A method and system for calculating the minimum detectable activity concentration of a radionuclide

Abstract

This invention relates to a method for calculating the minimum detectable activity concentration of a radionuclide, comprising the steps of: obtaining the source peak detection efficiency of a selected radionuclide; obtaining the background count of the selected radionuclide; calculating the minimum detectable activity concentration of the selected radionuclide; and forming a fitting formula based on the minimum detectable activity concentration of the selected radionuclide to calculate the minimum detectable activity concentration of other radionuclides in the same nuclear energy system. This invention also provides a system for calculating the minimum detectable activity concentration of a radionuclide. Using the method and system described in this invention, the minimum detectable activity concentration of other radionuclides in the nuclear energy system can be quickly calculated using the fitting formula to meet the accuracy requirements for engineering applications, reducing the workload of simulation calculations and saving manpower and time costs.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nuclear reactor radionuclide measurement, and particularly relates to a method and system for measuring minimum detectable activity concentration of radionuclides. BACKGROUND

[0002] In the early 21st century, nuclear energy is facing unprecedented development opportunities. Many developed countries and some developing countries are actively planning to build new nuclear power plants to cope with the possible energy crisis. Experts from the International Atomic Energy Agency (IAEA) predict that the world's nuclear power installed capacity will reach a minimum of 510 million kilowatts and a maximum of 810 million kilowatts by 2030. Nuclear safety is the premise of sustainable development of nuclear power, and nuclear radiation safety is a crucial part of nuclear safety. The radioactive source term in the reactor coolant is mainly composed of fission products and activation products. Complete reactor fuel elements can retain most of the radioactive fission products under normal operation and accident conditions of the reactor. However, defects may exist in the manufacturing process of fuel elements, and long-term work under harsh conditions such as high temperature, high pressure, and strong radiation in the reactor core may also cause damage. The fission products entering the primary loop significantly increase the radioactivity level of the primary loop, affecting the normal operation and radiation safety of the reactor, and posing a radiation exposure risk to workers. Through certain monitoring means, monitoring of fission products and activation products in the loop can not only evaluate the radiation safety of the reactor, but also obtain timely information on the performance of the core fuel elements, guiding workers to make appropriate emergency responses.

[0003] Before determining the monitoring system, it is necessary to evaluate whether the detection system and analysis method can reliably monitor the possibility of the to-be-measured nuclide, and determine the minimum detectable activity concentration (MDAC) of the radionuclide of the detection system and analysis method at a certain confidence level. For MDAC, it can be determined by experiment or combined or separately by simulation calculation. Experimental measurement is easily limited by devices, environment, funds, and other factors, while simulation calculation can highlight important factors and ignore secondary factors to obtain results consistent with experimental measurement values and meet the precision requirements of engineering applications, and has been widely used. MDAC calculation in low-level radioactive environments such as atmosphere, ocean, and soil is more common, while MDAC calculation on reactors is less common. In 2017, "Preliminary investigation for quali-quantitative characterization of soils contaminated with radionuclides", which is a report of the IAEA, calculated the MDAC of 137Cs in soil, and the results were consistent with the experimental values. However, the report did not mention the calculation method of MDAC, and the calculation method is not suitable for the calculation of MDAC of radionuclides in the reactor. 241Am and 152 The article “Detection efficiency and minimum detectable activity (MDA) concentration assessment of low-altitude unmanned aerial vehicles (UAVs) equipped with small-size gamma spectrometers” will be used as a reference for the calculation of the detection efficiency of the small-size CdTe detector on the UAV and the MDA concentration. 152 Eu and 241 Am as a simulated soil pollutant, the detection efficiency of the small-size CdTe detector on the UAV was measured experimentally, and the MDA concentration was calculated based on the background spectrum measured at different altitudes and inclination angles. 152 Eu and 241 Am. The article “Research on minimum detectable activity (MDA) of underwater gamma spectrometer for radioactivity measurement in the marine environment” from 2020 uses Monte Carlo simulation software to calculate the detection efficiency of detectors of different sizes and structural materials in the ocean. The background radiation at different depths in the ocean was measured experimentally, and finally the MDA concentration at different depths was calculated. 40 K and 137MDAC of Cs. The measurement of detection efficiency and background spectrum in real environment has limitations and cannot be carried out in all cases; there is also a certain difference between the background spectrum obtained by using a simple source item simulation and the background spectrum in the real environment. In 2021, the article "HPGe / BGO Compton suppression system: Monte Carlo study of radiation monitoring system for failed fuel detection in sodium-cooled fast reactors" simulated and calculated the MDAC of the Compton suppression system designed by the French Alternative Energies and Atomic Energy Commission (CEA) for the fuel failure monitoring of the sodium-cooled fast reactor using MCNP6, and the activation products were used as the source item to simulate the background spectrum of the selected fission products, but the influence of other fission nuclides on the background spectrum of the selected fission nuclides was not considered. Therefore, the workload of calculating the minimum detectable activity concentration of all nuclides in the complex source item is huge, and a large amount of manpower, time and other costs are required. In addition, the mutual relationship and influence between the nuclides should also be focused on in the above calculation process. SUMMARY

