Modelling instrumental response for neutron scattering experiments at CSNS

This paper presents a data reduction method and validates the CSNS in-house Monte Carlo code, Prompt, by demonstrating its ability to accurately reproduce thermal neutron scattering experiments on light and heavy water, including the elimination of inelasticity effects and the analysis of multiple scattering.

The Gist

Imagine you are trying to understand the layout of a crowded, dark room by throwing thousands of tiny, invisible ping-pong balls (neutrons) into it and listening to how they bounce off the furniture.

This paper is about building a perfect digital twin of a real-world neutron scattering experiment to see if our computer models can predict exactly what happens when those "ping-pong balls" hit water.

Here is the breakdown of their work, using some everyday analogies:

1. The Goal: The "Digital Twin"

Scientists at the China Spallation Neutron Source (CSNS) have a giant machine that shoots neutrons at samples (like light water and heavy water) to study their atomic structure.

• The Problem: Real experiments are messy. Neutrons don't just bounce once; they bounce off multiple atoms, lose energy, get absorbed, or change direction in complex ways. Traditional computer models often simplify these physics too much, like trying to predict traffic by assuming cars only drive in straight lines.
• The Solution: The team used a new, powerful computer code called Prompt. Think of Prompt as a hyper-realistic video game engine. Instead of making shortcuts, it simulates every single "ping-pong ball" (neutron) interacting with every single atom in the sample, including the messy stuff like energy loss and multiple bounces.

2. The Experiment: The "Water Test"

They tested this digital twin on two very familiar substances: Light Water (what you drink) and Heavy Water (used in nuclear reactors).

• Why these? Water is simple in theory but tricky in practice because hydrogen atoms are light and energetic. When a neutron hits a hydrogen atom, it's like a bowling ball hitting a ping-pong ball—the neutron loses a lot of energy and speeds up or slows down drastically. This is called inelastic scattering.
• The Setup: They ran the real experiment at their lab and ran the exact same scenario inside the Prompt computer simulation.

3. The "Ghost" in the Data: Inelasticity

Here is the most fascinating part of the paper.

• The Mystery: In the real experiment, the data showed some strange "ghost" peaks and dips that didn't seem to belong to the water itself. They looked like artifacts or errors.
• The Detective Work: The team realized these "ghosts" were actually caused by the inelasticity (the energy exchange).
  • Analogy: Imagine you are listening to a song played on a piano, but the piano keys are slightly sticky. The notes come out slightly faster or slower than they should. If you don't know the piano is sticky, you think the song is wrong.
  • In the simulation, when they ignored the energy exchange (pretending the neutrons didn't lose or gain energy), the "ghost" peaks appeared, just like in the real messy data.
  • When they included the energy exchange in the simulation, the "ghosts" disappeared, and the data matched the theoretical expectation perfectly.
• The Takeaway: They proved that those weird bumps in the data weren't errors; they were the fingerprint of the neutrons losing energy to the water molecules.

4. The "Bouncing Ball" Problem: Multiple Scattering

Another issue they tackled was multiple scattering.

• The Analogy: Imagine throwing a ball into a dense forest. Sometimes it hits one tree and bounces to the detector (good). Sometimes it hits a tree, bounces to another tree, hits a third, and then reaches the detector (bad). The second path gives you false information about where the ball came from.
• The Fix: Because the water sample was a bit thick, many neutrons bounced around too much. The team used a clever math trick (called "biasing") in their simulation to count these "extra bounces" more efficiently. They found that for thick samples, these extra bounces create a lot of "noise," but their new software could calculate exactly how much noise to subtract.

5. The Verdict: A Perfect Match

After all the hard work, they compared the Real World (the lab) with the Virtual World (the Prompt simulation).

• The Result: They matched almost perfectly. The computer simulation could reproduce the exact angles, wavelengths, and even the weird "ghost" peaks caused by energy loss.
• Why it Matters: This means scientists can now trust their computer models to "clean up" real experimental data. Instead of guessing how to fix the messy data, they can use the simulation to tell them exactly what the "true" signal looks like.

Summary in One Sentence

The authors built a super-accurate computer simulation of a neutron experiment that successfully mimics the messy reality of physics, proving that the strange "glitches" in their data were actually just the sound of neutrons losing energy to water molecules.

Technical Summary

Here is a detailed technical summary of the paper "Modelling instrumental response for neutron scattering experiments at CSNS":

1. Problem Statement

Neutron total scattering experiments are crucial for analyzing both long-range and short-range order in materials. However, interpreting data from thermal neutron scattering is challenging due to several factors:

• Instrumental Response: Accurate simulation of the instrument's response is necessary to optimize performance and interpret data correctly.
• Limitations of Existing Libraries: Standard nuclear data libraries (e.g., ENDF/B, JEFF) contain thermal neutron scattering cross-sections for only ~20 materials at fixed, often high, temperatures, limiting their applicability to precise experimental conditions for liquids and complex materials.
• Inelasticity Effects: In total scattering experiments, the energy transfer per event is unknown. For light-element-rich materials (like water), inelastic scattering causes significant distortions in the data (e.g., wavelength shifts) that are difficult to correct using traditional elastic approximations.
• Simulation Constraints: Traditional Monte Carlo ray-tracing tools (e.g., McStas) often rely on linear chain approximations and simplified physics, making it difficult to calculate absolute scattering intensities or model non-linear physical arrangements like complex detector geometries and multiple scattering events accurately.

