Monte Carlo Simulation and Analysis of Specified Element Samples by Nuclear Resonance Fluorescence Detection

Abstract

The detection of explosives and drugs in large cargo distribution centers such as customs and logistics stations has a great effect on preventing smuggling crimes and terrorist incidents. However, the relatively thick shielding of container cargo makes the material composition information obtained by conventional detection methods such as X-ray transmission detection and imaging technology very limited. Nuclear Resonance Fluorescence (NRF) is an emerging nondestructive assay technology that uses the specific resonance energy of nuclides to identify unknown nuclides, which can be used to detect and analyze the isotopic composition of the inspected cargo. In this paper, according to the theoretical analysis of NRF, Geant4 is used to build the NRF backscatter detection model, the collimator structure of the electron accelerator and the background shield of the NRF signal are optimized and calculated, and the NRF process with ¹²C as the target element is simulated and calculated. The results show that the simulated characteristic energy spectrum of NRF signal is consistent with the theory, the designed background shielding scheme meets the needs of NRF signal identification and detection, and the simulated signal-to-noise ratio data provides the basis for the experiment.

1 Introduction

In recent years, the transportation of cargo through customs containers and land trucks has become a major part of world trade. At the same time, illegal event such as smuggling commercial contraband, explosives, and special nuclear materials (SNM) through borders and customs are also rampant. According to the International Atomic Energy Agency's Illicit Trafficking Database (ITDB), between 1993 and 2021, countries reported a total of 3,928 nuclear safety incidents. In 2021 alone, 32 countries reported 120 incidents to the ITDB [1].

NRF has developed rapidly in the fields of explosives detection, container security inspection and nuclear weapons inspection in recent years. It describes that the nucleus absorbs a photon through resonance and is excited to a specific excited state, and then de-excited by emitting one or more photons, as shown in Fig. 1. For each isotope (Z > 2), the gamma-ray energy spectrum produced by NRF is different. If the gamma-ray beam is adjusted to a specific energy, specific nucleons can be detected by nuclear resonance fluorescence, and the isotopic composition of the cargo can be analyzed. In addition, the emitted NRF photon energy is several MeV, which can penetrate most materials and boxes.

Fig. 1.

NRF excitation-de-excitation process

In this paper, an optimization scheme is designed for NRF detection based on an electron accelerator. The influence of different shield thicknesses and different target thicknesses on the NRF count rate is studied from theoretical calculations and Monte Carlo analysis, and a target with ¹²C as the target element is simulated and calculated. The optimized simulation scheme and the characteristic energy spectrum of the NRF process of the target were obtained.

2 Physical Background

NRF is a typical $\mathrm{X}(\upgamma ,{\upgamma }^{\mathrm{^{\prime}}})\mathrm{X}$ reaction, which includes two basic processes: transition by absorbing energy; decay by releasing energy. At absolute zero T = 0K, when a photon with energy E is incident, the target atom absorbs energy through isolated resonance to reach the energy level ${E}_{r}$, and then decays to the energy level ${E}_{j}$, and its cross section follows the single-level Breit-Wigner profile [2]

$${\sigma }^{NRF}\left(E\right)=\pi \frac{2{J}_{1}+1}{{2(2J}_{0}+1)}{(\frac{\hslash c}{E})}^{2}\frac{{\Gamma }_{r,0}{\Gamma }_{r,j}}{{{(E-{\mathrm{E}}_{r})}^{2}+({\Gamma }_{r}/2)}^{2}}$$

(1)

where ${J}_{0}$ and ${J}_{r}$ are the nuclear spins at the ground state and resonance level, respectively. The terms ${\Gamma }_{r,0}$ and ${\Gamma }_{r,j}$ denote the partial widths of decay from ${\mathrm{E}}_{r}$ to ground state and from ${\mathrm{E}}_{r}$ to ${\mathrm{E}}_{j}$, while ${\Gamma }_{r}$ is the total width of the energy level transition. At non-absolute zero degrees (T ≠ 0K), the energy level broadening of the NRF reaction cross-section will decrease the NRF cross-section, but compared with the cross-section values of other electromagnetic interaction processes such as photoelectric effect, Compton scattering and electron pair effect, the NRF cross-section still comparable to or even exceeding [3], so even a small amount of special nuclear material can be detected with high sensitivity of the detection system. Due to the conservation of energy and momentum, free nuclei undergoing NRF will recoil with kinetic energy. The recoil energy ${E}_{rec}$ is determined by the following Compton-like formula [4]

$${E}_{rec}=E[1-\frac{1}{1+E(1-cos\chi )/M{c}^{2}}]\cong \frac{{E}^{2}}{M{c}^{2}}(1-cos\chi )$$

