evaluation of the $^{22}$Ne($\alpha$, n)$^{25}$Mg and $^{22}$Ne($\alpha$, $\gamma$)$^{26}$Mg reaction rates using updated nuclear data of $^{26}$Mg states. Previous rate evaluation by Adsley~\textit{et al.} and $R-$matrix calculations of Wiescher~\textit{et al.} were limited by using narrow resonance approximations and omission of the resonances below $E_r=705$ keV, respectively. In this work, the $R-$matrix fit to the available $^{22}$Ne($\alpha$, n)$^{25}$Mg reaction data is performed by including the contributions of previously neglected resonances below E$_r$=705 keV and considering the interference effects. 
The ($\alpha$, n) reaction rate from the present $R$-matrix evaluations is noticeably higher than the narrow resonance approximation calculations in the temperature range $0.1-0.3$ GK. 
In particular, the present ($\alpha$, n) reaction rate is significantly higher ($8-3.7$ times) compared to Adsley~\textit{et al.} at $0.2-0.3$ GK and $\approx 2$ times greater than Wiescher~\textit{et al.} at $0.3$ GK. The estimated reaction rate ratio of ($\alpha$, n) to ($\alpha, \gamma$) in the relevant temperature window $0.2-0.8$ GK indicates that the production of neutrons for the $s$-process is more likely than the radiative alpha capture reaction, compared to the previous estimate by Adsley~\textit{et al.}
Read full abstract