Low Energy Phonon Bursts Created By Fast Neutron Damage

This paper presents the first measurement of phonon bursts caused by fast neutron damage in solid-state calorimeters but concludes that such bursts do not dominate the low-energy event excess observed in dark matter and neutrino searches, based on differences in spectral shape, thermal history dependence, and exposure scaling compared to control detectors.

The Gist

The Big Picture: The "Ghost" in the Machine

Imagine you are trying to listen for a tiny, specific whisper in a very quiet room. This is what scientists do when they hunt for Dark Matter or rare neutrino interactions. They use super-sensitive detectors (like ultra-cold silicon crystals) that can hear the faintest "thump" of a particle hitting them.

However, there's a problem. The detectors are hearing a lot of ghostly whispers (low-energy noise) that shouldn't be there. Scientists call this the "Low Energy Excess" (LEE). For years, they've been trying to figure out what causes these ghosts.

One popular theory was: "Maybe cosmic rays (particles from space) hit our detectors, break some tiny atoms inside, and those broken atoms slowly 'heal' themselves over time, creating little bursts of heat (phonons) that look like dark matter."

This paper is the team's attempt to test that theory. They asked: "If we intentionally break the detector with a neutron gun, will it create the exact same ghostly whispers we see in nature?"

The Experiment: The "Stress Test"

To test this, the scientists built two sets of identical, super-sensitive detectors (Set A and Set B).

1. The "Control" Group: These detectors were left alone, only exposed to the natural background radiation of the universe (like a house left in a quiet neighborhood).
2. The "Irradiated" Group: These detectors were blasted with a massive dose of fast neutrons from a machine (like a house being hit by a firehose).

They then cooled both sets down to temperatures colder than outer space and listened to the noise they made.

The Findings: The "Broken Glass" vs. The "Cracked Wall"

Here is what they discovered, using some analogies:

1. The Damage is Real, But Different

When they blasted the detectors with neutrons, they did create extra noise. The detectors started making "phonon bursts" (little heat spikes).

• Analogy: Imagine a pristine glass window. If you throw a pebble at it, it cracks. As the glass settles, it might creak and groan. The scientists confirmed that hitting the crystal with neutrons does make it creak and groan.

However, the sound of this "creaking" was different from the ghostly whispers they usually see in nature.

• The Difference: The natural "ghosts" (LEE) have a smooth, broad distribution of energy. The "neutron damage" ghosts had a sharp, specific peak (like a specific musical note) and a different shape.
• The Metaphor: It's like trying to identify a bird by its song. The natural background noise sounds like a crow (a specific, rough caw). The neutron damage sounded like a chicken (a different, clucking sound). They are both birds (noise), but they aren't the same species.

2. The "Healing" Speed (Thermal History)

The scientists noticed something fascinating about how the damage changed over time and with temperature.

• The Warm-Up Test: They took the damaged detectors and warmed them up to a "warm" 50 Kelvin (still very cold, but warm for a super-cold detector).
• The Result: When they cooled them back down, the "neutron damage" noise dropped significantly. It was like the glass "healed" itself when warmed up.
• The Twist: The natural "ghosts" (the LEE) didn't behave this way. They didn't disappear or change as drastically when warmed up. This suggests the natural ghosts aren't caused by the same kind of damage that the neutrons created.

3. The Math Doesn't Add Up

The scientists did a back-of-the-envelope calculation.

• The Logic: If cosmic rays are causing the natural ghosts, then the amount of damage from cosmic rays over a few months should be roughly proportional to the damage from their neutron gun.
• The Reality: The neutron gun created thousands of times more damage than cosmic rays ever could. Yet, the extra noise in the neutron-blasted detector was only 10 times louder than the natural noise.
• The Conclusion: If the natural ghosts were caused by neutron damage, the natural noise should have been much, much louder. Since it wasn't, the "neutron damage" theory doesn't explain the main problem.

The Verdict: A New Clue, But Not the Smoking Gun

What did they prove?
They proved that fast neutrons do create low-energy noise in these detectors. This is a new piece of knowledge! If you are building a detector and you accidentally blast it with neutrons (like during calibration), you will get extra noise that looks like dark matter. You have to be careful.

What did they disprove?
They provided strong evidence that the main source of the "Low Energy Excess" (the annoying background noise that has plagued dark matter searches for years) is NOT caused by cosmic rays damaging the crystal and letting it heal slowly.

The Takeaway for the General Public

Think of the detector as a very sensitive microphone.

• The Mystery: The microphone is picking up static that looks like a secret message.
• The Old Theory: "Maybe the wind (cosmic rays) is shaking the microphone stand, causing the static."
• The Experiment: The scientists shook the microphone stand violently with a machine to see if it made the same static.
• The Result: The machine shaking made static, but it sounded different and faded away differently than the natural static.
• The Conclusion: The wind isn't the main culprit. The "ghosts" are likely coming from somewhere else entirely—perhaps tiny flaws inside the crystal made when it was grown, or some other mystery we haven't solved yet.

This paper is a crucial step in "debugging" the universe's most sensitive instruments, helping scientists know what to ignore and what to keep looking for.

Technical Summary

1. Problem Statement

Solid-state athermal phonon calorimeters, used for searching for low-mass dark matter and coherent neutrino-nucleus interactions, suffer from a persistent background known as the "Low Energy Excess" (LEE). This manifests as an unexpected surplus of events below a few hundred eV. While various mechanisms have been proposed (e.g., stress, surface effects), the dominant source remains unexplained.

