  This work reports on accurate, high-resolution measurements of the
$^{25}$Mg($n, \gamma$)$^{26}$Mg and $^{25}$Mg($n, tot$) cross sections in the
neutron energy range from thermal to about 300 keV, leading to a significantly
improved $^{25}$Mg($n, \gamma$)$^{26}$Mg parametrization. The relevant
resonances for $n+^{25}$Mg were characterized from a combined R-matrix analysis
of the experimental data. This resulted in an unambiguous spin/parity
assignment of the corresponding excited states in $^{26}$Mg. With this
information experimental upper limits of the reaction rates for
$^{22}$Ne($\alpha, n$)$^{25}$Mg and $^{22}$Ne($\alpha, \gamma$)$^{26}$Mg were
established, potentially leading to a significantly higher ($\alpha,
n$)/($\alpha, \gamma$) ratio than previously evaluated. The impact of these
results have been studied for stellar models in the mass range 2 to 25
$M_{\odot}$.
