  The 95Zr(n,gamma)96Zr reaction cross section is crucial in the modelling of
s-process nucleosynthesis in asymptotic giant branch stars because it controls
the operation of the branching point at the unstable 95Zr and the subsequent
production of 96Zr. We have carried out the measurement of the 94Zr(18O,16O)
and 90Zr(18O,16O) reactions and obtained the gamma-decay probability ratio of
96Zr* and 92Zr* to determine the 95Zr(n,gamma)96Zr reaction cross sections with
the surrogate ratio method. Our deduced maxwellian-averaged cross section of
66+-16 mb at 30 keV is close to the value recommended by Bao et al. (2000), but
30% and more than a factor of two larger than the values proposed by Toukan &
Kappeler (1990) and Lugaro et al. (2014), respectively, and routinely used in
s-process models. We tested the new rate in stellar models with masses between
2 and 6 Msun and metallicities 0.014 and 0.03. The largest changes - up 80%
variations in 96Zr - are seen in models of mass 3-4 Msun, where the 22Ne
neutron source is mildly activated. The new rate can still provide a match to
data from meteoritic stardust silicon carbide grains, provided the maximum mass
of the parent stars is below 4 Msun, for a metallicity of 0.03.
