Background: Nuclear recoil from scattering with weakly interacting massive particles (WIMPs) is a signature searched for in direct detection of dark matter. The underlying WIMP-nucleon interactions could be spin and/or orbital angular momentum (in)dependent. Evaluation of nuclear recoil rates through these interactions requires accounting for nuclear structure, e.g., through shell model calculations. Purpose: To evaluate nuclear response functions induced by these interactions for $^{ 19}$F, $^{ 23}$Na, $^{ 28, 29, 30}$Si, $^{ 40}$Ar, $^{ 70,72,73,74,76}$Ge, $^{ 127}$I, and $^{ 128, 129, 130, 131, 132, 134, 136}$Xe nuclei that are relevant to current direct detection experiments, and to estimate their sensitivity to shell model interactions. Methods: Shell model calculations are performed with the NuShellX solver. Nuclear response functions from non-relativistic effective field theory (NREFT) are evaluated and integrated over transferred momentum for quantitative comparisons. Results: Although the standard spin independent response is barely sensitive to the structure of the nuclei, large variations with the shell model interaction are often observed for the other channels. Conclusions: Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modelling. These uncertainties should be accounted for in analyses of direct detection experiments.
Categories: hep-ph nucl-th