Experimental methodology

The experiment was carried out at the Radioactive Ion Beam Line in Lanzhou (RIBLL) [36, 37], using an 80.5 MeV/u ¹²C primary beam. The beam was delivered in continuous-wave mode by the Heavy Ion Research Facility in Lanzhou (HIRFL) [38, 39] at the Institute of Modern Physics, Chinese Academy of Sciences.

Figure 1 shows the layout of the neutron source experimental device. In this work, the broad-spectrum neutrons generated by this setup served as the incident neutrons for the ²³⁸U target sample. The transmitted neutron spectrum was subsequently measured. The ¹²C ions were accelerated to an energy of 80.5 MeV/u and focused onto a natural tungsten cylindrical target (diameter 50 mm, thickness 5 mm). The tungsten target was attached to the exit window, which was made of a 3-mm-thick iron plate at the end of the vacuum chamber. The bombardment of the tungsten target by the ¹²C beam generated a large number of secondary particles, including neutrons, gamma rays, protons, deuterons, tritons, and ³He nuclei. After traversing the target region and the surrounding air, part of this mixed secondary-particle field reached the EJ212 and BC501A detectors.

Fig. 1Full-screen View

(Color online) Schematic layout of the neutron-source experimental setup

Figure 2 shows the experimental setup for the transport of broad-spectrum neutrons in the ²³⁸U target (dimensions: 100 mm × 100 mm × 20 mm; thickness along the neutron penetration direction: d=20 mm; purity: p=99.9%; density: ρ = 18.79 g/cm³). In this experiment, the time-of-flight method was employed to measure the transmission neutron spectrum. As shown in the figure, the experimental device was largely identical to that used for the neutron-source measurement (Fig. 1). The difference is that the plastic scintillator detector (Veto) and the ²³⁸U sample were placed outside of the vacuum chamber. The Veto was used to reject charged-particle events during data analysis. The beam pickup detector (TP, a plastic scintillator detector) positioned within the vacuum chamber is located 67 cm upstream of the tungsten target. During the experiment, the TP served to monitor beam parameters, provide beam-timing information and incident-particle counts, and act as the stop signal for the neutron TOF measurement. Additionally, ¹²C ions were fully stopped in the primary target (tungsten target), with their range calculated using LISE++ being equal to 1.912 mm. In this experiment, the detection system consisted of an EJ212 plastic scintillator detector (Veto) and a BC501A liquid scintillator detector (N1). This system enabled charged-particle rejection; after removal of charged-particle events, neutron and gamma signals recorded by the liquid scintillator were separated by pulse shape discrimination (PSD), as shown in Fig. 3. The BC501A liquid scintillator detector consists of a cylindrical liquid-scintillator cell, an optical collection system, a photomultiplier tube, and a voltage divider. The liquid scintillator crystal inside the BC501A probe has a diameter and length of 12.7 cm each, a maximum emission wavelength of 425 nm, and an emission decay time of approximately 3.2 ns. The EJ212 plastic scintillator detector is a rectangular plate with dimensions of 12.7 cm × 12.7 cm × 5 mm and has a square cross-section facing the incident beam direction. Its distinguishing characteristic is a very low probability of interaction with neutral particles, while it exhibits high sensitivity to charged particles.

Fig. 2Full-screen View

(Color online) Schematic layout of the experimental setup for neutron transport through the ²³⁸U sample

Fig. 3Full-screen View

(Color online) QDC output spectrum with total and slow gates

Electronics and data acquisition

Figure 4 shows a schematic diagram of the electronics and data acquisition system employed in the neutron transport experiment for ²³⁸U. As shown in the figure, the signal from the beam pickup detector (TP, denoted BM in the electronics diagram) located in the target chamber is divided into four channels. The signal from Channel 1 was fed into a charge-to-digital converter (QDC) to record beam-energy information. The signal from Channel 2 is processed by a Constant Fraction Discriminator (CFD) and then fed into a Time-to-Digital Converter (TDC) to serve as the stop signal for neutron time-of-flight measurement. The signal from Channel 3 passes through the CFD and enters the Scaler. The signal from Channel 4 is processed by the CFD and then directed to a Logic Coincidence Unit (Coin), where it is used in coincidence with the output signal from the neutron detector to identify true nuclear reaction events. This coincident signal is subsequently sent to the Scaler and also serves as the electronics trigger signal (Trigger) for the entire experiment. Signals from the plastic scintillator detectors (Veto1 and Veto2) are directly input to the QDC for removing charged particle events during data analysis. The output signal from the liquid scintillator detector (BC501A) is split into three channels as illustrated: the Channel 1 signal was processed by the CFD and then fed into the TDC as the start signal for neutron TOF measurement; the Channel 2 signal was integrated over short and long gates in the QDC for PSD; and the Channel 3 signal passed through the CFD before entering the coincidence unit for coincidence measurement with the BM signal.