[0004] In view of the defects in the prior art, the purpose of the present application is to provide a method and system for calculating the minimum detectable activity concentration of radioactive nuclides, which can calculate the minimum detectable activity concentration of all other nuclides in the nuclear energy system that meets the engineering application precision simply and quickly by using the radioactive conditions of some typical or a few nuclides with high radioactivity without obtaining the activity concentration of all radioactive nuclides in the nuclear energy system.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is: a method for calculating the minimum detectable activity concentration of radioactive nuclides, comprising the steps of: obtaining the source peak detection efficiency of the selected nuclide; obtaining the background count of the selected nuclide; calculating the minimum detectable activity concentration of the selected nuclide; and forming a fitting formula according to the minimum detectable activity concentration of the selected nuclide to calculate the minimum detectable activity concentration of other nuclides in the same nuclear energy system.

[0006] Further, the fitting formula is: lgMDAC=C-lgP; wherein MDAC is the minimum detectable activity concentration of the radioactive nuclide, C is a fitting parameter, which is a constant, and P is the characteristic gamma ray emission branching ratio of the corresponding nuclide.

[0007] Further, the fitting formula is: MDACxP=H(E)=xxE y+ z; wherein, MDAC is the minimum detectable activity concentration of the radionuclide, E is the energy of the characteristic gamma ray of the nuclide, x, y, z are fitting parameters, P is the emission branch ratio of the characteristic gamma ray of the nuclide.

[0008] Further, the step of obtaining the source peak detection efficiency of the selected nuclide further comprises the steps of: constructing a nuclear detection system model; and simulating and calculating the source peak detection efficiency by the nuclear detection system model.

[0009] Further, the step of constructing the nuclear detection system model comprises the steps of: setting a detector and a particle source term, defining the interaction process of the particle of interest and a substance, performing event initialization, and performing statistics and outputting information of interest.

[0010] Further, in the step of simulating and calculating the nuclear detection system model, the simulation and calculation of the detection efficiency of the detector uses mono-energetic gamma ray simulation.

[0011] Further, the step of obtaining the background count of the selected nuclide further comprises the steps of: simulating an original background energy deposition spectrum; obtaining a Gaussian broadening coefficient and performing energy spectrum broadening; and counting the counts in the region of interest.

[0012] Further, in the step of simulating the original background energy deposition spectrum, the characteristic gamma ray of the radionuclide that mainly contributes to the radioactivity of the nuclear energy system is simulated.

[0013] Further, in the step of obtaining the Gaussian broadening coefficient, the MCNP broadening model is used to obtain the Gaussian broadening coefficient, the gamma rays emitted by the multi-gamma emission source are detected by the detector, data of at least three full energy peaks of the gamma rays are obtained, the full energy peaks are fitted and the energy scale of the channel address is performed, and finally the full width at half maximum of different gamma ray energies is obtained.

[0014] Then, the full width at half maximum corresponding to different energies is substituted into the MCNP broadening model formula to solve the Gaussian broadening coefficient:

[0015]

[0016] In the formula, a, b, and c are Gaussian broadening coefficients; FWHM is the full width at half maximum of the full energy peak, E s is the energy of the gamma ray at the peak of the full energy peak;

[0017] Finally, according to the formula:

[0018]

[0019] The original background energy deposition spectrum is converted into a broadened energy spectrum, wherein E' is the energy after broadening; and ξ is a random number ranging from 0 to 1.

[0020] The application also provides a system for calculating the minimum detectable activity concentration of a radionuclide, comprising a source peak detection efficiency module for obtaining the source peak detection efficiency of a selected radionuclide; a background count module for obtaining the background count of the selected radionuclide; a minimum detectable concentration activity calculation module for calculating the minimum detectable activity concentration of the selected radionuclide; and a fitting module for forming a fitting formula according to the minimum detectable activity concentration of the selected radionuclide, so as to calculate the minimum detectable activity concentration of other radionuclides in the same nuclear energy system.

