The neutron capture cross section of the unstable nucleus ~(185)W has been derived from experimental photo-activation data of the inverse reaction ~(186)W(γ, n) ~(185)W. The new result of σ = 687 +- 110 mbarn confirms the theoretically predicted neutron capture cross section of ~(185)W of σ≈ 700 mbarn at κT = 30 keV. A neutron density in the classical s-process of n_n = (3.8_(-0.9)~(+1.1)) x 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.
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