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 { Ne } ( \alpha,n ) { } ^ { 25 } \mathrm { Mg } reaction during the He-core and C-shell burning phases of massive stars . This reaction , as well as the competing ^ { 22 } \mathrm { Ne } ( \alpha, \gamma ) { } ^ { 26 } \mathrm { Mg } 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 { Ne } ( { } ^ { 6 } \mathrm { Li } ,d ) { } ^ { 26 } \mathrm { Mg } reaction in inverse kinematics , detecting the outgoing deuterons and ^ { 25 , 26 } \mathrm { Mg } recoils in coincidence . We have established a new n / \gamma decay branching ratio of 1.14 ( 26 ) for the key E _ { x } = 11.32 MeV resonance in ^ { 26 } \mathrm { Mg } , 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 { Ne } ( \alpha,n ) { } ^ { 25 } \mathrm { Mg } and ^ { 22 } \mathrm { Ne } ( \alpha, \gamma ) { } ^ { 26 } \mathrm { Mg } 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 .