A recent hypothesis (Ref. 13) suggested that fast neutrons (primarily from cosmic ray secondaries) interact with the detector crystal, creating lattice defects (displaced atoms). These defects are metastable and relax over long timescales, emitting bursts of athermal phonons that mimic the observed LEE. This paper aims to test this hypothesis by artificially inducing such damage and comparing the resulting phonon bursts to the natural LEE background.

2. Methodology

The TESSERACT Collaboration conducted a controlled experiment comparing irradiated detectors against control (unexposed) detectors.

• Detectors: Two sets of identically fabricated 1 mm thick, 1 cm² silicon athermal phonon detectors were used. They utilized Transition Edge Sensors (TESs) coupled to aluminum phonon collection fins in a QET (Quasiparticle-trap-assisted Electrothermal-feedback Transition-edge-sensor) configuration.
  • Set A: Standard design.
  • Set B: Modified design with shorter fins and longer TESs (higher saturation energy).
• Neutron Exposure:
  • Irradiated Detectors: Exposed to high-flux artificial neutron sources:
    • DD Generator: 2.45 MeV neutrons (Deuterium-Deuterium fusion).
    • AmBe Source: 0–11 MeV neutrons (Americium-Beryllium).
  • Control Detectors: Kept in the same environment but shielded from artificial sources, exposed only to ambient cosmic ray neutrons.
• Operation: Detectors were cooled to millikelvin temperatures in a dilution refrigerator. Data was collected over several months, including a "warm-up" cycle where detectors were heated to ~50 K for three days to test thermal annealing effects.
• Data Analysis:
  • Events were filtered to remove vibration-induced noise (correlated with wire bond vibrations) and coincident background events (EMI or PCB scintillation).
  • Spectral shapes and event rates (15–30 eV range) were analyzed as a function of time since cooldown.
  • Damage estimates were calculated using Geant4 simulations combined with Lindhard yield models and Non-Ionizing Energy Loss (NIEL) calculations to quantify the energy deposited into the crystal lattice.

3. Key Contributions

• First Direct Measurement: This is the first measurement of phonon bursts specifically caused by the relaxation of damage induced by fast neutrons in silicon detectors.
• Quantification of Damage: The authors quantified the non-ionizing energy deposited by artificial neutron sources versus cosmic rays, finding that the artificial sources delivered 3–4 orders of magnitude more damage energy.
• Thermal Annealing Study: The experiment included a controlled warm-up to 50 K, demonstrating that neutron-induced defects can be annealed (removed) at relatively low temperatures, significantly altering the background rate.
• Hypothesis Testing: The study provides a rigorous test of the "neutron damage relaxation" hypothesis for the LEE, comparing spectral shapes, time evolution, and thermal history dependencies.

4. Key Results

• Observation of Phonon Bursts: The irradiated detectors exhibited a significant excess of events above ~10 eV compared to controls.
  • Set A (High Exposure): Showed a distinct Gaussian peak centered at 20.1 ± 0.1 eV (width ~4.4 eV) on top of the standard LEE background. This suggests the relaxation of specific, complex defect states.
  • Set B (Lower Exposure): Showed a more uniform enhancement of the background without a clear peak.
• Spectral Differences: The spectral shape of the neutron-induced bursts in irradiated detectors was significantly different from the natural LEE observed in control detectors. The natural LEE is broader and lacks the distinct 20 eV peak seen in the heavily irradiated samples.
• Rate Discrepancy:
  • The rate of events in irradiated detectors was higher than controls but not as high as predicted if cosmic ray damage were the sole source of LEE.
  • Scaling the artificial damage to the expected cosmic ray flux suggests that if cosmic ray damage were the dominant LEE source, the observed rates would be much higher than what is actually measured.
• Thermal History Dependence:
  • Both irradiated and control detectors showed a power-law decay in event rates over time ($R \propto t^{-\alpha}$).
  • Crucially, after warming the detectors to 50 K, the event rate in the irradiated detector dropped significantly, and the spectral shape changed, becoming more similar to the control. This indicates that the neutron-induced defects responsible for the bursts are annealed at 50 K, whereas the natural LEE mechanism appears less sensitive to this specific thermal cycle or follows a different relaxation dynamic.
• Defect Lifetime: Based on the decay of the excess rate between two runs separated by ~75 days, the lifetime of room-temperature neutron-induced defects was estimated to be approximately 75 days.

5. Significance and Conclusion

The study concludes that while fast neutron damage does create low-energy phonon bursts, these bursts are not the dominant source of the Low Energy Excess (LEE) observed in standard dark matter detectors operating in low-background environments.

• Spectral Mismatch: The distinct 20 eV peak in irradiated detectors is absent in the natural LEE.
• Rate Mismatch: The observed LEE rate is too low to be explained by the relaxation of cosmic ray-induced damage at the levels calculated.
• Thermal Mismatch: The response to the 50 K warm-up differs between the induced damage and the natural background.

Implications:

1. Calibration Caution: Experiments using high-flux neutron sources for calibration must be aware that they induce long-lived (months) phonon bursts that can contaminate data.
2. Lingering Mystery: The origin of the natural LEE remains unresolved. It is likely caused by a different mechanism, such as defects formed during crystal growth, stress-induced relaxation, or a specific type of cosmic ray interaction not fully captured by the current damage models.
3. Future Work: Further research is needed to distinguish between cosmic-ray-induced defects and other bulk crystal defects, potentially requiring different thermal cycling strategies or alternative detector materials.