⚛️ nuclear theory

Dark Matter Inelastic Scattering with Nuclei for Direct Detection

This paper investigates nuclear responses for WIMP-nucleus scattering in dark matter direct detection, specifically focusing on inelastic channels in $^{129}$ Xe and $^{131}$ Xe isotopes using relativistic configuration-interaction density functional theory to demonstrate that inelastic contributions can significantly dominate elastic ones and substantially impact the interpretation of detection results.

Original authors: Shao-Feng Ge, Oleg Titov, Yakun Wang

Published 2026-09-16

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Shao-Feng Ge, Oleg Titov, Yakun Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, physicists have been hunting for the invisible substance that makes up most of the matter in our universe. They call it dark matter, and while they cannot see it directly, they believe it is everywhere, drifting through the space between stars and planets. The leading theory suggests that this dark matter is made of heavy, slow-moving particles that rarely interact with ordinary matter. To catch a glimpse of them, scientists have built massive detectors deep underground, filled with tons of liquid xenon. The idea is simple: if a dark matter particle bumps into a xenon atom, it should give the atom a tiny kick, creating a flash of light that sensitive sensors can record. For years, researchers have focused on the most common type of bump, where the dark matter particle hits the atom and bounces off, leaving the atom in its normal, calm state. This is known as elastic scattering.

However, there is another possibility that has been largely overlooked until now. Just as a billiard ball can hit another ball hard enough to make it spin or vibrate, a dark matter particle might hit a xenon atom with enough energy to shake it into a higher, excited state. This is called inelastic scattering. In this scenario, the atom doesn't just recoil; it also holds onto some of the energy, waiting to release it later as it settles back down. Because the energy required to shake the atom is specific, this process only happens if the dark matter particle is moving fast enough and is heavy enough. For a long time, scientists assumed these "shaken" atoms were too rare to matter, or that they would be too difficult to calculate. But a new study suggests that ignoring this second type of collision could be a serious mistake, potentially hiding the very signal researchers are looking for.

A team of researchers from Shanghai Jiao Tong University and Beihang University has taken a fresh look at how dark matter interacts with xenon atoms, specifically focusing on these excited states. They realized that to understand what happens inside the atom during a collision, you need a very detailed map of the atom's internal structure. Previous studies used a method called the nuclear shell model, which treats the atom like a building with a fixed number of rooms where particles live. While useful, this method becomes very difficult to use for heavy atoms like xenon because the number of possible arrangements grows too large to handle without making simplifying cuts. The new team used a more modern and powerful approach called relativistic configuration-interaction density functional theory. This method treats every single particle inside the atom as an active participant, allowing for a much more complete and accurate picture of how the atom behaves when it gets hit.

Their calculations revealed that the inelastic channel is not a minor footnote; for certain types of dark matter interactions, it can be just as important as the elastic one, and for some specific cases, it can be a thousand times stronger. The researchers found that when dark matter hits the two specific types of xenon atoms that have a nuclear spin, the atom can be excited to a higher energy level. In some scenarios, the signal from these excited atoms is so strong that it completely dominates the total signal, dwarfing the standard elastic collisions. Furthermore, they discovered that it is not just the first excited state that matters. If the dark matter particle is heavy enough, it can kick the atom into even higher energy levels, and these higher states can contribute significantly to the total number of events detected. In fact, for some interactions, the signal from the second excited state is nearly as strong as the signal from the first.

The implications of these findings are profound for ongoing experiments like the LUX-ZEPLIN (LZ) detector, which recently reported a single event that looked like a dark matter collision. The energy of this event was quite high, around 248 kiloelectronvolts. Previous analyses assumed that this event was an elastic collision and tried to explain it using older calculation methods. However, when the new team applied their more accurate model to this specific event, the picture changed dramatically. Their calculations showed that the probability of seeing such a high-energy event from a standard elastic collision is actually much lower than previously thought. Instead, the new model suggests that the event rate at this energy is dominated by the inelastic channel, but even then, the predicted number of events is far lower than what the older models suggested. This means that the single event observed by the LZ collaboration might not be a sign of dark matter at all, or at least not the kind of dark matter that was being tested.

The study also highlights a deeper issue with how scientists interpret data from these detectors. The shape of the signal—the way the number of events changes as the energy of the recoil changes—looks very different depending on which calculation method is used. The older method predicted a peak in the number of events right around the energy where the LZ detector saw its signal. The new, more detailed method predicts a dip in that same region, with the signal actually being at its lowest point. This difference is not a small error; it is a factor of twenty-five. If the new calculations are correct, the signal seen by LZ is much harder to explain as a dark matter detection, because the expected background from dark matter is so much lower than what was previously assumed.

Ultimately, this work serves as a crucial reminder that the tools used to interpret experimental data are just as important as the data itself. By using a more sophisticated way to model the atomic nucleus, the researchers have shown that the rules governing how dark matter might interact with matter are more complex and varied than previously believed. They have demonstrated that ignoring the possibility of atoms being shaken into excited states could lead scientists to miss a major part of the story or, conversely, to misinterpret a random fluctuation as a discovery. As detectors become more sensitive and capable of seeing these subtle details, the need for equally precise theoretical models becomes critical. The hunt for dark matter is not just about building bigger tanks of liquid xenon; it is also about understanding the intricate dance of particles inside those atoms with a clarity that only the most advanced theories can provide.