[0021] The application has the effect that the minimum detectable activity concentration of other radionuclides in the nuclear energy system can be calculated through the fitting formula, and the calculation result is in the same order of magnitude as the experimental and simulated results. When the minimum detectable activity concentration of other radionuclides is needed, the fitting formula can be directly used to quickly calculate the minimum detectable activity concentration of other radionuclides in the nuclear energy system that meets the precision requirements of engineering applications, thereby reducing the workload of simulation calculation and saving manpower and time costs. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0023] Figure 2 The application is a method for calculating the minimum detectable activity concentration of a radionuclide. Figure 1 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0024] Figure 3 The application is a method for calculating the minimum detectable activity concentration of a radionuclide. Figure 1 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0025] Figure 4 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0026] Figure 5 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0027] Figure 6 The application is a method for calculating the minimum detectable activity concentration of a radionuclide.

[0028] Figure 7 The application is a method for calculating the minimum detectable activity concentration of a radionuclide. DETAILED DESCRIPTION

[0029] The application will be further described below in combination with the drawings and specific embodiments.

[0030] In radioactivity measurement, in order to select a suitable measuring device and analysis program (including sampling, sample preparation, measurement and data processing method) for a certain object to be measured, or select a suitable analysis program when a given measuring device is selected, or limited by objective conditions, when the measuring device and analysis program are determined, it is necessary to pre-evaluate the detection system and analysis method, and to determine the minimum radioactivity level of the sample that can be analyzed qualitatively and quantitatively (even with a certain accuracy), i.e. the minimum detectable activity concentration MDAC. At present, various methods have been developed to determine MDAC (Currie 1968; Anicin and Yap 1987; Currie 1995; Shi et al. 2005), and existing methods have been measured on site (Nir-El and Haquin 2001). Among them, Currie's MDAC calculation method has been widely used, as follows:

[0031]

[0032] In the formula: L D is the expected value of the minimum detectable net count; ε is the full-energy peak detection efficiency; V is the volume of the detected bulk source; P is the branching ratio of the full-energy peak peak value corresponding to γ rays; T is the measurement time.

[0033] When the expected value of the background count of radioactivity measurement is M B , the background variance When the expected value of the total count of radioactivity measurement is M 2 , the total count variance σ Δ = M. At this time, the expected value of the net count of radioactivity measurement is M B = M-M Δ , and the net count variance When the expected value of the net count is M C = 0, i.e. no radioactivity, In order to limit the first type of error that the sample to be measured has no radioactivity but is judged to have radioactivity, it is necessary to set the judgment limit L C = K0σ0. When the measured count is > L C , it is considered to have radioactivity; when the measured count is < L Δ , it cannot be judged to have radioactivity. When the expected value of the net count M C is not very large, in order to limit the probability of the second type of error that we cannot judge it to have radioactivity when it has radioactivity, i.e. the probability of the measured count < L Δ , the expected value of the net count M Δ = K0σ0+K Δ σ DGenerally, the two misjudgment probabilities are both 5%, that is, the confidence level is 95%, and K0=K Δ =K=1.645,

[0034]

[0035] Solving

[0036]

[0037] For solving the expected value L D of the minimum detectable net count, the focus is on the calculation of the background M B . In the calculation of M B , as many background counts as possible should be counted, including Compton scattering background, environmental background, and other interference background of full energy peak. When the background spectrum is used for background calculation, the interval for calculating the background is 2.54 FWHM of the full energy peak, which is called the region of interest (ROI).

[0038] As shown in Figure 1 , the application provides a method for calculating the minimum detectable activity concentration of a radionuclide, which comprises the following steps:

[0039] S1, obtaining the source peak detection efficiency of the selected nuclide;

[0040] Specifically, the source peak detection efficiency of the main characteristic gamma ray of the selected nuclide is obtained by experiment or simulation calculation, and preferably, the source peak detection efficiency of the main characteristic gamma ray of the selected nuclide is obtained by simulation calculation based on the limitation of experimental measurement.

[0041] S2, obtaining the background count of the selected nuclide;

[0042] Specifically, when calculating the background count of a characteristic gamma ray of a certain inert gas fissile nuclide, the original background energy deposition spectrum excluding the characteristic gamma ray needs to be broadened, and the broadened background spectrum is the background spectrum of the characteristic gamma ray. The background count is the count of the region of interest (2.54 FWHM) of the characteristic gamma ray on the background spectrum.

[0043] S3, calculating the minimum detectable activity concentration of the selected nuclide;

[0044] Specifically, after obtaining the source peak detection efficiency and the background count of the selected nuclide, the minimum detectable net count L D is calculated according to formula (3) by using the background count. DThe minimum detectable activity concentration of an inert gas fission nuclide corresponding to a given characteristic gamma ray can be calculated by taking the detection efficiency ε, the system source term volume V, the calculated emission branching ratio P of the characteristic gamma ray, and the set measurement time T. The minimum detectable activity concentrations calculated for the main characteristic gamma rays of the nuclide are compared, and the smallest one is selected as the minimum detectable activity concentration of that nuclide.

