Gaseous forms of $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{124}$Sn, and $^{130}$Te: new avenues to future $0\nu\beta\beta$ time projection chambers

This paper proposes a new strategy for scaling neutrinoless double beta decay searches to the kiloton level by identifying affordable, electropositive gaseous compounds of isotopes like $^{76}$Ge and $^{100}$Mo that enable electron-drift time projection chambers, thereby overcoming the supply limitations of xenon while leveraging mature gas-gain readout technologies.

The Gist

The Big Picture: The Search for a Ghost

Imagine physicists are hunting for a very shy ghost called "neutrinoless double beta decay." Finding this ghost would prove that tiny particles called neutrinos are their own antiparticles and have mass. To catch this ghost, scientists need a massive net.

Currently, the best nets are made of Xenon (a heavy gas). Xenon works well, but it's like trying to build a skyscraper out of a rare, expensive diamond. There isn't enough of it in the world to build the giant nets (100 tons or even 1,000 tons) needed to catch the ghost with high confidence. The supply chain is tiny, and the cost is astronomical.

The Paper's Idea:
The authors ask: "What if we stop using diamonds and start using something more common, like steel or wood?" They propose building these giant nets using different gases that contain other rare atoms (like Selenium, Tellurium, or Germanium).

The Challenge: The "Sticky" Problem

To catch the ghost, the gas inside the net needs to let electrons (the signal of the ghost) float freely from one end of the room to the other, like a balloon drifting in a gentle breeze.

• The Problem: Many gases are "sticky" (electronegative). If you put an electron in them, the gas molecules grab onto it like Velcro. The electron stops moving, and you can't read the signal.
• The Solution: The authors looked for "non-sticky" (electropositive) gases. These gases let electrons drift freely so they can be caught by sensors at the other end.

The Treasure Hunt: Finding New Gases

The authors went on a chemical treasure hunt. They scanned thousands of chemical compounds to find ones that:

1. Contain the specific atoms needed for the experiment (like Selenium or Molybdenum).
2. Are gases (or can easily become gases) at reasonable temperatures.
3. Are not sticky to electrons.

The Result: They found a list of 18 new candidate gases. Many are organic compounds (containing carbon and hydrogen) that have never been used for this before.

• Examples: Hydrogen Selenide (smells like rotten eggs), Methaneselenol (smells like garlic), and Tellurophene.
• The Catch: These gases are toxic and flammable. The authors admit this is a safety nightmare, but they argue that with the right engineering (like sealed underground caves and safety scrubbers), we can handle them.

The "Tangled Track" Analogy

How do you know if a new gas is better than Xenon? It's not just about how many atoms you have; it's about how clearly you can see the path the electron takes.

Imagine you are trying to identify a runner in a crowded stadium by looking at their footprints in the mud.

• Xenon (The Heavy Mud): The mud is thick and full of heavy rocks (heavy atoms). When the runner steps, their foot gets knocked sideways easily. The footprints become a messy, tangled spaghetti of tracks. It's hard to tell if it was one runner or two.
• The New Gases (The Lighter Mud): Some of the new gases are made of lighter ingredients. The runner's footprints are straighter and cleaner. Even if the mud is slightly stickier, the path is so clear that you can easily distinguish a single runner from a pair.

The authors created a "Scorecard" (called a Figure-of-Merit) that weighs two things:

1. How many atoms are in the room? (More atoms = more chances to catch the ghost).
2. How straight are the footprints? (Straighter tracks = easier to tell signal from background noise).

The Verdict: Better Than the Diamond

When they ran the numbers on their new list of gases, the results were surprising:

• Selenium and Tellurium gases scored much higher than Xenon. Because their footprints are straighter and they are cheaper to get in bulk, a giant net made of these gases could be 10 times more sensitive than a Xenon net of the same size.
• Germanium and Tin gases are competitive with Xenon.
• Molybdenum is also a strong contender.

The Future: Building the Giant Caves

The paper concludes that we don't need to wait for more Xenon. Instead, we can build massive underground caverns (like lined rock tunnels used for storing natural gas) and fill them with these new, cheaper, non-sticky gases.

While these gases are dangerous (toxic and flammable), the authors argue that the chemical industry already knows how to handle such materials safely. If we can build the safety infrastructure, we could scale these experiments up to 100 tons or even 1,000 tons, giving us the best possible chance to finally catch that elusive neutrino ghost.

In short: The paper says, "Stop trying to build a bigger net out of rare diamonds. We found a bunch of common, non-sticky woods that make even better nets, provided we build a safe shed to keep them from catching fire."

Technical Summary

1. Problem Statement

Neutrinoless double beta decay ($0\nu\beta\beta$) searches are scaling toward tonne-scale targets to probe the Majorana nature of neutrinos. While Time Projection Chambers (TPCs) offer excellent scalability and track topology capabilities for background rejection, current leading candidates rely on Xenon-136 ($^{136}$Xe).

• The Bottleneck: Xenon is a scarce atmospheric trace gas. Its supply chain is constrained by the steel industry's cryogenic air separation processes. Scaling to 100-ton or kiloton-scale experiments (e.g., Origin-X) is economically and logistically prohibitive due to xenon's scarcity and cost.
• The Gap: There is a lack of alternative target materials that can be used in gas-phase TPCs capable of electron drift. Most existing non-noble gases are electronegative (capturing electrons to form slow-moving anions), which precludes the use of mature, high-gain electron readout technologies (like Micromegas or GEMs) essential for large-scale detectors.

