Probing Internal Conversion and Dark-Matter-Induced De-excitation of 180mTa with a gamma-ray TES Array

TL;DR

This work investigates a source-equals-detector gamma-ray TES approach to search for the de-excitation of the long-lived isomer $^{180\mathrm{m}}\mathrm{Ta}$, exploiting calorimetric energy measurement to capture internal conversion electrons, X rays, and nuclear recoils, paired with a delayed-coincidence tag from the EC decay to $^{180}\mathrm{Hf}$. It provides a quantitative sensitivity study for both standard IC de-excitation and DM-induced processes, considering strongly interacting DM and inelastic DM scenarios across different TES-array scales. The results show that medium-scale arrays ($N_{\mathrm{TES}} \sim 10^2$–$10^3$) can reach the theoretical IC half-life within a few years, while larger arrays ($N_{\mathrm{TES}} \sim 10^4$) with five years of data can probe DM parameter spaces beyond current HPGe constraints, leveraging event-by-event discrimination enabled by calorimetry. The study emphasizes the importance of empirically measuring the $^{180\mathrm{m}}\mathrm{Ta}$ IC half-life to calibrate nuclear-structure inputs and outlines a path toward prototype demonstrations and eventual deployment in underground laboratories such as Kamioka.

Abstract

We propose and evaluate a source-as-detector search for the de-excitation of the long-lived isomer $^{180\mathrm{m}}\mathrm{Ta}$ in natural tantalum (Ta), using a $γ$-ray transition-edge-sensor (TES) array. We exploit two capabilities not available in conventional high-purity germanium (HPGe) searches: (i) near-unity containment of low-energy secondaries (internal-conversion electrons and characteristic X rays), as well as the nuclear recoil, enabling a calorimetric, event-by-event measurement of the total energy deposited in the absorber; and (ii) a delayed-coincidence tag based on the subsequent ${}^{180}$Ta electron-capture (EC) decay to ${}^{180}$Hf. We evaluate the $3σ$ discovery reach for internal conversion (IC) and for dark-matter-induced de-excitation in two benchmark scenarios: a strongly interacting dark-matter (DM) subcomponent and inelastic DM with off-diagonal couplings. Using a background model based on intrinsic radioactivity in the Ta absorber and realistic detector performance, we show that arrays with $N_{\mathrm{TES}}=256$ and $1{,}000$ pixels can reach the theoretically expected IC half-life within $2.6$~yr and $0.66$~yr, respectively. For an array with $N_{\mathrm{TES}}=10^4$ and a five-year exposure, the projected sensitivity to DM-induced de-excitation surpasses limits inferred from HPGe non-observations of ${}^{180\mathrm{m}}$Ta and probes regions of parameter space not covered by current direct-detection experiments.

Figures (6)

• Figure 1: Deposited–energy distributions in a single Ta absorber for (top) internal conversion (IC), (middle) strongly interacting DM–induced de–excitation, and (bottom) inelastic DM–induced de–excitation. The spectra are obtained from Geant4 simulations including full containment of low–energy secondaries and folded with the assumed TES energy resolution. The middle and bottom panels are shown for a DM mass $m_\chi =1$ TeV; for inelastic DM we take a representative mass splitting $\Delta m = 50$ keV.
• Figure 2: Deposited–energy distribution for the delayed EC channel in a single Ta absorber. The spectrum shows a prominent peak at the K–shell binding energy $E_K\simeq65.35~\mathrm{keV}$ and, when the de–excitation $\gamma$ ray of energy ($E_{\gamma}=93.3~\mathrm{keV}$) is fully contained, a second peak at $E_K + E_{\gamma} \simeq 158.7~\mathrm{keV}$
• Figure 3: Simulated background energy spectra in the Ta absorber for the intrinsic $^{238}$U and $^{232}$Th contaminations assumed in this work. The contributions from $^{210}$Pb and $^{210}$Bi are also shown; the sequential $^{210}$Pb $\to$$^{210}$Bi decay constitutes a correlated background that can pass the delayed-coincidence selection.
• Figure 4: Half-life $T_{1/2}$ at the $3\sigma$ discovery level as a function of observation time $T_{\mathrm{obs}}$ with $N_{\mathrm{TES}}=256$ and $N_{\mathrm{TES}}=1,000$. The dashed horizontal line indicates the theoretical expectation for the IC half–life of $^{180\mathrm{m}}$Ta Ejiri:2017dro.
• Figure 5: $3\sigma$ discovery reach in the combination $f\,\eta\,\sigma_n$ as a function of DM mass $m_\chi$ for strongly interacting DM. We assume an array with $N_{\mathrm{TES}}=10,000$ and five years of observation.