Optimized running conditions and sensitivity for direction sensitive detectors of WIMP dark matter

Optimum fill pressures for direction-sensitive dark matter detectors based on tracking in gases are considered. Given the minimum resolvable track length and the gas fill, the Lindhard–Scharf stopping model leads to the existence of an optimum pressure which maximizes the specific event rate R (event rate per unit detector volume). In addition, maximizing the detectibility of the recoil nucleus diurnal asymmetry is considered. Optimum fill pressures are calculated for Ar, CF4, CS2 and Xe gas fills, as a function of the WIMP mass and the minimum resolvable track length. The associated minimum target volumes required to achieve currently competitive WIMP-nucleon cross-section sensitivity are also calculated. The standard isothermal sphere model of the galactic WIMP halo is used throughout, but the method could be extended to use any desired WIMP distribution function.