A method for simultaneous quantitative measurement of liquid scintillation double nuclides based on mixed spectrum deconvolution

Abstract

The application discloses a kind of liquid scintillation double-nucleus simultaneous quantitative measurement methods based on mixed spectrum, comprising preparing double-nucleus mixed sample;Establish the spectrum theoretical description model of single nucleon;T pipe, D pipe energy spectrum is solved by using nonlinear fitting method jointly;T pipe and D pipe count value are obtained by being based on the theoretical description model to the T pipe, D pipe energy spectrum and being solved spectrum;The TDCR liquid scintillation system with T, D pipe energy spectrum output function in the application does not need a large number of pre-calibration work and standard quenching series source, does not depend on the accuracy of calibration, compared with function fitting stripping method, T, D spectrum is calculated simultaneously in the process of spectrum analysis, and absolute measurement is realized based on the mutual constraint of parameters.

Description

Technical Field

[0001] This invention relates to the field of radionuclide detection and measurement technology, and in particular to a method for simultaneous quantitative measurement of two nuclides in liquid scintillator based on mixed spectrum interpretation. Background Technology

[0002] Liquid scintillation counting (LSC) is a widely used technique for measuring radionuclides, particularly suitable for detecting low-energy beta-ray nuclides. This technique utilizes the interaction between a liquid scintillator and beta particles to generate scintillation signals. Photon pulses are collected by a photomultiplier tube (PMT), and energy spectrum information is obtained using a multichannel analyzer (MCA), thereby enabling the measurement and quantitative analysis of radionuclides.

[0003] Conventional liquid scintillation methods typically measure only one type of radionuclide or a mixture in equilibrium. However, many disciplines, such as nuclear energy, environmental science, and biomedicine, require simultaneous analysis of mixtures of two radionuclides. For β-nuclides, their energy distribution is a continuous distribution from 0 to the maximum β-particle emission energy of each nuclide. Therefore, the energy spectrum contribution of low-energy β-nuclides completely overlaps with that of high-energy β-nuclides. Traditional single-energy windows or simple counting methods are insufficient to effectively distinguish the contributions of each nuclide, making the simultaneous analysis of two radionuclides challenging.

[0004] Therefore, the current mainstream method is to divide the corresponding intervals according to the number of nuclides, and separately calibrate the relationship between the efficiency of nuclide A in interval A, the efficiency of nuclide A in interval B, the efficiency of nuclide B in interval A, the efficiency of nuclide B in interval B, and the external standard source indication parameters. When measuring actual samples, the activity of each nuclide is solved according to the external standard source indication parameters and the efficiency calibration curve. This requires that the liquid scintillation instrument used for measurement be equipped with an external standard source, and that the curve be calibrated in advance using a standard quenching series source. Moreover, only relative measurements can be performed, and the accuracy of the measurement depends on the accuracy of the calibration.

[0005] For pure β nuclides such as H-3 and C-14, it is usually necessary to use a liquid scintillation counter to measure their activity. In the case of a mixed sample, chemical separation is usually required first, followed by measurement of individual nuclides, which brings great difficulty to the sample preparation process. When directly measuring mixed nuclides, it is necessary to calculate the content of the two components by interpreting the spectrum and then calculate the activity. The current conventional mixed spectrum interpretation methods mainly include the dual-interval efficiency calibration method [1], the nuclide library quenching series spectrum calibration method [2], and the function fitting spectrum stripping method.

[0006] The first two methods rely on accurate calibration. The dual-interval efficiency calibration method requires prior calibration of efficiency curves using a large number of quenched source series, while the nuclide library quenched source series calibration method requires calibration of a large number of standard energy spectrum libraries using quenched source series. Both methods also require the use of liquid scintillation instruments with external standard sources and the measurement of the external standard source indication parameters, typically enabling only relative measurements. The function fitting stripping method requires a large energy difference between the two nuclides in the mixed sample, and the stripping effect and accuracy depend entirely on the selection of the fitting function, lacking theoretical basis and typically only used for relative measurements. Therefore, a method for simultaneous quantitative measurement of two nuclides using liquid scintillation based on mixed spectrum decomposition is needed. Summary of the Invention

[0007] The purpose of this invention is to provide a method for simultaneous quantitative measurement of liquid scintillator dual nuclides based on mixed spectrum interpretation, which does not require an external standard source or extensive pre-calibration work, and can achieve the requirement of absolute (direct) measurement, thereby improving the existing mixed nuclide measurement capabilities.

