Impact of shell model interactions on nuclear responses to WIMP elastic scattering

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.