2. Methodology

The authors employed a multi-step approach to identify and evaluate new gaseous target materials:

• Chemical Screening: They surveyed chemical literature to identify compounds containing $0\nu\beta\beta$ target isotopes ($^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{124}$Sn, $^{130}$Te) that are volatile (boiling points $\lesssim 135^\circ$C for gases, $\lesssim 113^\circ$C for liquids).
• Electron Affinity (EA) Calculation: To determine if a gas is electropositive (allows free electron drift) rather than electronegative, the authors calculated Electron Affinities using Density Functional Theory (DFT) with the ORCA package (B3LYP functional, def2-TZVP basis sets).
  • Criterion: A negative EA (or a positive energy requirement for dissociative attachment) indicates the gas is electropositive and suitable for electron drift.
• Figure-of-Merit (FoM) Development: Recognizing that different gases scatter electrons differently, the authors defined a novel metric called the Tangled Track Reconstruction Figure of Merit ($F_{TTR}$).
  • This metric combines stopping power (track length), radiation length (scattering/tangling propensity), and spatial resolution.
  • It accounts for the "tangling power" ($\theta_t$), which quantifies how much a track kinks due to large-angle scattering off high-Z atoms.
  • The goal is to maximize the number of target atoms per unit volume while maintaining sufficient track linearity for background rejection via topology.

3. Key Contributions

A. Identification of Candidate Gases

The paper identifies 18 candidate electropositive compounds (mostly previously unconsidered for this application) across six isotopes. Key candidates include:

• Selenium ($^{82}$Se): Hydrogen selenide ($H_2Se$), Carbonyl selenide ($CSeO$), Methaneselenol ($CH_3SeH$), Selenophene, and Benzeneselenol.
• Tellurium ($^{130}$Te): Tellurophene and Tetrahydrotellurophene.
• Germanium ($^{76}$Ge): Germane ($GeH_4$) and Tetramethylgermanium.
• Tin ($^{124}$Sn): Stannane ($SnH_4$) and Tetramethyltin.
• Zirconium ($^{96}$Zr): Zirconium(IV) tert-butoxide and Tetrakis(dimethylamino)zirconium.
• Molybdenum ($^{100}$Mo): Bis(ethylbenzene)molybdenum.

Note: The authors acknowledge these gases are generally toxic and flammable, requiring significant engineering safeguards, but argue their abundance makes them viable for massive scales.

B. The "Tangled Track" Figure of Merit

The authors introduced a rigorous method to compare gases not just by density, but by their ability to preserve track topology.

• Key Insight: High-Z atoms cause significant scattering (tangling), making single-electron tracks harder to distinguish from background.
• Result: The FoM ($F_{TTR}$) allows researchers to calculate the optimal operating pressure for a given gas to match the tracking performance of Xenon, balancing density gains against scattering losses.

C. Scalability Analysis

The paper argues that 100-ton to kiloton-scale gas TPCs are feasible without unprecedented underground infrastructure.

• Pressure Strategies: Detectors can operate at ambient pressure (eliminating heavy pressure vessels) or utilize Lined Rock Caverns (LRCs)—a gas storage technology using thin steel skins in rock caverns to hold high pressures (up to 500 bar) without massive individual vessels.

4. Results

• Performance vs. Xenon:

  • Selenium compounds (e.g., $H_2Se$) show a discovery potential ($\Gamma_{TTR}$) roughly 8–8.4 times higher than natural Xenon. This is due to a combination of favorable nuclear physics (higher Q-value, better matrix elements) and superior tracking properties (longer, straighter tracks).
  • Tellurophene ($^{130}$Te) offers the highest discovery potential among unenriched options, with a $\Gamma_{TTR}$ ratio of 11.3 compared to natural Xenon.
  • Germanium and Tin compounds are competitive with Xenon, offering similar or slightly better performance depending on enrichment levels.
  • Zirconium and Molybdenum compounds, despite having higher stopping powers (shorter tracks), still outperform Xenon due to their very high Q-values ($>3$ MeV) and favorable nuclear matrix elements.

• Enrichment Economics:

  • Switching from natural Xenon to enriched $^{136}$Xe gains a factor of ~11.6 in decay rate.
  • Switching from natural Xenon to natural Tellurium ($^{130}$Te) gains a factor of ~11, but at a significantly lower cost because Te is a byproduct of copper mining and is far more abundant than Xe.

• Infrastructure Feasibility:

  • A 10-ton $^{82}$Se TPC could fit in a standard cavern (e.g., SNOLab Cube Hall) at ambient pressure.
  • A 100-ton scale is achievable in existing large caverns (e.g., SuperK size) at modest pressures (5–20 atm).

5. Significance and Conclusion

This paper fundamentally shifts the paradigm for next-generation $0\nu\beta\beta$ experiments:

1. Breaking the Xenon Bottleneck: It demonstrates that the supply chain limitations of Xenon are not a hard limit on discovery potential. Abundant, non-noble elements can be used in gas-phase TPCs.
2. Enabling Kiloton Scales: By identifying electropositive gases and establishing a framework for "tangled track" optimization, the authors provide a realistic pathway to 100-ton and kiloton-scale detectors. These scales are necessary to probe the inverted hierarchy of neutrino masses.
3. Background Rejection: The work emphasizes that track topology remains the most powerful background rejection tool. The proposed gases, particularly Selenium and Tellurium compounds, offer superior track linearity compared to Xenon, enhancing the signal-to-noise ratio.
4. Engineering Challenge: While the physics case is strong, the paper highlights that the primary hurdles are now chemical safety (handling toxic/flammable gases) and radiopurity of the new compounds, rather than fundamental physics or supply scarcity.

In summary, the authors propose a viable, scalable, and potentially more sensitive alternative to Xenon-based TPCs, utilizing a diverse suite of electropositive organometallic and inorganic gases to push the frontiers of neutrino physics.