[0008] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0009] The first aspect of this invention provides a method for simultaneous quantitative measurement of two liquid scintillation nuclides based on mixed spectrum interpretation, wherein the activity of the two nuclides is simultaneously measured using liquid scintillation and absolute measurement is achieved through mixed spectrum interpretation, comprising the following steps:

[0010] Step 1: Prepare a dual-nucleoside mixed sample;

[0011] Step 2: Establish a spectral theory description model for single nuclides;

[0012] Step 3: Use a nonlinear fitting method to jointly solve the energy spectra of the T-tube and D-tube;

[0013] Step 4: Deconstruct the energy spectra of the T-tube and D-tube based on the theoretical description model to obtain the count values ​​of the T-tube and D-tube;

[0014] Step 5: The activity of each nuclide is calculated by using the three-double coincidence ratio method to calculate the count values ​​of the T tubes and D tubes.

[0015] Furthermore, in step 2, the method for establishing a spectral theory description model for a single nuclide specifically includes:

[0016] 2-1 Calculate the emission spectrum of a nuclide and construct a functional expression for the emission energy spectrum of β particles for β-decayed nuclides;

[0017] 2-2 Calculate the energy deposition spectrum. For low-energy pure β nuclides, the emission spectrum of the nuclide is used as the energy deposition spectrum. For high-energy β nuclides or nuclides with other decay branches, the energy deposition spectrum is calculated by Monte Carlo method, and then the function expression is obtained by interpolation.

[0018] 2-3 Calculate the energy spectrum after ionization quenching, based on the Birks ionization quenching function to describe the conversion of electron energy into effective energy for luminescence;

[0019] 2-4 Convert the energy x-axis to a channel, establish the relationship between energy and channel through a scale formula, and solve using nonlinear fitting.

[0020] Further, in step 2-1, the emission spectrum of the nuclide is calculated, and the energy spectrum of the β particle emitted during β decay is expressed as:

[0021]

[0022] in, , where is the total energy of the β particles. For the kinetic energy of the β particle, Let be the rest mass of the β particle. Let be the momentum of the β particle. , where represents the energy of the corresponding neutrino. This represents the maximum total energy of β particles, corresponding to the maximum energy of the β energy spectrum. , Let be the shape factor, denoted as . ;

[0023] The Fermi function, used to correct energy spectrum distortions caused by the electric field of atomic nuclei, is expressed as:

[0024]

[0025] in, , It is the atomic number. For fine structure constants, , , where is the radius of the atomic nucleus. The mass number of the atomic nucleus. For the gamma function, the complex gamma function in the above equation is calculated as:

[0026]

[0027] in .

[0028] Furthermore, the set of equations for jointly solving the energy spectra of the T-tube and D-tube is as follows:

[0029]

[0030] in, The energy deposition spectrum of nuclide 1, The energy deposition spectrum of nuclide 2. The total energy spectrum of the T-tube was collected in the experiment. The total energy spectrum of the T-tube collected in the experiment is denoted by λ, which is a free parameter, a is the quadratic coefficient of the energy scale, b is the linear coefficient of the energy scale, and c is the constant term of the energy scale. AT is the energy spectrum height of the T-tube, AD is the energy spectrum height of the D-tube, and r is the ratio coefficient of the two nuclides. Since the energy spectra of the two nuclides are not normalized, they are not equal to the activity ratio or the count ratio.

[0031] Furthermore, the formulas for calculating the T and D energy spectra are as follows:

[0032]

[0033]

[0034]

[0035]

[0036] in, To determine the T-tube energy spectrum contribution of nuclide 1, To determine the energy spectrum contribution of nuclide 1 in the D tube, To determine the T-tube energy spectrum contribution of nuclide 2, To determine the D-tube energy spectrum contribution of nuclide 2, the four energy spectra mentioned above are converted to the following values ​​according to the calibration formula: , , , The restored energy spectrum area is the T and D count values ​​of the two nuclides respectively, and the count rates of T and D can then be calculated.