Fig. 4Full-screen View

(Color online) Schematic of the electronics and data-acquisition system

Monte Carlo calculations

GEANT4 is a versatile Monte Carlo software toolkit for the calculation of the passage of particles through matter. It is widely used across various fields, including high-energy physics, accelerator physics, astrophysics and space science, medical physics and radiation protection. GEANT4 provides a variety of physics models describing the interaction between particles and nuclei, along with comprehensive lists of associated models for users to utilize, such as BERT (Bertini intranuclear cascade model), BIC (Binary cascade model), and INCL++ (Liège intranuclear cascade model). BERT combines the Bertini intranuclear cascade model, pre-equilibrium model, fission model, and evaporation model. It is capable of simulating nuclear reactions induced by hadrons and gamma rays with energies up to 10 GeV. BIC simulates the cascade transport process of primary and secondary particles within the nucleus. It only considers the two-body interactions between primary or secondary particles and individual nucleons within the nucleus. INCL++ is applicable for simulating particle bombardment of target nuclei heavier than deuterium within the energy range of 1 MeV/u to 20 GeV/u. However, its applicability to light and unstable nuclei has not yet been comprehensively validated.

To benchmark the reliability of GEANT4 for the present transport problem, version 10.7.4 was used to simulate the experiment by combining the INCL++, BIC, and BERT physics models with the ENDF/B-VIII.0, JEFF-3.3, and JENDL-4.0 evaluated databases. The transmission neutron spectra were then calculated under the same experimental conditions as in the measurement.

Neutron energy calculation

The time-of-flight (TOF) method for measuring neutron energy spectra is based on the principle that neutrons with different energies require different amounts of time to travel the same distance. It is a measurement technique that calculates neutron energy based on the known flight distance and corresponding travel time, and it is now widely used in neutron experiments [40-43]. In this experiment, the flight distance L is defined as the distance between the center of the target sample and the geometric center of the detector. It should be noted that since the beam pickup detector is positioned at a certain distance upstream from the target, the time difference between the trigger signal and the stop signal cannot be directly used as the neutron time of flight. The actual neutron time of flight is obtained by taking the time difference between the neutron peak and the gamma peak in the TOF spectrum, plus the flight time of the gamma rays from the target center to the detector center. Figure 5 displays the time-of-flight spectra of neutrons and gamma rays, with the charged-particle background removed. The neutron energy can then be derived from the TOF spectrum using Eq. (1):(1)where E is the energy of the neutron, L is the flight distance from the center of the target to the geometric center of the detector, ΔT is the difference in flight time between the prompt gamma ray and the neutron, c is the velocity of light in a vacuum, and m_n is the neutron rest mass.

Fig. 5Full-screen View

Time-of-flight (TOF) spectrum of neutrons and gamma rays measured at 0°

Energy calibration and neutron-detection efficiency

The energy calibration of the neutron detector directly affects the accuracy and reliability of the transmission spectrum and is therefore essential in neutron-transport experiments. Based on the principle that the light output of low-energy electrons in the liquid scintillator detector is linearly related to the electron energy, standard gamma-ray sources (¹³⁷Cs, ⁶⁰Co, and ²²Na) were used to calibrate the energy of the BC501A (N1) detector. The energy calibration results are shown in Fig. 6.

Fig. 6Full-screen View

(Color online) QDC spectra for the standard sources (a) and the energy-calibration result (b) for the BC501A detector

The detection efficiency (η) is defined as the ratio of the number of detected particles to the number of particles incident on the detector. Due to the limitations imposed by detector type, geometric dimensions, energy threshold, the type and energy of the incident particles, as well as the dead time of the data acquisition system, not all neutrons entering the detector can be recorded. To obtain a more accurate neutron transmission spectrum, the neutron detection efficiency must therefore be determined. In this experiment, the SCINFUL-QMD [44, 45] simulation program was used to calculate the detection efficiency of the liquid scintillator detector under different detection thresholds. When the neutron energy is below 80 MeV, the software employs the SCINFUL model for calculations; for energies above 80 MeV but below 3 GeV, it utilizes the Quantum Molecular Dynamics (QMD) model and the Statistical Decay Model (SDM) for calculations. In previous work, the software has been benchmarked and applied to neutron transport experiments. The result is shown in Fig. 7.

Fig. 7Full-screen View

(Color online) Calculated neutron-detection efficiency of the BC501A detector

Experimental background

Background neutron measurements were conducted to evaluate the background contribution of scattered neutrons in the experimental hall. Figure 8 shows the experimental setup for measuring scattered background neutrons. A shadow bar made of iron, measuring 15 cm × 15 cm in cross-section and 100 cm in length, was placed along the flight path from the target to the liquid scintillator detector. This setup blocked almost all direct neutrons, allowing only the scattered components to reach the neutron detector. Figure 9 displays the time-of-flight spectrum of the background neutrons.

Fig. 8Full-screen View

(Color online) Schematic layout for the background-neutron measurement setup

Fig. 9Full-screen View

Time-of-flight (TOF) spectrum of the background neutrons

Uncertainty and energy resolution

The uncertainty of the experimental data consists of statistical and systematic components. The statistical uncertainty was less than 5% below 20 MeV and increased to about 35% at the highest energies because of limited neutron statistics. The dominant systematic component arose from the uncertainty in the calculated detection efficiency; it was estimated to be less than 10% for incident neutron energies in the range 0.1–80 MeV and approximately 15% for higher-energy neutrons. The energy resolution can be expressed by the following Eq. (2):(2)where ϒ is the Lorentz factor, L is the flight distance from the center of the target to the geometric center of the detector, ΔL is the uncertainty in the flight distance and was less than 1 cm, ΔT is the difference in flight time between the prompt gamma ray and the neutron, and the time resolution Δt was estimated to be 1.5 ns from the full width at half maximum (FWHM) of the prompt gamma-ray peak shown in Fig. 5.