Limits on the spin-dependent WIMP-nucleon cross-sections from the first science run of the ZEPLIN-III experiment

We present new experimental constraints on the WIMP-nucleon spin-dependent elastic cross-sections using data from the first science run of ZEPLIN-III, a two-phase xenon experiment searching for galactic dark matter WIMPs based at the Boulby mine. Analysis of $\sim$450 kg$\cdot$days fiducial exposure revealed a most likely signal of zero events, leading to a 90%-confidence upper limit on the pure WIMP-neutron cross-section of $\sigma_n=1.8\times 10^{-2}$ pb at 55 GeV/$c^2$ WIMP mass. Recent calculations of the nuclear spin structure based on the Bonn CD nucleon-nucleon potential were used for the odd-neutron isotopes $^{129}$Xe and $^{131}$Xe. These indicate that the sensitivity of xenon targets to the spin-dependent WIMP-proton interaction is much lower than implied by previous calculations, whereas the WIMP-neutron sensitivity is impaired only by a factor of $\sim$2.