Dark Matter Inelastic Scattering with Nuclei for Direct Detection

Abstract

We investigate the nuclear responses for the WIMP-nucleus scattering in the dark matter direct detection with particular emphasis on the inelastic channel for the $^{129}$Xe and $^{131}$Xe isotopes. Our generalization incorporates both the elastic and inelastic scattering channels. With multipole expansion of the effective operators, the angular momentum, parity and time-reversal selection rules can effectively determine the allowed transitions. Instead of the nuclear shell model, we use the state-of-the-art relativistic configuration-interaction density functional theory, which is more suitable for heavy nuclei such as xenon isotopes, to calculate the nuclear response functions. For certain interaction operators, the inelastic contribution can be comparable as its elastic counterpart and some can even dominate by up to three orders of magnitude. Additionally, the higher excited nuclear states can have comparable signal rate as the first excited states. We compare our results with the nuclear shell model calculation. The differences would have significant effects for interpreting the dark matter direct detection searches.