(2)

where $\chi$ is the photon scattering angle relative to the incident direction. For bound nuclei in the atomic lattice, ${E}_{rec}$ may be large enough to overcome the lattice displacement energy ${E}_{d}$, in which case the kinetic energy transfer is ${E}_{rec}-{E}_{d}$. For unbound nuclei ${\mathrm{E}}_{\mathrm{rec}}{\mathrm{E}}_{\mathrm{rec}}$ less than ${E}_{d}$, the recoil is transferred across the entire lattice and recoilless NRF is achieved. For outgoing photons, the energy decreases accordingly by ${\mathrm{E}}_{\mathrm{rec}}\gg\Delta {\mathrm{E}}_{\mathrm{rec}}$, but the energy of photons emitted in the backward direction will be much lower than the resonance energy ${E}_{r}$ and it is highly unlikely that another NRF interaction will occur in the same target atom. According to the definition of the angle integral, the differential angular cross-section of the NRF outgoing photon is defined as

$$\frac{d{\sigma }_{r}^{NRF}\left(E\right)}{d\Omega }=\frac{W(\chi )}{4\pi }{\sigma }_{r}^{NRF}\left(E\right)$$

(3)

The angular correlation function [5] W(χ) is symmetric around χ = π/2, so W(χ) = W(θ), where the emission angle θ is relative to the back-beam direction. Then, the angular correlation function W(θ) is shown in formula (4)

$$ W\left( \theta \right) = 1 + \left( {R/Q} \right)cos^{2} \theta + \left( {S/Q} \right)cos^{4} \theta $$

(4)

The constants (R/Q) and (S/Q) represent the contributions of dipole and quadrupole transitions, respectively, and are determined by the sequence of spins ${J}_{0}\to {J}_{r}\to {J}_{j}$. In most experiments, it was roughly isotropically distributed. According to formula (4), the scattering angle of the NRF of ¹²C is calculated in the order of ${0}^{+}\to {2}^{+}\to {0}^{+}$. The parameters and calculation results are shown in Table 1.

Table 1. Resonance excitation-de-excitation parameters, NRF cross section and scattering angle of ¹²C

3 Simulation Setup

Figure 2 is a schematic of the constructed Geant4 simulation model. The model is as follows: the backscattering method is adopted as a whole, a high-energy electron beam is generated by an electron accelerator, electron beam produces X-rays via bremsstrahlung, the collimator confines X-rays to a certain angle range, then high-energy X-rays bombard the target to generate an NRF reaction. The HPGe detector located at 110° relative to the main beam direction receives the NRF photon signal. The detector is provided with a low-energy background shielding lead on the axial end face, and a thick shielding lead facing the accelerator to block the X-Rays from the accelerator.

Fig. 2.

NRF detection design structure

Figure 3 shows the design structure of the collimator. The overall design is a cylinder. The radius of the inlet end and the outlet end of the cylinder are different, so that the X-ray with the second highest dose at the scattering angle of 3° –7° is not shielded, and the lifting device overall efficiency. The tungsten alloy converter is placed at the exit of the accelerator beam and at the entrance of the collimator. The inner diameter of the inlet end of the collimator is 0.5 cm, the outer diameter is 5 cm, the inner diameter of the outlet end is 1.2 cm, the outer diameter is 5 cm, and the overall axial length is 10 cm. The diameter of the inlet end of the collimator completely fits the diameter of the converter.

Fig. 3.

Collimator structure diagram

The target material is graphite with ¹²C as the target element. The target shape is a square thick sheet, the width is 10.2 cm × 10.2 cm, and the target thickness is 1.25 cm. The count rate of the NRF peak corresponds to the mass thickness $\rho D$ of the measurement object. As thickness increases, NRF photon yield increases according to a power function variant relationship; the NRF photons emitted forward in the thick target have no recoil energy reduction, and the emitted photons can also cause NRF reactions. The thin lead shielding layer of the detector entrance window is 1.25 cm, which can reduce the low-energy background from the target and improve the NRF count rate of the detector. The detector faces the accelerator lead shield of 25 cm, which shields the background photons from the accelerator and other scatterers.