[0045] S4. Based on the minimum detectable activity concentration of the selected nuclide, a fitting formula is formed to calculate the minimum detectable activity concentration of other nuclides in the same nuclear energy system.

[0046] Specifically, the calculated minimum detectable activity concentration is fitted to form a fitting formula, which can then be used to estimate the minimum detectable activity concentration of other nuclides. Thus, without obtaining the activity concentrations of all radionuclides in the system, the minimum detectable activity concentrations of all other nuclides can be calculated using the radioactivity of a selected nuclide.

[0047] In this embodiment, it can be seen from formula (1) that MDAC×P is a function related to the γ-ray energy E, and the result obtained from the previous simulation is fitted according to MDAC×P=H(E). Considering the different fitting accuracy, two fitting methods can be considered: H(E) is a constant H and H(E) is a function of E.

[0048] When H(E) is considered to be a constant H, the fitting formula is: lgMDAC=C-lgP;

[0049] In the formula, MDAC is the minimum detectable activity concentration of the radionuclide; C (C = lgH) is the fitting parameter, a constant, which varies depending on the detection system; P is the characteristic gamma-ray emission branching ratio of the corresponding nuclide. Fitting is performed to obtain the fitting parameter C, and then this formula is used to calculate the minimum detectable activity concentration of other nuclides. When considering H(E) as a function of gamma-ray energy E, the fitting formula is specifically as follows:

[0050] MDAC×P=H(E=x×E y +z; where MDAC is the minimum detectable activity concentration of the radionuclide, E is the energy of the characteristic gamma rays of the corresponding radionuclide, x, y, and z are fitting parameters, and P is the emission branching ratio of the characteristic gamma rays of the corresponding radionuclide. By fitting the parameters x, y, and z, the minimum detectable activity concentration of other radionuclides can be calculated using this formula.

[0051] It is understandable that the selected nuclide can be chosen according to the actual situation, as long as a fitting formula can be formed based on the minimum detectable activity concentration of the selected nuclide, and the minimum detectable activity concentration of other nuclides in the same system can be calculated through the fitting formula.

[0052] Please seeFigure 2 , step S1 further comprises a sub-step of:

[0053] S11, constructing a nuclear detection system model;

[0054] Specifically, the Monte Carlo program is used to construct the nuclear detection system model, the detector and particle source term are set, the interaction process of the particle of interest and the material is defined, the event initialization is performed, and the information of interest is counted and output. Among them, setting the detector includes setting the detector shape, geometric size and using materials, performing event initialization includes setting the energy, flight direction, position information, etc. of the simulated source term particles.

[0055] In this embodiment, the Geant4 (GEometry ANd Tracking) program is used to construct the nuclear detection system model. Geant4 is a Monte Carlo toolkit based on C++ object-oriented technology developed by the European Nuclear Center and the Japanese High Energy Physics Center, which is used to simulate the physical transport process of particles in matter. Geant4 has the characteristics of completely open code, and users can change or supplement related code according to different simulation needs. Similar to a "collection" of C++ classes, users need to call and overload related classes when using Geant4 for simulation calculation. Geant4 integrates the processes and knowledge of particle interactions in existing theoretical systems, applies professional knowledge such as cross-section data, calculation formulas from experiments in various regions around the world, and theoretical research to simulation, and the reliability of its calculation results has been verified by many people. Geant4 has been widely used in particle detection, radiation protection and other related fields. Geant4 provides a complete toolkit for detector simulation, including geometric model construction, material property setting, initial particle generation, particle detection, particle trajectory tracking, visualization interface, user interface, etc., which can easily simulate the interaction between different particles and detectors of different shapes and different material compositions, visualize the detector and the particle motion trajectory.

[0056] It can be understood that setting the detector shape, geometric size and using materials can be described in detail by inheriting the base class G4VUserDetectorConstrucion provided by the program. In the event initialization, the energy, flight direction, position, etc. of the simulated source term particles can be initialized by inheriting the base class G4VUserPrimaryCeneratorAction provided by the program. In the definition of the particle species and characteristics of the particle of interest and the interaction process of interest in the particle and material interaction process, the base class G4VModularPhysicList provided by the program can be inherited to complete the definition.

[0057] It can be understood that in the process of constructing the nuclear detection system model, some "G4Action" classes need to be defined according to the simulation process of interest or the information of interest in the simulation process, which are implemented by inheriting the corresponding base classes.

[0058] It can be understood that in some embodiments, the commonly used particle transport Monte Carlo programs such as EGS, MCNP, FLUKA, SRIM, etc. can also be used to construct the nuclear detection system model.

