The neutron capture cross section of the unstable s -process branching nucleus ^ { 185 } W has been derived from experimental data of the inverse ^ { 186 } W ( \gamma , n ) ^ { 185 } W photodisintegration taken with monochromatic photon beams from laser Compton scattering . The result of \sigma = 553 \pm 60 mb at kT = 30 keV leads to a relatively high effective neutron density in the classical s -process of N _ { n } = 4.7 \times 10 ^ { 8 } { cm } ^ { -3 } . A realistic model for the s -process in thermally pulsing AGB stars overestimates the abundance of ^ { 186 } Os significantly because of the relatively small neutron capture cross section of ^ { 185 } W .