According to the NRF photon exit angle of ¹²C, it can be seen that the optimal setting angle of the detector is 90°. However, the interrogation system needs to inspect various explosives and nuclear materials. Combined with the 125° scattering angle set for the nuclear material ²³⁸U and the approximate isotropic NRF scattering angle characteristics, this design adopts a 110° scattering angle design.

The isotope contained in nuclear materials include ²³⁸U, ²³⁵U, and the isotope contained in explosives include ¹²C, ¹⁴N, ¹⁶O, etc. The NRF energy levels of ²³⁸U and ²³⁵U are concentrated in 1.5 MeV–2.5 MeV, while the NRF energy levels of ¹²C, ¹⁴N, and ¹⁶O are concentrated in 4 MeV–7.5 MeV, the photons in this energy range can easily penetrate the planar and coaxial HPGe detectors with low relative efficiency, and NRF requires excitation at higher incident energy. Therefore, this paper chooses the coaxial HPGe detector with a relative efficiency of 95%, the axial length of the crystal is 80.5 mm, and the radius is 79.5 mm.

4 Simulation Results

The simulation setup for the electron accelerator is as follows: the angular distribution is a Gaussian distribution with a one-dimensional 5° broadening, the energy is a Gaussian distribution with a center value of 10 MeV and a 0.001 MeV broadening, and the number of incident γ particles is 2 × 10⁷. Figure 4 is a thermal diagram of the X-ray count rate at a distance of 20 cm from the converter without a collimator, bright colors indicate high counts, cold colors indicate low counts, and the horizontal and vertical coordinates indicate distances in millimeters. It can be seen that the X-ray count at the central position is higher, and the count rate gradually decreases with the increase of the distance from the central axis.

Fig. 4.

X-ray energy spectrum generated by converter and count distribution at 20 cm

The selection of the distance between the target and the collimator is constrained by the beam diffusion angle of the collimator and the limitation of the target area; at the same time, the target and the detector have a linkage relationship, that is, if the target is too close to the collimator, the detector will move, increasing its background value. In order to make the X-rays completely incident on the target, the X-ray count rate distributions on the target were measured at distances of 40 cm and 50 cm from the target and the collimator, respectively, as shown in Fig. 5.

Fig. 5.

Count distribution on target Left: Distance 40 cm; Right: Distance 50 cm

It can be seen from the Fig. 5 that as the distance increases, the count rate distribution area on the target increases. When the distance is 50 cm, the counted area ratio can reach 65.6%, and no X-rays escape from the target, which can provide the highest NRF signal rate, which meets the experimental requirements. The purpose of masking is to obtain a clearer NRF peak, and the evaluation factor is introduced accordingly

$${Y}_{0}={n}_{{E}_{r}}/{n}_{off}$$

where ${n}_{{E}_{r}}$ is the NRF photon count generated at a specific resonance energy level when the incident energy is E, ${n}_{off}$ is the total count of scattered X-rays (background part) received on the detector from the electron accelerator when the source term is unchanged, Its significance is to test the ability of lead shielding to block the corresponding background when generating quantitative target counts (NRF photons). The NRF photons is recorded by the detector, contributing ${\eta }_{n}$. Then

$$ \eta _{n} = \left\{ {\begin{array}{*{20}c} 1 & {{\text{Record}}} \\ 0 & {~{\text{not}}\,{\text{recorded}}} \\ \end{array} } \right. $$

To count the number of all NRF photons recorded by the detector as ${N}_{1}$, the approximate probability of generating an NRF signal is ${\widehat{P}}_{N}^{(1)}$, when the confidence coefficient is 1-α = 0.95, the error of ${\widehat{P}}_{N}^{(1)}$ is

$$\left|{\widehat{P}}_{N}^{(1)}-P\right|<1.96{\sigma }_{\eta }/\sqrt{N}$$

${\sigma }_{\eta }$ is the mean square error of $\eta$. Since $\eta$ obeys the binomial distribution, according to the simulation analysis, P is 10^–6. If the relative error is required to be less than 5%, The magnitude of N is 10⁹. A bias factor of 10 is applied to the physical process of bremsstrahlung of electrons, and the simulation result with a detector shielding thickness of 25 cm is counted as 3. This count can be considered to be no statistically. At this time, the evaluation factor ${Y}_{0}$ can meet the design requirements.

Fig. 6.