[0059] Taking a specific example as an illustration, a kind of online radionuclide discrimination monitoring system for radioactive noble gas fission nuclides is designed based on the gamma radiation monitoring channel at the inlet of the helium purification system of the Shandong Shidaowan High-temperature Gas-cooled Reactor Pebble-bed Module Nuclear Power Demonstration Plant (HTR-PM). In order to preliminarily evaluate the feasibility of the detection system for monitoring radioactive noble gas fission nuclides in the primary coolant, the minimum detectable activity concentration of the detection system for radioactive noble gas fission nuclides in the primary coolant needs to be calculated. Geant4 is used to construct the nuclear detection system model, including part of the system pipeline, the primary coolant, the detection channel and the shielding lead chamber. The materials used in the detection system model are shown in Table 1, and the simulated detector is an HPGe detector with a size of GEM60P4-83.

[0060] Structure Material Density / (g / cm 3 )]]> Tube wall 321 stainless steel 8.03 Insulation layer Asbestos (KAlSi3O8) 0.12 Shielding lead Pb: 96 wt%; Sb: 4 wt% 11.15 Primary coolant He 0.0063336 Detector HPGe 6.24

[0061] Table 1

[0062] Considering the complexity of the source terms in the primary helium gas, the study only selects the noble gas fission nuclides that mainly contribute to the radioactivity of the primary loop for simulation. Because the complexity of the types and energies of particles emitted by the nuclide decay is not conducive to data processing and analysis, the study uses different intensity and energy gamma ray sources to replace the simulated nuclides. The ray sources are uniformly distributed in the simulated helium gas and are isotropically emitted. In order to completely simulate the interaction and transport process of gamma rays and electrons with materials, photoelectric effect, Compton effect and electron pair effect are considered in the simulation calculation, and the G4EmStandardPhysics data package provided by the system is used, with the default cutoff value.

[0063] S12, simulating and calculating the source peak detection efficiency through the nuclear detection system model;

[0064] Specifically, the source peak detection efficiency of the simulation calculation is the ratio of the particle number recorded by the full energy peak to the particle number emitted by the source. The main characteristic gamma rays of the corresponding nuclide are selected for simulation. The gamma rays are uniformly distributed in the primary coolant constructed by the Geant4 program. The particle number is set, and the energy deposition in the detector is counted. The ratio of the statistical count at the corresponding gamma ray energy to the total gamma ray emission particle number set in the primary coolant is the source peak detection efficiency of the corresponding gamma ray.

[0065] Taking a specific example as an illustration, the detection efficiency simulation calculation of the detector uses single-energy gamma ray simulation. Ten 8 particles are emitted each time, and the count at the corresponding energy in the energy deposition spectrum is counted.

[0066] The selected characteristic gamma rays of the inert gas fissile nuclide and the simulation results are shown in Table 2.

[0067]

[0068]

[0069] Table 2

[0070] Please refer to Figures 3-4 , step S2 further comprises the following sub-steps:

[0071] S21, simulating the original background energy deposition spectrum;

[0072] Specifically, obtaining the background spectrum is the prerequisite for background calculation. In order to be as close as possible to the real radiation environment in the nuclear energy system, the characteristic gamma rays of the radioactive nuclides that mainly contribute to the radioactivity of the nuclear energy system should be selected for simulation (the characteristic gamma rays should not include the characteristic gamma rays of the nuclide to be calculated). According to the radioactivity concentration of these nuclides, the particle number of these characteristic gamma rays uniformly distributed in the simulation source term under the corresponding measurement time is calculated according to the simulation source term volume, the emission branching ratio of the characteristic gamma rays, and the preset measurement time. The intensity setting method in the GPS source term setting method in the Geant4 program is used to set the intensity according to the ratio of the particle number of these characteristic gamma rays to the particle number of all gamma rays. Then, the simulation is carried out, the energy deposition of these gamma rays in the detector is counted, and the original background energy deposition spectrum is obtained.

[0073] Taking a specific example as an illustration, the types of radioactive nuclides in the primary coolant of HTR-PM are nearly 50, and the radioactivity of Kr, Xe, I, Cs and other fission products accounts for about 85% of the total activity. The activity concentration of the fissile nuclides in the primary coolant of the equilibrium core of HTR-PM can be calculated by using the core inventory of the nuclides according to the Booth diffusion release model and the primary nuclide migration model. The calculation results are shown in Table 3.

