Theory of Migdal Effect Detection
The Migdal effect, stemming from neutron–nucleus scattering, is described by a differential cross-section formula that sums contributions from various nuclear processes and electron ionization probabilities. The scattering cross-section incorporates elastic, inelastic, fission, and radiative capture processes, obtained from databases like ENDF/B-VIII.0. Electron ionization probabilities are derived using methods like Dirac–Hartree–Fock. For 2.5-MeV D–D neutrons and a 50 keV nuclear recoil threshold, chemical bonds are easily broken, allowing C, H, and O to be treated as free atoms. The total Migdal cross-section is calculated by integrating over nuclear recoil and electron energy ranges.
Detector Assembly and Electronics
The detector unit is designed for high gas tightness and mechanical stability, using brazing and laser welding. Key components like ceramics, Kovar alloys, beryllium, and lead glass ensure a low out-gas rate. The detector includes a metal ceramic tube shell with ceramic rings for insulation and Kovar alloy rings for sealing and mounting a gas microchannel plate (GMCP). A pixel chip is mounted on a ceramic pedestal for data acquisition.
The electronic system is composed of three layers: a front-end board hosting the gas pixel detector (GPD) and readout circuit, a back-end board with an FPGA for multi-channel signal processing and data storage, and a high-voltage board for generating and regulating GMCP voltage and trigger signals.
Detector Calibration
Energy resolution is calibrated using a 5.9-keV 55Fe source, yielding a 26.54% resolution at 5.9 keV and demonstrating linear energy response proportional to 1/√E. Position resolution is evaluated using a deconvolution method with a copper plate obstructing X-rays. The average σ in X and Y directions is measured at 2.4 pixels (200 μm).
Simulation Framework
The Star-XP software, built on GEANT4, is used for simulating Migdal events and incorporating high-precision neutron collision data. It models charged particle motion and ionization in gas, includes electronic logic, and integrates a dedicated Migdal effect generator. A comprehensive GEANT4 simulation includes all main structural components like the gas-sensitive detector, beryllium window, and lead shielding, along with a liquid scintillator for neutron flux monitoring.
Neutron Flux and Experimental Details
D–D neutron flux and spectrum are measured using a 2″ × 2″ EJ309 liquid scintillator detector, calibrated using gamma sources and simulated with GEANT4. Neutron signals are distinguished from gamma background using pulse shape discrimination, and an iterative unfolding process determines the neutron spectrum, peaking at 2.5 MeV.
Experiments were conducted in two runs (March and July 2024), with neutron beam monitoring and detector gain calibration performed daily. Detector chamber pressure and temperature were continuously monitored, indicating stable gas conditions.
Track Identification and Event Selection
YOLOv8m is employed for identifying electron recoil (ER) and nuclear recoil (NR) tracks, achieving 99.0% ER accuracy and 99.7% NR accuracy. For Migdal event selection, NRs are reconstructed by fitting pixels with high ADC values to a straight line. Morphological erosion is applied to remove NR influence before reconstructing ER tracks. Events are retained if the ER vertex is close to the NR endpoints (R < 0.5) and ER track length exceeds a threshold. Cuts are applied to mitigate edge distortions, accidental coincidences, and multi-track backgrounds.
Quenching Effect and Background Analysis
The quenching effect, where kinetic energy of ions dissipates through inelastic collisions in gas, is incorporated into simulations using factors from the TRIM database.
Key background sources include:
- Secondary effects from neutron recoil: Delta electrons, secondary NRs, de-excitation radiation, and bremsstrahlung.
- Beam-related background: Gamma rays from non-elastic neutron collisions and β decay from activated gas atoms.
- Environmental background: Radioactive elements in air/materials and cosmic muon-induced delta electrons.
Detailed analysis and estimation of specific background components include:
- Recoil-induced δ-ray: Estimated from experimental data and Monte Carlo simulations.
- Particle-induced X-ray emission: Auger electrons and photoelectrons from gas are below the detection threshold (5–10 keV).
- Bremsstrahlung processes: Quasi-free electron, secondary electron, atomic, and nuclear bremsstrahlung are estimated to contribute negligible background.
- Random track coincidences: Characterized through data-driven methods and full GEANT4 simulations, showing good agreement.
- Neutron activation: Production rates of unstable nuclides (3H, 14C) are low and negligible due to long half-lives.
- Trace contaminants: Radioisotopes like 3H, 14C, 222Rn, 85Kr, 39Ar, and 210Pb contribute a small, estimated background.
- Muon-induced δ-rays: Estimated using local cosmic muon flux measurements and simulations.
- Secondary NR fork: Simulated using GEANT4 and TRIM, with cuts reducing the background yield.
Uncertainty and Significance
Background error estimation accounts for systematic uncertainties from the YOLO model, electron discrimination, wobble parameters, and detector energy resolution extrapolation. Cross-section and significance calculations utilize the profile likelihood method, with observed counts modeled by a Poisson distribution (μ + b) and background counts by a Gaussian distribution (b, σb). The minimum of the likelihood function at μ = 5.77 provides significant evidence for the Migdal effect (greater than 5σ). The method also determines upper and lower limits for the cross-section probability errors, incorporating signal efficiency and its uncertainty.