2. Methodology

The authors utilized the Prompt Monte Carlo particle transport code, developed by researchers at the China Spallation Neutron Source (CSNS), to model the interaction of incident beams with samples and compare results directly with experimental data.

• Experimental Setup: Experiments were conducted on the Multi-Physics Instrument (MPI) at CSNS using liquid light water ($H_2O$) and heavy water ($D_2O$) at room temperature. The setup included a time-of-flight (TOF) system with a decoupled water moderator, a six-channel collimator, and 28 detector modules covering scattering angles from $31^\circ$to$170^\circ$.
• Simulation Framework:
  • Physics Engine: The simulation incorporated the NCrystal library for detailed scattering processes (elastic, inelastic, coherent, incoherent) and used the CAB models for $H_2O$ and $D_2O$ cross-sections.
  • Geometry: The MPI geometry, including the moderator, slits, collimators, and detector tubes (modeled as $^3He$ gas), was reconstructed in Prompt.
  • Data Reduction: A unified data reduction method was developed to process both measured and simulated detector events. This involved converting TOF and spatial data into differential counts ($\lambda_e, \theta$), normalizing against a vanadium standard and a monitor, and applying distortion factors for absorption and multiple scattering.
  • Biasing Techniques: Variance reduction (biasing) techniques were employed to efficiently evaluate contributions from multiple scattering events, which are rare in standard simulations but significant in thick samples.

3. Key Contributions

• Development of a Unified Reduction Method: The paper presents a robust method to process both experimental and simulated data on the same footing, allowing for a direct comparison of angular distributions, wavelength distributions, and differential cross-sections without relying solely on post-hoc correction algorithms.
• Absolute Scale Simulation: By integrating detailed physics (including inelasticity and multiple scattering) within the Prompt code, the study achieves simulation results on an absolute scale, overcoming the limitations of relative intensity simulations common in ray-tracing codes.
• Inelasticity Signature Identification: The authors successfully identified and modeled specific "inelasticity signatures" in the data—unexpected peak structures in the calibrated intensity that correspond to dips in the incident neutron spectrum.
• Quantification of Multiple Scattering: The study quantified the impact of sample thickness on multiple scattering, demonstrating that reducing sample thickness significantly lowers the ratio of double-scattering events relative to single-scattering events.

4. Results

• Consistency: There is a high degree of consistency between the simulation and experimental results for both $H_2O$ and $D_2O$. The simulated angular and wavelength distributions, as well as the derived differential cross-sections, match the experimental data closely (disagreements < 15% for $Q_e > 1.5 \text{ \AA}^{-1}$).
• Reproduction of Inelasticity Effects:
  • Experiments showed distinct "valleys" or dips in the calibrated intensity at specific wavelengths (e.g., 4.05 Å).
  • Simulations using an elastic approximation (assuming no energy exchange) reproduced these dips as artificial peaks, confirming they are signatures of inelasticity.
  • When the simulation explicitly included energy exchange (inelastic scattering), these artificial peaks were eliminated, proving that the observed distortions in the raw data are caused by the shift of scattered neutron wavelengths due to inelastic interactions with hydrogen atoms.
• Multiple Scattering Analysis:
  • For the cylindrical $D_2O$ sample (thickness ~9 mm), double scattering accounted for 19.2% of the total event count.
  • Reducing the sample thickness to 1 mm lowered this ratio to 6.8%.
  • The biasing technique significantly improved the statistical quality of high-order scattering simulations, making the analysis of multiple scattering computationally feasible.
• Vanadium Calibration: The simulations accurately reproduced the Bragg peaks of the vanadium container used for calibration, validating the geometric and divergence modeling of the instrument.

5. Significance

• Validation of Prompt Code: This work validates the Prompt Monte Carlo code as a powerful tool for simulating thermal neutron scattering with absolute accuracy, capable of handling complex geometries and detailed physics processes that traditional ray-tracing codes cannot.
• Improved Data Interpretation: By demonstrating that inelasticity effects can be accurately reproduced and understood through simulation, the study provides a new pathway for interpreting total scattering data. It suggests that rather than just correcting data post-measurement, researchers can use simulations to understand the origin of distortions.
• Future Data Correction: The ability to model and "remove" inelasticity signatures in simulations serves as a benchmark for developing future data correction algorithms. The authors propose that the elimination of these signatures will be a key criterion for assessing the effectiveness of such algorithms.
• Instrument Optimization: The methodology offers a framework for optimizing neutron instrument designs and sample environments (e.g., determining optimal sample thickness) to minimize multiple scattering noise before experiments are conducted.

In conclusion, this paper bridges the gap between complex experimental neutron scattering data and high-fidelity Monte Carlo simulations, providing a comprehensive toolkit for understanding and correcting instrumental and physical distortions in thermal neutron total scattering experiments.