[0074] Nuclide Primary nuclide balance activity concentration (Bq / L) 83 Kr]]> ​ 1.34 x 10 4 ]]> 85 Kr]]> ​ 1.43 x 10 2 ]]> 85m Kr]]> ​ 5.79 x 10 4 ]]> 87 Kr]]> ​ 6.43 x 10 4 ]] 88 Kr]]> ​ 1.34 x 10 5 ]]> 89 Kr]]> ​ 2.55 x 10 4 ]]> 90 Kr]]> ​ 1.08 x 10 4 ]]> 131m Xe]] ​ 3.15 x 10 3 ]]> 133 Xe]]> ​ 7.65 x 10 5 ]]> 133m Xe]]> ​ 2.32 x 10 4 ]] 135 Xe]]> ​ 1.35 x 10 5 ]]> 135m Xe]]> ​ 1.19 x 10 4 ]] 137 Xe]]> ​ 5.35 x 10 4 ]]> 138 Xe]]> ​ 9.83 x 10 4 ]] 139 Xe]]> ​ 1.84 x 10 4 ]]> 131 I]]> ​ 1.8 x 10 2 ]]> 132 I]]> ​ 2.3 x 10 3 ]]> 133 I]]> ​ 9.2 x 10 2 ]]> 134 I]]> ​ 4.7 x 10 3 ]]> 135 I]]> ​ 1.4 x 10 3 ]]> 134 Cs]]> ​ 3.8 x 10 -1 ]]> 137 Cs]]> ​ 4.9 x 10 -1 ]]> 138 Cs]]> ​ 1.6 x 10 3 ]]>

[0075] Table 3

[0076] Following the selection criteria, characteristic gamma rays of nuclides were selected for simulation. The ratio of simulated gamma-ray particles to the total number of particles was calculated over a 5-minute measurement period. The GPS source term for the Geant4 model was then set. The energy deposition in the detector was statistically analyzed to obtain the original background energy deposition spectrum, such as... Figure 4 As shown.

[0077] S22, obtain the Gaussian broadening coefficient and perform energy spectrum broadening;

[0078] Specifically, because the simulation yields an energy deposition spectrum, when the simulated detector absorbs the same particle energy, the simulated energy spectrum will be a straight line, while the actual detector outputs a broadened spectrum. Geant4 can broaden the energy deposition spectrum using the MCNP broadening model, as shown in the following equation:

[0079]

[0080]

[0081] δ is the standard error of the full-energy peak, E s E′ represents the energy of the corresponding ray, E′ represents the energy obtained from the final detector simulation calculation, and ξ represents a random number (ranging from 0 to 1).

[0082] The gamma rays emitted by multiple gamma emission sources are detected using a detector. The gamma energy spectrum of the multiple gamma emission sources is obtained by subtracting the background environment spectrum from the measured source gamma spectrum. The data of at least three full-energy peaks are fitted using the Gauss function of Origin to obtain the address full width at half maximum (FWHM) of the full-energy peaks. At the same time, it is necessary to perform energy scaling based on the address and energy corresponding to the peak value of the full-energy peaks, and convert the fitted address full width at half maximum (FWHM) into energy full width at half maximum (FWHM) (MeV). Substituting the FWHM corresponding to different energies into formula (4), the nonlinear equation system is solved using the fsolve function in MATLAB to obtain the Gaussian broadening coefficients a, b, and c. In ROOT, the energy spectrum is broadened according to formula (5) to obtain the broadened background spectrum.

[0083] To illustrate with a specific example, let's use an HPGe detector to... 137 Cs、 60 The three γ peaks of 0.662, 1.173 and 1.332 MeV of the Co combined source were measured. The net γ spectrum was fitted using the Gauss function of Origin and the energy FWHM was obtained by energy calibration, as shown in Table 4.

[0084]

[0085] Table 4

[0086] The data in the table is moved to the right after squaring both sides of the equation (4), and the following nonlinear equations are obtained:

[0087]

[0088] The fsolve function in MATLAB is used to solve the above nonlinear equations, and a set of a, b, c obtained by solving is shown in Table 5.

[0089] Detector a b c HPGe 0.0014 0.001 0.01

[0090] Table 5

[0091] In ROOT, the spectrum is broadened according to formula (5), and the broadened background spectrum is obtained.

[0092] S23, count the counts of the region of interest;

[0093] Specifically, the background count is the count of the region of interest (2.54 FWHM) of the characteristic gamma ray on the broadened background spectrum, that is, the count of the region of interest, so as to obtain the background count of the selected nuclide.

[0094] Taking a specific example as an illustration, after obtaining the background count of the nuclide, the minimum detectable net count L D When the volume V of the simulated body source is 1.3014L, the measurement time T is 300s, and the emission branch ratio P and the detection efficiency ε of the gamma ray adopt the data in Table 2, the calculation results of the minimum detectable concentration activity are shown in Table 6.

[0095]

[0096]

[0097]

[0098] Table 6

[0099] Please refer to Figure 5 In step S4, when considering the first fitting formula, that is, MDACXP=H (constant), the calculated minimum detectable activity concentration MDAC is fitted according to the formula lgMDAC=C-lgP (C=lgH), and the fitting results are shown in Table 7.

