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Light and charge yields from nuclear recoils in noble liquids: From sub-keV energies to 1 MeV

This paper presents a first-principles model for light and charge yields from nuclear recoils in noble liquids, utilizing a newly defined electronic scaling length and the Thomas-Imel box model to provide a consistent description of experimental data from sub-keV to 1 MeV energies that outperforms existing NEST predictions for LAr and offers new insights for LXe.

Original authors: Y. Sarkis, Juan Carlos D'Olivo, Alexis Aguilar-Arevalo

Published 2026-10-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Y. Sarkis, Juan Carlos D'Olivo, Alexis Aguilar-Arevalo

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

Deep beneath the Earth's surface, in laboratories shielded from the constant rain of cosmic rays, scientists hunt for the universe's most elusive inhabitants: dark matter. To find these invisible particles, researchers use tanks filled with noble liquids like argon and xenon, cooled to temperatures colder than outer space. When a dark matter particle strikes an atom in this liquid, it creates a tiny, violent recoil, much like a billiard ball hitting another. This collision releases energy, but not in a way that is easy to see. Instead of a simple flash, the energy transforms into a complex mix of light and electric charge. The ability to detect these faint signals depends entirely on understanding exactly how much light and how many electrons are produced for every bit of energy deposited. Without a precise map of this conversion, the faint whisper of a dark matter particle could easily be lost in the static of background noise, or worse, mistaken for something else entirely.

For decades, physicists have relied on a standard set of rules to predict how noble liquids respond to these nuclear recoils. However, these rules were built on approximations that work well for high-energy events but begin to falter when the energy drops to the sub-keV range, the very scale where dark matter signals are expected to hide. The old models often treated the atoms as simple, featureless spheres, ignoring the intricate dance of electrons that occurs when an atom is struck. This led to significant uncertainties, particularly in the lowest energy regions where the distinction between a dark matter signal and a neutrino interaction becomes critical. To solve this, a team of researchers has developed a new, first-principles approach that looks at the problem from the ground up, modeling the actual behavior of atoms and their electrons during a collision.

The researchers began by revisiting the fundamental equations that describe how an atom moves when hit. They moved beyond the simplified versions used in the past and solved a more complex mathematical description that accounts for the specific way electrons scatter and lose energy. A key part of their work involved introducing a new parameter, a scaling length that acts as a physical ruler for how electrons behave within the liquid. This parameter is not just a number they picked to make the math work; it is derived directly from the physical properties of the atoms themselves, specifically how their electrons are arranged and how they interact with the nucleus. By calculating this value from first principles, they removed the need for many of the arbitrary adjustments that previous models required.

Once they understood how the energy was initially distributed among the atoms, the team turned their attention to what happens next: the recombination process. When an atom is knocked loose, it leaves behind a trail of positive ions and free electrons. In the absence of an electric field, these electrons would simply drift back and recombine with the ions, releasing their energy as light. However, in the detectors used for dark matter searches, a strong electric field is applied to pull the electrons away so they can be counted. The size of the region where this recombination happens changes depending on the strength of the electric field. The researchers built a model to describe this region, or "box," not as a fixed shape, but as a dynamic space determined by the balance between the electric field pulling the electrons apart and the natural attraction between the positive and negative charges. This allowed them to predict how the amount of light and charge changes as the electric field is adjusted, a behavior that had previously been difficult to explain without relying on experimental data to fill in the gaps.

Another crucial insight came from looking at the specific ways electrons are emitted during the collision. The team realized that for heavier noble elements like xenon, a process where electrons are directly knocked out of their orbits plays a much larger role than previously thought. They incorporated a detailed model of these interactions, which depend on the spin and energy of the electrons, to better predict the ratio of light-producing excitations to charge-producing ions. This refinement was essential for explaining why the detectors behave differently at very low energies compared to higher ones. By combining these improved descriptions of the initial collision, the electron emission, and the recombination process, the team created a unified model that covers a vast energy range, from a fraction of a kiloelectronvolt up to one megaelectronvolt.

When the researchers tested their new model against real-world data from experiments using liquid argon and liquid xenon, the results were striking. Their predictions matched the observed light and charge yields with a level of precision that surpassed existing simulation tools, particularly in the low-energy regime where the old models struggled. The new approach successfully described the behavior of the detectors across different electric field strengths without needing to change its core parameters for every new dataset. It offered a consistent explanation for why the detectors respond the way they do, providing a solid theoretical foundation that had been missing. This work does not just refine the numbers; it provides a clearer, more reliable way to interpret the signals that might one day reveal the nature of dark matter, turning a source of uncertainty into a tool for discovery.

