Electronic structure of liquid xenon in the context of light dark matter direct detection

TL;DR

This paper models the electronic structure of liquid xenon to improve understanding of dark matter-induced ionization, finding that liquid phase effects are significant mainly for dark matter masses below 6 MeV.

Contribution

It introduces a method to incorporate the electronic density of states of liquid xenon into dark matter detection rate calculations, bridging atomic and condensed phase properties.

Findings

Broadening of 5p levels affects ionization rates below 6 MeV.

Electronic charge densities are similar in atom and liquid phases.

The proposed scheme simplifies calculations of dark matter-electron scattering.

Abstract

We present a description of the electronic structure of xenon within the density-functional theory formalism with the goal of accurately modeling dark-matter-induced ionisation in liquid xenon detectors. We compare the calculated electronic structures of the atomic, liquid and crystalline solid phases, and find that the electronic charge density and its derivatives in momentum space are similar in the atom and the liquid, consistent with the weak interatomic van der Waals bonding. The only notable difference is a band broadening of the highest occupied $5p$ levels, reflected in the densities of states of the condensed phases, as a result of the inter-atomic interactions. We therefore use the calculated density of states of the liquid phase, combined with the standard literature approach for the isolated atom, to recompute ionisation rates and exclusion limit curves for the XENON10 and XENON1T experiments. We find that the broadening of the 5$p$ levels induced by the liquid phase is relevant only for dark matter masses below 6 MeV, where it increases the ionisation rate relative to that of the isolated atom. For most of the explored mass range, the energies of the discrete 4$d$ and 5$s$ levels have the strongest effect on the rate. Our findings suggest a simple scheme for calculating dark matter-electron scattering rates in liquid noble gas detectors, using the calculated values for the atom weighted by the density of states of the condensed phase.