[0100] Detector C Fitting formula [R 2 ]] HPGe 3.317 lgMDAC = C-lgP 0.8794

[0101] Table 7

[0102] Please refer to Figure 6In step S4, when MDACxP=H(E) is considered, the calculated minimum detectable activity concentration MDAC is obtained according to the formula MDACxP=xxE y The fitting results are shown in Table 8.

[0103]

[0104] Table 8

[0105] It can be understood that, by comparison, the relative error of the fitting formula formed when H(E) is considered as a function of gamma ray energy E is smaller than that of the fitting formula formed when H(E) is considered as a constant, and the calculation accuracy is higher, and the comparison results are shown in Table 9.

[0106]

[0107]

[0108] Table 9

[0109] The minimum detectable activity concentration MDAC of other nuclides is calculated by using the fitting formula, and the results are shown in Table 10.

[0110]

[0111] Table 10

[0112] Please refer to Figure 7 In the application, a method for measuring and calculating the minimum detectable activity concentration of a radioactive nuclide has the following principles:

[0113] First, the structure size, material and other information of the detection system to be simulated are determined, and a detection system model is constructed by using Monte Carlo software; then, the source peak detection efficiency of the characteristic gamma rays of the selected radioactive nuclide is simulated and calculated by using the Monte Carlo software, and then, according to the activity concentration of the radioactive nuclide which mainly contributes to the nuclear energy system, the non-broadened original background deposition spectrum of the characteristic gamma rays of the selected radioactive nuclide under a certain measurement time is simulated; the Gaussian broadening coefficient of the detector is obtained by fitting the energy spectrum through experimental measurement; the background count of the region of interest of the characteristic gamma rays of the corresponding radioactive nuclide is counted by broadening the background energy deposition spectrum according to the Gaussian broadening coefficient; the MDAC of the characteristic gamma rays is calculated according to the MDAC calculation formula, and the final MDAC of the nuclide is obtained by comparison; finally, the fitting formula is formed by the final MDAC of the nuclide, and the minimum detectable activity concentration of other nuclides can be calculated by using the fitting formula.

[0114] The application also provides a system for measuring and calculating the minimum detectable activity concentration of a radioactive nuclide, which comprises:

[0115] a source peak detection efficiency module configured to obtain a source peak detection efficiency of the selected nuclide;

[0116] a background count module configured to obtain a background count of the selected nuclide;

[0117] a minimum detectable concentration activity calculation module configured to calculate a minimum detectable activity concentration of the selected nuclide;

[0118] a fitting module configured to form a fitting formula according to the minimum detectable activity concentration of the selected nuclide, so as to calculate a minimum detectable activity concentration of other nuclides in the same nuclear energy system.

[0119] Further, the source peak detection efficiency module comprises a model construction unit and a simulation calculation unit, wherein the model construction unit is configured to construct a nuclear detection system model, and the simulation calculation unit is configured to simulate and calculate the source peak detection efficiency through the nuclear detection system model.

[0120] Further, the background count module comprises a spectrum unit, a broadening unit and a statistical unit, wherein the spectrum unit is configured to simulate an original background energy deposition spectrum, the broadening unit is configured to obtain a Gaussian broadening coefficient, and the statistical unit is configured to count counts in a region of interest.

[0121] As can be seen from the above embodiments, the present application can calculate the minimum detectable activity concentration of the selected nuclide, and establish a fitting formula, so as to calculate the minimum detectable activity concentration of other nuclides in the same nuclear energy system through the fitting formula, and the calculation result is in the same order of magnitude as the experimental and simulation results. When the minimum detectable activity concentration of other nuclides needs to be known, the fitting formula is directly used to make a quick calculation of the minimum detectable activity concentration of other nuclides that meets the precision requirements of engineering applications, thereby reducing the workload of simulation calculation and saving manpower and time cost.

[0122] Meanwhile, the method for calculating the minimum detectable activity concentration of the nuclide in the nuclear energy system is realized through simulation calculation and in combination with the characteristic parameters of the detector, thereby avoiding many limitations of radioactive experimental measurement on the reactor.

[0123] The method and system described in the present application are not limited to the embodiments described in the specific embodiments, and other embodiments can be derived by those skilled in the art according to the technical solutions of the present application, which also belong to the technical innovation range of the present application.

