Neutron multiplicity measurement in muon capture on oxygen nuclei in the Gd-loaded Super-Kamiokande detector

Using cosmic ray muons in the gadolinium-loaded Super-Kamiokande detector, this study presents the first threshold-free measurement of neutron multiplicity in muon capture on oxygen nuclei, determining the probabilities for emitting zero to three neutrons with a detection efficiency of approximately 50%.

The Gist

Imagine the Super-Kamiokande detector as a massive, underground swimming pool filled with ultra-pure water. It's so sensitive that it can "see" the faint flashes of light (Cherenkov radiation) created when particles zoom through the water. Scientists use this pool to catch elusive ghosts called neutrinos, but to do that, they have to filter out a lot of "noise" from the background.

One major source of noise comes from neutrons. These are tiny, neutral particles that bounce around and can trick the detector into thinking a neutrino arrived when it didn't. To fix this, scientists added a secret ingredient to the water: Gadolinium. Think of Gadolinium as a "neutron magnet." When a neutron hits a Gadolinium atom, it gets captured and lets out a bright flash of gamma rays, acting like a flare gun that says, "Hey! I'm a neutron!"

The Problem: We Didn't Know the "Neutron Count"

Scientists knew these neutrons were there, but they didn't know exactly how many came out at once during a specific event.

Imagine you're at a party. You know that when the host (a muon) gets captured by the house (an oxygen nucleus), they throw a party that releases guests (neutrons). But you don't know if the host throws out 0 guests, 1 guest, or a whole crowd of 3 or 4. Without knowing the exact number of guests, it's hard to tell if a noise in the room is a real guest or just a false alarm.

The Experiment: Catching the "Stop-and-Go" Muons

In this paper, the researchers used cosmic ray muons as their test subjects. These are particles raining down from space.

1. The Setup: They waited for a muon to dive into the water, slow down, and come to a complete stop inside the pool.
2. The Capture: Once stopped, the muon gets "captured" by an oxygen atom in the water. This is like a guest arriving at a house and immediately getting locked in the basement.
3. The Explosion: When the muon is captured, the oxygen nucleus gets excited and spits out neutrons.
4. The Count: Because of the Gadolinium, every neutron that gets caught lights up. The scientists counted how many flares went off for each captured muon.

The Big Discovery: How Many Neutrons?

Before this study, scientists had to guess or use complex models to estimate the neutron count, often missing the low-energy ones. This was like trying to count people in a dark room by only counting the ones wearing bright neon vests.

This experiment was the first to count everyone, regardless of how "quiet" or low-energy they were. Here is what they found when they looked at the "guest list" for the oxygen nucleus:

• 0 Neutrons (24%): About a quarter of the time, the muon gets captured, but the oxygen nucleus doesn't spit out any neutrons at all. It's a quiet night.
• 1 Neutron (70%): Most of the time (7 out of 10), the nucleus spits out exactly one neutron. This is the standard party.
• 2 Neutrons (6%): Sometimes, it's a double feature. About 6% of the time, two neutrons escape together.
• 3+ Neutrons (Less than 1%): Very rarely, the nucleus gets really excited and throws out three or more.

Why Does This Matter?

Think of the detector as a high-security building.

• The Old Way: Security guards were guessing how many intruders (neutrons) might be hiding. Sometimes they missed the quiet ones, leading to false alarms or missed real threats.
• The New Way: Now, thanks to this paper, the guards have a perfect attendance sheet. They know exactly how many neutrons to expect in 24% of cases, 70% of cases, etc.

This precision helps scientists:

1. Clean up the data: They can now subtract the "neutron noise" much more accurately, making their search for rare events (like protons decaying or ancient supernova signals) much sharper.
2. Understand the nucleus: It tells us how the "engine" inside the oxygen atom works when it gets hit by a muon, helping us understand the fundamental rules of nuclear physics.

The Bottom Line

This paper is like the first time someone walked into a crowded room with a perfect headcount and a list of exactly how many people leave the room in groups of 1, 2, or 3. By adding "neutron magnets" (Gadolinium) to the water, the Super-Kamiokande team finally solved the mystery of the neutron count, making the world's most sensitive underwater telescope even more powerful.

Technical Summary

1. Problem Statement

In water Cherenkov detectors (like Super-Kamiokande), neutrons produced in neutrino interactions are critical for:

• Reducing background events in searches for the diffuse supernova neutrino background and nucleon decay.
• Distinguishing between neutrinos and antineutrinos in oscillation analyses.

