Metastable nuclear isomers as dark matter accelerators

Inelastic dark matter and strongly interacting dark matter are poorly constrained by direct detection experiments since they both require the scattering event to deliver energy from the nucleus into the dark matter in order to have observable effects. We propose to test these scenarios by searching for the collisional deexcitation of metastable nuclear isomers by the dark matter particles. The longevity of these isomers is related to a strong suppression of $\gamma$- and $\beta$-transitions, typically inhibited by a large difference in the angular momentum for the nuclear transition. The collisional deexcitation by dark matter is possible since heavy dark matter particles can have a momentum exchange with the nucleus comparable to the inverse nuclear size, hence lifting tremendous angular momentum suppression of the nuclear transition. This deexcitation can be observed either by searching for the direct effects of the decaying isomer, or through the rescattering or decay of excited dark matter states in a nearby conventional dark matter detector setup. Existing nuclear isomer sources such as naturally occurring ${}^{180m}\mathrm{Ta}$, ${}^{137m}\mathrm{Ba}$ produced in decaying Cesium in nuclear waste, ${}^{177m}\mathrm{Lu}$ from medical waste, and ${}^{178m}\mathrm{Hf}$ from the Department of Energy storage can be combined with current dark matter detector technology to search for this class of dark matter.

Figure 1

Form factors for different $\mathrm{\Delta }J$. For small $(q·R)$ relevant to $\gamma$ decay, there is severe suppression for large $\mathrm{\Delta }J$. If the typical momentum required for scattering is much larger, the form-factor suppression is ameliorated.

Figure 2

(Left panel) Density enhancement $\eta$, 300 m below the surface, for three different DM masses, $M_{\chi }=100\mathrm{GeV}$, $M_{\chi }=1\mathrm{TeV}$, and $M_{\chi }=10\mathrm{TeV}$ as a function of reference nucleon cross section ${\sigma }_n$. (Right panel) Contours of constant density enhancement $\eta$ in the ${\sigma }_n$ vs $M_{\chi }$ plane.

Figure 3

Projections for limits on nucleon cross section for DM that interacts strongly with nuclei that correspond to 1 g yr exposure for ${}^{180m}\mathrm{Ta}$.

Figure 4

DM-nucleon cross-section reach for different isomeric nuclei for corresponding exposure. Also shown are “inelastic frontier” limits from CRESST. The sensitivity is derived assuming three detectable interactions per year. These limits are for illustrative purposes only. Limits on concrete models with detection signature are displayed in Figs. 5 and 6.

Figure 5

Reach for different isomeric nuclei for the dark photon DM model. Limits from LZ/PANDAX and CRESST do not have any reach for $\delta M_{\chi }>450\mathrm{keV}$. Also shown in gray are loop constraints from LZ/Icecube and limits on the dark photon mediator from BABAR and projections for Belle II (dashed line). Contours of the constant mean-free path for excited DM in a conventional DM detector are also marked.

Figure 6

Reach for electric dipole DM for different metastable isomer targets. Current limits on this model from CRESST and the loop constraint from LZ/Icecube are also shown. The unitarity and perturbativity constraints are marked by dashed gray lines. Contours of constant lifetime of the excited DM state are also displayed.