Claims

1. A method of calculating a minimum detectable activity concentration of a radionuclide, characterized by, The method comprises the steps of: obtaining source peak detection efficiency of the selected nuclide; obtaining background count of the selected nuclide; calculating minimum detectable activity concentration of the selected nuclide; forming a fitting formula according to the minimum detectable activity concentration of the selected nuclide to calculate minimum detectable activity concentration of other nuclides in the same nuclear energy system; The step of obtaining the background count of the selected nuclide further comprises the steps of: simulate the original background energy deposition spectrum; obtain the Gaussian broadening coefficient and perform energy spectrum broadening; count the counts in the region of interest; In the process of simulating the original background energy deposition spectrum, the characteristic gamma rays of the radioactive nuclides that mainly contribute to the radioactivity of the nuclear energy system are selected for simulation; When obtaining the Gaussian broadening coefficient, the MCNP broadening model is used to obtain the Gaussian broadening coefficient, that is, the gamma rays emitted by the multi-gamma emission source are detected by the detector, and the data of at least three gamma ray full energy peaks are obtained. Fit the full energy peak and perform channel address energy calibration to finally obtain the full width at half maximum of different gamma ray energy peaks; Then, the full width at half maximum corresponding to gamma rays of different energies is substituted into the MCNP broadening model formula to solve the Gaussian broadening coefficient: ； In the formula: a, b, c are Gaussian spread coefficients; FWHM is the full width at half maximum of the full energy peak, is the corresponding gamma-ray energy at the peak of the full energy peak; Finally, according to the formula: ； transforming the original background energy deposition spectrum into a broadened energy spectrum, wherein, is the broadened energy; is a random number in the range 0-1.

2. The method for calculating the minimum detectable activity concentration of a radioactive nuclide according to claim 1, characterized in that: The fitting formula is: lgMDAC=C-lgP; Where MDAC is the minimum detectable activity concentration of the radioactive nuclide, C is the fitting parameter, which is a constant, and P is the emission branching ratio of the characteristic gamma rays of the corresponding nuclide.

3. The method for calculating the minimum detectable activity concentration of a radioactive nuclide according to claim 1, characterized in that: The fitting formula is: MDAC x P = H(E) = x x E y + z; Where MDAC is the minimum detectable activity concentration of the radioactive nuclide, E is the energy of the characteristic gamma rays of the corresponding nuclide, x, y, and z are fitting parameters, and P is the emission branching ratio of the characteristic gamma rays of the corresponding nuclide.

4. The method for calculating the minimum detectable activity concentration of a radionuclide as described in claim 1, characterized in that, The step of obtaining the source peak detection efficiency of the selected nuclide further comprises the steps of: constructing a nuclear detection system model; calculating the source peak detection efficiency by the nuclear detection system model.

5. The method for calculating the minimum detectable activity concentration of a radioactive nuclide according to claim 4, characterized in that: The construction of the nuclear detection system model includes setting the detector and the particle source term, defining the interaction process of the particles of interest with the material, performing event initialization, and counting and outputting the information of interest.

6. The method for calculating the minimum detectable activity concentration of a radioactive nuclide according to claim 4, characterized in that: When the nuclear detection system model is simulated and calculated, the detection efficiency simulation and calculation of the detector uses single-energy gamma ray simulation.

7. A system for calculating a minimum detectable activity concentration of a radionuclide, characterized by It comprises: a source peak detection efficiency module for obtaining the source peak detection efficiency of the selected nuclide; a background count module for obtaining the background count of the selected nuclide; a minimum detectable activity concentration calculation module for calculating the minimum detectable activity concentration of the selected nuclide; a fitting module for forming a fitting formula according to the minimum detectable activity concentration of the selected nuclide to calculate the minimum detectable activity concentration of other nuclides in the same nuclear energy system; The step of obtaining the background count of the selected nuclide comprises the steps of: simulate the original background energy deposition spectrum; obtain the Gaussian broadening coefficient and perform energy spectrum broadening; Counting the statistical region of interest; In the process of simulating the original background energy deposition spectrum, the characteristic gamma rays of the radioactive nuclides which mainly contribute to the radioactivity of the nuclear energy system are simulated; In the process of obtaining the Gaussian broadening coefficient, the MCNP broadening model is used to obtain the Gaussian broadening coefficient, that is, the gamma rays emitted by the multi-gamma emission source are detected by using the detector, the data of at least three gamma ray full energy peaks are obtained, the full energy peak is fitted and the energy scale of the channel address is carried out, and finally the full width at half maximum of different gamma ray energy peaks is obtained; Then, the full width at half maximum corresponding to the gamma rays of different energies is substituted into the MCNP broadening model formula to solve the Gaussian broadening coefficient: ； In the formula: a, b, c are Gaussian spread coefficients; FWHM is the full width at half maximum of the full energy peak, is the corresponding gamma-ray energy at the peak of the full energy peak; Finally, according to the formula: ； transforming the original background energy deposition spectrum into a broadened energy spectrum, wherein, is the energy after broadening; is a random number in the range 0-1.

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