The neutron capture cross section of the unstable nucleus ^ { 185 } W has been derived from experimental photoactivation data of the inverse reaction ^ { 186 } W ( \gamma , n ) ^ { 185 } W. The new result of \sigma = ( 687 \pm 110 ) mbarn confirms the theoretically predicted neutron capture cross section of ^ { 185 } W of \sigma \approx 700 mbarn at kT = 30 keV . A neutron density in the classical s -process of n _ { n } = ( 3.8 ^ { +0.9 } _ { -0.8 } ) \times 10 ^ { 8 } cm ^ { -3 } is derived from the new data for the ^ { 185 } W branching . In a stellar s -process model one finds a significant overproduction of the residual s -only nucleus ^ { 186 } Os .