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 xenonexperiment searching for galactic dark matter weakly interacting massive particlesbased at the Boulby mine. Analysis of approx450 kgcentre dotdays fiducial exposure allow us to place a 90%-confidence upper limit on the pure WIMP- neutron cross sectionof sigma{sub n}=1.9x10{sup -2} pb at 55 GeV/c{sup 2} WIMPmass. Recent calculations of the nuclear spin structurebased on the Bonn charge-dependent nucleon-nucleon potential were used for the odd-neutron isotopes {sup 129}Xe and {sup 131}Xe. These indicate that the sensitivity of xenontargets 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 approx2.