In this paper we calculate the structure functions and event rates of spin-dependent elastic and inelastic WIMP-nucleus scattering off the odd-$A$ thallium nuclei ${}^{203,205}\mathrm{Tl}$. These nuclei are used as active dopants in sodium and cesium iodide scintillators in many dark-matter experiments. We begin by presenting nuclear shell-model calculations of the nuclei, then compare the calculated energy spectra, nuclear moments and electromagnetic transitions to their experimental values to establish the validity of our nuclear model. Then, we proceed to calculate the structure functions for both elastic and inelastic WIMP scattering, and after that we calculate the differential event rates for WIMPs of various masses (100, 200, 500, and 1000 GeV). We employ a state-of-the-art WIMP-nucleus-scattering formalism that takes into account all pion-exchange, pion-pole, and contact currents. The present work is the first time that two-body currents have been taken into account for ${}^{203,205}\mathrm{Tl}$ in WIMP-scattering calculations. The results show that elastic scattering is at least an order of magnitude more important than inelastic scattering in all the cases studied. Elastic scattering structure functions were found to be of similar magnitude to other nuclei.

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• Dark matter direct detection
• Nuclear reactions
• Weakly interacting massive particles
• 190 ≤ A ≤ 219
• Nuclear structure & decays
• Shell model