Detector shield entrance window energy spectrum

In addition, comparing the X-ray energy spectrum before and after adding the shield on the side of the detector facing the accelerator is helpful to evaluate the performance of the shield. Figure 6 shows the X-ray energy spectrum of the shielded entrance end of the detector when the incident particle is 2 × 10⁷. The number of X-ray particles can be statistically 1.5 × 10⁵, while the statistical particle number on the target is 3.3 × 10⁵. According to the calculation of the shielding effect, when the incident particle is 10⁹, the shielding ability of X-rays is 7.5 × 10⁶, and it is 1.6 × 10⁷ on the main beam, so the shielding effect of this thickness can at least reach 1.6 × 10⁷ particles (the shielding effect is at least 6.3 × 10^–8) on the main beam, the detector will receive the background from the electron accelerator.

The source term of the NRF simulation adopts a Gaussian distribution with an energy center of 4.438 MeV and a spread of 0.001 MeV. The surface source is 0.5 mm × 0.5 mm, the length and width are spread by 0.1 mm, and the angular distribution is spread by 0.5° along the axial direction facing the target. The incident particle is γ, and the number is 2 × 10⁷. When the distance between the target and the detector is 20 cm, the thickness of the target is 1.25 cm, 2.5 cm, 3.75 cm, 5.0 cm respectively, and the simulation is carried out without adding a thin lead shielding layer on the axial plane of the detector, as shown in Fig. 7 for the detector energy spectrum.

Fig. 7.

Detector energy spectrum when the target thickness is 1.25 cm, 2.5 cm, 3.75 cm and 5.0 cm

It can be seen from Fig. 7 that the change of target thickness has no significant effect in the energy spectrum of the signal generated by the target, and the shape of the energy spectrum after normalization has no significant difference. Secondly, in the experimental measurement, the thickness of the sample is expected to be as thin as possible. The purpose of thinning is to reduce the absorption of the γ-ray by the sample material when it is transported in the sample, which is commonly referred to as “self-absorption” [6], thin sample thickness can weaken the count stacking of the detector.

Adding a thin lead shield to the detector entrance window can reduce the low-energy background from the target, thereby increasing the detector's NRF count rate. When the distance between the target and the detector is 20 cm, and the source term is set as above, compare the NRF counts before and after adding a thin lead layer and with different lead layer thicknesses (1.25 cm, 2.5 cm, 3.75 cm lead layer thickness), as shown in the Fig. 8. It can be known that adding a thin lead layer to the detector entrance window, with the increase of lead layer thickness, the shielding effect on the low-energy background from the target becomes more and more significant. For low background counts, 1460.75 keV of low-background nuclide ⁴⁰K, which is common in the laboratory, is used as the counting threshold, and those below this threshold are counted into statistics. The significance of this evaluation factor is to select the maximum relative NRF photon rate to obtain a clearer energy spectrum through long-term measurement in the experiment. The calculation results based on this evaluation factor are listed in Table 2.

Fig. 8.

The order from top to bottom and left to right is lead-free layer, 1.25 cm, 2.5 cm, 3.75 cm lead layer thickness

Table 2. Thin lead layer thickness and count

It can be seen from the Table 2 that as the thickness of the thin lead layer increases, the low background count decreases rapidly, and the low background count changes weakly after the lead shielding thickness reaches 2.5 cm; considering that the resonance energy peak region of ²³⁸U and ²³⁵U is 1.5 MeV–2.5 MeV, the attenuation amplitude should not be too large, and the thickness of the thin lead layer of 2.5cm is suitable.

5 Conclusion

In this paper, by analyzing the relationship between the physical process of X-ray excited NRF process and setting different target parameters, shield thickness and detection efficiency, the following conclusions can be drawn: (1) The yield of NRF photons is ~ 10⁶/An incident particle under the calculation conditions in this paper, which requires long-time detection. Optimizing the parameters of the shielding material can improve the de-spectral efficiency; (2) Optimized lead shield thickness for X-rays from accelerators. At a thickness of 25 cm, the shielding effect can be improved. The main beam/background is ~ 6.3 × 10⁸; (3) The thickness of the target has a weak influence on the detection efficiency, and the computational performance can be reduced in order to reduce “self-absorption” and prevent wasted computing performance of emitted recoilless NRF photons.

This paper provides a design method of an NRF backscatter detection scheme. The advantages of this structure design are: on the basis of ensuring the NRF detection efficiency, the design reduces the thickness of the shield, reduces the overall weight of the equipment, and improves the feasibility and practicality of technology application.