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

TL;DR

The paper investigates how shell-model interactions influence nuclear response functions for WIMP elastic scattering within the non-relativistic EFT framework, across a broad set of DD-relevant nuclei. Using NuShellX with multiple valence spaces and interactions, it computes nuclear response functions and integrated form factors to quantify uncertainties due to nuclear structure. The SI channel remains largely insensitive to the details of the nuclear wave function, while subleading channels exhibit substantial variations (often tens of percent to factors of several) depending on the interaction and model space, sometimes with strong proton or neutron dominance. The findings emphasize that nuclear-structure uncertainties must be incorporated in direct-detection analyses, especially for heavy targets like iodine and xenon, and the authors provide OBDMEs and density matrices to facilitate reuse in the community.

Abstract

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.

Figures (20)

• Figure 1: $^{19}$F energy levels (keV) from USD and USDB interactions in the $sd$ model space are compared with experiment (only positive parity levels are shown).
• Figure 2: Same as Fig. \ref{['fig:19Flevels']} for $^{23}$Na.
• Figure 3: $^{127}$I energy spectra (keV) for experimental data, as well as the SN100PN and GCN5082 interactions in a restricted model space.
• Figure 4: $^{127}$I proton-proton (solid lines) and neutron-neutron (dashed lines) nuclear response functions $F^{(N,N)}_X (q^2)$ obtained with three different shell model interactions. The B&D results are from Anand:2013yka.
• Figure 5: $^{127}$I SI nuclear response function $F_M (q^2)$ obtained with three different shell model interactions, with the Helm response plotted for comparison.