Despite their importance, the mechanisms of neutron production and their multiplicity distributions (the number of neutrons emitted per interaction) in light nuclei like oxygen ($^{16}\text{O}$) were not well understood. Previous studies on muon capture on oxygen relied on coincident measurements of neutrons and de-excitation gamma rays, which introduced energy thresholds and selection biases. Specifically, no experiment had directly measured the neutron multiplicity distribution without a lower energy threshold for the neutrons.

2. Methodology

The study utilized the Gadolinium-loaded Super-Kamiokande (SK) detector to perform an unbiased measurement.

• Detector Setup: The SK detector is a 50-kton water Cherenkov detector. In 2020, it was loaded with Gadolinium (Gd) sulfate to a concentration of 0.011%. Gd has a high neutron capture cross-section, releasing an $\sim$8 MeV gamma-ray cascade upon capturing a thermal neutron, significantly improving neutron detection efficiency compared to pure water (which relies on 2.2 MeV gamma rays from proton capture).
• Data Source: The analysis used stopping cosmic-ray muons recorded during normal data-taking (2020–2022). Negative muons ($\mu^-$) stopping in the detector are captured by oxygen nuclei ($^{16}\text{O}$) with a probability of $18.4 \pm 0.1\%$.
• Neutron Tagging Efficiency Calibration:
  • To determine the detection efficiency ($\epsilon$), the authors used a "control sample" of muon capture events followed by high-energy de-excitation gamma rays ($>5$ MeV).
  • These gamma rays predominantly originate from the $^{15}\text{N}$ excited state, which is associated with single-neutron emission.
  • By counting the number of tagged neutrons in this control sample and comparing it to the expected number of gamma-ray events, the tagging efficiency was calculated.
• Multiplicity Measurement:
  • The authors analyzed the full sample of stopping muon events (excluding those with high-energy decay electrons to isolate capture events).
  • They observed the distribution of tagged neutrons per event.
  • Using a statistical unfolding method (minimizing a $\chi^2$ statistic), they corrected the observed distribution for:
    1. Detection Efficiency ($\epsilon$): The probability of detecting a generated neutron.
    2. False Tagging Rate ($p$): The probability of a background signal being misidentified as a neutron.
  • The unfolding equation relates the true multiplicity ($n_i$) to the observed multiplicity ($t_i$) considering binomial detection probabilities and background contamination.

3. Key Contributions

• First Threshold-Free Measurement: This is the first direct measurement of neutron multiplicity in muon capture on oxygen without a neutron energy threshold. Previous measurements were biased toward higher-energy neutrons due to detection limitations.
• Efficiency Determination: The paper provides a rigorous determination of the neutron tagging efficiency in Gd-loaded water ($50.2\%$), validated using a specific control sample of single-neutron events.
• Unbiased Multiplicity Distribution: By removing the requirement for coincident gamma rays, the study captures the full spectrum of neutron emissions, including low-energy neutrons that were previously missed.

4. Results

The study measured the probability $P(i)$ of emitting $i$ neutrons in the muon capture reaction on natural abundance oxygen ($^{16}\text{O}$):

• Neutron Tagging Efficiency: $50.2^{+2.0}_{-2.1}\%$.
• Multiplicity Probabilities:
  • 0 Neutrons: $P(0) = 24 \pm 3\%$
  • 1 Neutron: $P(1) = 70^{+3}_{-2}\%$
  • 2 Neutrons: $P(2) = 6.1 \pm 0.5\%$
  • 3 Neutrons: $P(3) = 0.38 \pm 0.09\%$
• Comparison with Previous Data: The measured probability for emitting two neutrons ($P(2) = 6.1\%$) is significantly larger than previous measurements (which reported lower values).
  • Interpretation: This discrepancy suggests that previous experiments, which had energy thresholds, missed a significant population of low-energy neutrons. The new results indicate that muon capture on oxygen produces more low-energy neutrons than previously modeled.

5. Significance

• Improved Neutrino Physics: Accurate neutron multiplicity models are essential for reducing background noise in searches for rare events (e.g., proton decay, supernova neutrinos) and for improving the precision of neutrino oscillation measurements (specifically distinguishing $\nu$ from $\bar{\nu}$).
• Nuclear Physics Insights: The results provide constraints on the excitation function of nucleons in oxygen nuclei and offer new data on the nucleon momentum distribution within the nucleus.
• Detector Simulation: The measured distribution will allow for more accurate Monte Carlo simulations of neutron production in water Cherenkov detectors, leading to better event reconstruction and background rejection in current and future experiments (e.g., Hyper-Kamiokande).

In summary, this paper establishes a new benchmark for neutron detection in water Cherenkov detectors, revealing a higher yield of multi-neutron events (particularly low-energy ones) than previously understood, which has immediate implications for neutrino physics and nuclear structure studies.