Technical Summary: Light and Charge Yields from Nuclear Recoils in Noble Liquids

Problem Statement
The direct detection of dark matter (DM) and coherent elastic neutrino-nucleus scattering (CE $\nu$ NS) relies heavily on dual-phase time projection chambers (TPCs) using liquid argon (LAr) and liquid xenon (LXe). A critical limitation in these experiments is the accurate calibration of detector response in the sub-keV energy regime. Specifically, the conversion of nuclear recoil energy into detectable quanta (photons and electrons) remains the dominant source of systematic uncertainty.

Existing theoretical frameworks face significant challenges. Standard Lindhard theory, while foundational, fails to describe quenching behavior below 10 keV because it neglects underlying atomic structure and non-linear electronic stopping effects. Conversely, semi-empirical frameworks like the Noble Element Simulation Technique (NEST) rely on extensive fitting to experimental data. While effective, these models often lack a fundamental predictive basis and may require distinct parameterizations for different experimental setups, limiting their ability to provide a unified description across broad energy ranges.

Methodology
The authors present a first-principles study of total quanta and charge recombination in noble liquids. The methodology integrates several physical components:

Atomic Motion and Stopping Powers: The study solves Lindhard's integro-differential equation for atomic motion, incorporating electronic straggling and detailed modeling of inter-atomic potentials. This solution accounts for electronic and nuclear stopping powers, binding energy, and electronic straggling.
Electronic Scaling Length ( $\xi_e$ ): A fundamental parameter, $\xi_e$ , is introduced as an electronic scaling length related to a physical observable. It is derived from Thomas-Fermi (TF) theory using a plane-wave approximation for electrons, accounting for the Pauli exclusion principle and the energy dependence of electronic excitations.
Quanta Production Channels: The model classifies dielectronic processes into:
- Passive Channels: Elastic and inelastic processes where the projectile electron remains in its ground state, forming a quasi-molecule.
- Active Channels: Direct Coulomb interactions between valence electrons of the projectile and target, leading to inelastic electron emission.
Exciton-to-Ion Ratio ( $N_{ex}/N_i$ ): The energy and electric-field dependence of this ratio is modeled using the Bates-Griffing (BG) process adapted for keV energies. This includes semiclassical atomic interactions and spin exchange effects in binary collisions.
Recombination Modeling: The recombination probability is expressed through an extended Thomas-Imel box model. Unlike previous approaches that use empirical power-law fits for the box size ( $a_B$ ), this model derives $a_B$ from electrostatic equilibrium between the external electric field and the electron-ion interaction within the box. This approach incorporates a polarizability model for the electric field dependence of $N_{ex}/N_i$ and provides an analytical calculation of Birks' constant.

Key Contributions and Results

Unified Description: The model provides a consistent description of light and charge yields from sub-keV energies up to 1 MeV using only one adjustable parameter (associated with the recombination process) and fundamental atomic properties.
Improved Low-Energy Physics: By solving the second-order integro-differential equation and incorporating the active Bates-Griffing channel, the model addresses the deficiencies of standard Lindhard theory at low energies. It explicitly accounts for inelastic electron emission, which is crucial for elements with high atomic numbers (e.g., LXe).
Physical Explanation of Field Dependence: The paper offers a physical explanation for the electric-field dependence of the "box size" in the Thomas-Imel model. By deriving the box size from electrostatic equilibrium, the model avoids empirical power-law fits and predicts a non-hyperbolic dependence of the recombination parameter $\xi$ on the electric field.
Comparison with Data:
- The model is compared with recent measurements of the electric-field dependence of the box size in LAr and LXe.
- It demonstrates better overall agreement with existing LAr data than NEST, particularly in the low-energy regime.
- The model yields predictions for LXe and provides a unified framework for Neon, Argon, and Xenon.
- Calculations of the exciton-to-ion ratio as a function of energy and electric field show consistency with experimental data (e.g., SCENE data for LAr).

Significance and Claims
The authors claim that their approach provides the theoretical precision required for the next generation of CE $\nu$ NS and DM experiments. By moving away from purely empirical parameterizations toward a first-principles derivation, the model offers a robust tool for interpreting detector responses in the sub-keV regime.

The paper emphasizes that the inclusion of the Bates-Griffing dielectronic process and the introduction of the electronic scaling length $\xi_e$ are significant advancements. These elements allow for a more precise description of electronic orbitals during the nuclear cascade and a better characterization of the exciton-to-ion ratio as a function of energy and electric field, rather than as a constant. The results suggest that the model can predict substantially higher light and charge yields than empirical methods like NEST in the low-energy regime, which is critical for distinguishing DM signals from the "neutrino fog" and for precision measurements of non-standard interactions.

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