We report experimental upper limits on WIMP-nucleon elastic scattering cross sections from the second science run of ZEPLIN-III at the Boulby Underground Laboratory. A raw fiducial exposure of 1,344 kg.days was accrued over 319 days of continuous operation between June 2010 and May 2011. A total of eight events was observed in the signal acceptance region in the nuclear recoil energy range 7-29 keV, which is compatible with background expectations. This allows the exclusion of the scalar cross-section above 4.8E-8 pb near 50 GeV/c^2 WIMP mass with 90% confidence. Combined with data from the first run, this result improves to 3.9E-8 pb. The corresponding WIMP-neutron spin-dependent cross-section limit is 8.0E-3 pb. The ZEPLIN programme reaches thus its conclusion at Boulby, having deployed and exploited successfully three liquid xenon experiments of increasing reach.
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