  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.
