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

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. We evaluate nuclear response functions induced by these interactions for ${}^{19}\mathrm{F}$, ${}^{23}\mathrm{Na}$, ${}^{28,29,30}\mathrm{Si}$, ${}^{40}\mathrm{Ar}$, ${}^{70,72,73,74,76}\mathrm{Ge}$, ${}^{127}\mathrm{I}$, and ${}^{128,129,130,131,132,134,136}\mathrm{Xe}$ nuclei that are relevant to current direct detection experiments, and estimate their sensitivity to shell model interactions. Shell model calculations are performed with the NuShellX solver. Nuclear response functions from nonrelativistic effective field theory are evaluated and integrated over transferred momentum for quantitative comparisons. We show that 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. Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modeling. These uncertainties should be accounted for in analyses of direct detection experiments.

Figure 1

${}^{19}\mathrm{F}$ 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. 1 for ${}^{23}\mathrm{Na}$.

Figure 3

${}^{127}\mathrm{I}$ energy spectra (keV) for experimental data, as well as the SN100PN and GCN5082 interactions in a restricted model space. GCN5082* refers to GCN5082 Expanded.

Figure 4

${}^{127}\mathrm{I}$ proton-proton (solid lines) and neutron-neutron (dashed lines) nuclear response functions $F_X^{(N,N)}(q^2)$ obtained with three different shell model interactions. The B&D results are from [16].

Figure 5

${}^{127}\mathrm{I}$ SI nuclear response function $F_M(q^2)$ obtained with three different shell model interactions, with the Helm response plotted for comparison.

Figure 6

${}^{127}\mathrm{I}$ proton IFF values in units of $(\mathrm{MeV}{)}^2$, evaluated using Eq. (8).

Figure 7

Same as Fig. 6 for ${}^{127}\mathrm{I}$ neutron IFF.

Figure 8

Same as Fig. 6 for different SN100PN valence space truncation.

Figure 9

Same as Fig. 7 for different SN100PN valence space truncation.

Figure 10

Same as Fig. 6 for different GCN5082 valence space truncation.

Figure 11

Same as Fig. 7 for different GCN5082 valence space truncation.

Figure 12

Same as Fig. 6 for ${}^{19}\mathrm{F}$ proton IFF.

Figure 13

Same as Fig. 6 for ${}^{19}\mathrm{F}$ neutron IFF.

Figure 14

Same as Fig. 6 for ${}^{23}\mathrm{Na}$ proton IFF.

Figure 15

Same as Fig. 6 for ${}^{23}\mathrm{Na}$ neutron IFF.

Figure 16

Same as Fig. 6 for silicon proton IFF.

Figure 17

Same as Fig. 6 for silicon neutron IFF.

Figure 18

Proton (top) and neutron (bottom) IFF values for ${}^{40}\mathrm{Ar}$ with the SDPF-MU and EPQQM interactions in the restricted $sdpf$ valence space.

Figure 19

Same as Fig. 6 for germanium proton IFF.

Figure 20

Same as Fig. 6 for germanium neutron IFF.

Figure 21

Same as Fig. 6 for xenon proton IFF.

Figure 22

Same as Fig. 6 for xenon neutron IFF.

Figure 23

Same as Fig. 1 for ${}^{29}\mathrm{Si}$.

Figure 24

${}^{73}\mathrm{Ge}$ energy spectra (keV) for experimental data, as well as the jj44b and JUN45 interactions in an unrestricted model space.

Figure 25

${}^{129}\mathrm{Xe}$ energy spectra (keV) for experimental data, as well as the SN100PN interaction in a restricted model space.

Figure 26

${}^{131}\mathrm{Xe}$ energy spectra (keV) for experimental data, as well as the SN100PN interaction in an unrestricted model space.