Technical Summary: Dark Matter Inelastic Scattering with Nuclei for Direct Detection

Problem Statement
Direct detection of Weakly Interacting Massive Particles (WIMPs) traditionally focuses on elastic scattering, where the target nucleus remains in its ground state. However, for sufficiently heavy WIMPs, the kinetic energy transfer can excite target nuclei to low-lying excited states, leading to inelastic scattering. While previous studies have acknowledged the potential of inelastic channels, particularly for spin-dependent (SD) interactions in xenon isotopes, existing theoretical frameworks face two primary limitations:

Model Space Restrictions: Most calculations rely on the Nuclear Shell Model (NSM), which requires truncating the configuration space for heavy nuclei like xenon ( $^{129,131}$ Xe) due to combinatorial growth. These truncations raise questions about the convergence and accuracy of nuclear response functions.
Limited State Coverage: Previous NSM studies have predominantly focused on transitions to the first excited state. The contributions of higher-lying excited states to the total event rate have not been systematically explored, despite being kinematically accessible for heavy Dark Matter (DM).

Methodology
The authors address these limitations by employing a unified theoretical framework combining Non-Relativistic Effective Field Theory (NR EFT) with the Relativistic Configuration-Interaction Density Functional (ReCD) theory.

Kinematics and Formalism: The study establishes the kinematic constraints for inelastic scattering, deriving the minimum DM mass required to excite specific nuclear levels in natural xenon. It generalizes the NR EFT formalism to include inelastic transitions, utilizing a multipole expansion of effective operators. This approach allows for the derivation of rigorous selection rules based on angular momentum, parity, and time-reversal symmetry, determining which operators contribute to elastic versus inelastic channels.
Nuclear Structure Calculation (ReCD): Instead of the NSM, the authors utilize ReCD theory. This method treats all nucleons as active particles within a large single-particle space, avoiding the severe model-space truncations typical of NSM. It incorporates many-body correlations through configuration mixing (mixing of different quasiparticle configurations) and angular momentum projection to restore rotational symmetry broken by the mean-field approximation.
Comparison: The authors explicitly compare their ReCD results with existing NSM calculations (specifically those used in Refs. [20] and [22]) to quantify the impact of nuclear structure modeling on predicted event rates.

Key Contributions and Results

Reevaluation of Inelastic vs. Elastic Rates:
Using ReCD, the authors calculate the ratio of inelastic to elastic event rates ( $R_{inel}/R_{el}$ ) for all 15 NR EFT operators.
- For operators $O_1, O_3, O_8, O_{11}, O_{12}, O_{15}$ , inelastic contributions are negligible ( $\lesssim 1\%$ ).
- For operators $O_4, O_5, O_6, O_9, O_{10}$ , inelastic contributions are significant ( $\sim 10\%$ ).
- For operators $O_7, O_{13}, O_{14}$ , the inelastic channel can dominate or be comparable to the elastic channel. Specifically, for $O_{13}$ , the inelastic rate is comparable to the elastic rate. For $O_7$ and $O_{14}$ , the inelastic contribution can exceed the elastic rate by factors of $10^2$ to $10^3$ .
Impact of Higher Excited States:
The paper quantitatively demonstrates that transitions to higher excited states (beyond the first) are not always subdominant.
- For $m_\chi = 10$ TeV, the second excited state of $^{131}$ Xe contributes significantly for certain operators.
- For operator $O_9$ , the second excited state contributes $\sim 70\%$ of the elastic rate, exceeding the contribution of the first excited state ( $\sim 50\%$ ). Including these higher states can increase the total predicted event rate for $^{131}$ Xe by a factor of 2.
Discrepancies with Nuclear Shell Model (NSM):
The ReCD calculations reveal significant deviations from NSM results, particularly at higher momentum transfers ( $|q| > 100$ MeV).
- Response Functions: The nuclear response functions ( $W_T$ ) calculated via ReCD differ substantially from NSM. For example, for operator $\Sigma''$ , ReCD results are approximately five times larger than NSM results.
- Oscillatory Behavior: NSM results exhibit sharp dips in response functions at specific momentum transfers, whereas ReCD results show smoother oscillations. These differences arise from variations in the underlying nuclear density matrices, particularly the relative amplitudes of contributions from specific single-particle orbits (e.g., $1d_{3/2}$ vs. $2s_{1/2}$ ).
Implications for LZ Event Interpretation:
The authors apply their findings to the recent LUX-ZEPLIN (LZ) observation of a single event with a recoil energy of $E_R \approx 248$ keV.
- NSM Prediction: The NSM-based analysis predicts a local maximum in the differential event rate around 200–250 keV, which could accommodate the observed event.
- ReCD Prediction: The ReCD calculation predicts a local minimum at $E_R \approx 250$ keV, with the event rate being roughly 25 times smaller than the NSM prediction at this energy. Furthermore, ReCD predicts a global maximum at low recoil energies ( $\sim 50$ keV), which contradicts the non-observation of low-energy events.
- Conclusion: The paper suggests that the interpretation of the LZ event as a DM signal is highly sensitive to the nuclear model used; under ReCD inputs, the signal hypothesis becomes significantly less favorable.

Significance
The paper claims that accurate predictions for DM direct detection, particularly for heavy WIMPs and spin-dependent interactions, require a reliable description of nuclear many-body structure that goes beyond the truncated configuration spaces of the NSM. By utilizing ReCD theory, the authors demonstrate that:

Inelastic scattering is a critical component of the total signal for specific interaction operators, potentially dominating the event rate.
Higher excited states must be included in the analysis to avoid underestimating event rates.
The choice of nuclear model (ReCD vs. NSM) can lead to order-of-magnitude differences in predicted event rates and spectral shapes, significantly altering the interpretation of experimental data such as the recent LZ event.

The work provides a more robust theoretical foundation for interpreting current and future xenon-based direct detection experiments, emphasizing the necessity of advanced nuclear structure calculations in the search for Dark Matter.

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