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 weakly interacting massive particles based at the Boulby mine. Analysis of similar to 450 kg . days fiducial exposure allow us to place a 90%-confidence upper limit on the pure WIMP-neutron cross section of sigma(n) = 1.9 x 10(-2) pb at 55 GeV/c(2) WIMP mass. Recent calculations of the nuclear spin structure based on the Bonn charge-dependent nucleon-nucleon potential were used for the odd-neutron isotopes Xe-129 and Xe-131. These indicate that the sensitivity of xenon targets to the spin-dependent WIMP-proton interaction could be much lower than implied by previous calculations, whereas the WIMP-neutron sensitivity is impaired only by a factor of similar to 2.