[0037] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects:

[0038] This invention utilizes a TDCR liquid scintillation system with T and D tube energy spectrum output functions. It eliminates the need for extensive pre-calibration work and standard quenching series sources, and is independent of calibration accuracy. Compared to the function fitting spectral stripping method, this invention's scheme is based on theoretical spectral description, with the spectral shape constrained by the theoretical model. During the spectral interpretation process, T and D spectra are calculated simultaneously, achieving absolute measurement based on the mutual constraints of parameters. Attached Figure Description

[0039] Figure 1 This is a flowchart of a method for simultaneous quantitative measurement of liquid scintillator dual nuclides based on mixed spectrum interpretation according to the present invention;

[0040] Figure 2 A flowchart for establishing a spectral theory description model for a single nuclide in this invention;

[0041] Figure 3This is a comparison chart of the energy spectrum parameters of the T and D tubes in an embodiment of the present invention;

[0042] Figure 4 This is a comparison chart of parameters solved using the nonlinear fitting method in the embodiments of the present invention;

[0043] Figure 5 This is a comparison chart of parameter solution results in an embodiment of the present invention; Detailed Implementation

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0045] Reference Figure 1 and 2 As shown, step 1: Prepare a dual-nucleoside mixed sample according to the conventional method of liquid scintillation measurement. Usually, a small amount of sample is added to 15 mL of scintillation fluid. The overall activity is moderate and can form an energy spectrum with good statistical properties.

[0046] Step 2: Establish a spectral theory description model for single nuclides

[0047] In this step, it is necessary to refer to the following: Figure 2 The energy spectrum of a single nuclide can be described as a functional expression:

[0048] Step 2-1: First, calculate the emission spectrum of the nuclide. The energy spectrum of the β particle emitted during β decay is expressed as follows:

[0049]

[0050] in, , where is the total energy of the β particles. For the kinetic energy of the β particle, Let be the rest mass of the β particle. Let be the momentum of the β particle. , where represents the energy of the corresponding neutrino. This represents the maximum total energy of β particles, corresponding to the maximum energy of the β energy spectrum. . Let be the shape factor, denoted as . ;

[0051] The Fermi function, used to correct energy spectrum distortions caused by the electric field of atomic nuclei, is expressed as:

[0052]

[0053] in, , It is the atomic number. For fine structure constants, . , where is the radius of the atomic nucleus. This is the mass number of the atomic nucleus. Let gamma be the complex gamma function, and in the above equation, the complex gamma function is calculated as follows:

[0054]

[0055] in .

[0056] The form factor varies depending on the type of nuclide and has different functional forms. For example, if the decay mechanism is relatively simple, the form factor is also very simple. For instance, the form factors of common low-energy β nuclides H-3 and C-14 can both be denoted as [form factor not provided in the original text]. .

[0057] Step 2-2: Calculate the energy deposition spectrum

[0058] For low-energy pure β nuclides, this step can be skipped, and the emission spectrum can be directly used as the energy deposition spectrum. For high-energy β nuclides or nuclides with other decay branches, the energy deposition spectrum is calculated using the Monte Carlo method, and its functional expression is obtained through interpolation. The energy deposition spectrum obtained in this step is denoted as... .

[0059] Steps 2-3: Calculate the energy spectrum after ionization quenching

[0060] The ionization quenching process is calculated based on a free-parameter model. In the decay of β-nuclides in scintillation fluid, part of the electron's energy excites the scintillation fluid to emit light, which is then converted into photon energy; the remaining energy is lost due to quenching. This results in a non-linear relationship between the final energy converted into effective fluorescence and the initial electron energy. The Birks ionization quenching function describes the coefficient by which electron energy is converted into effective energy for luminescence.

[0061]

[0062] Wherein, kB is the ionization quenching constant (Birks factor), which is only related to the scintillation fluid used and can also be obtained by testing a series of quenching sources; The scintillation fluid's ability to stop β particles, with dimensions of... It can be obtained using the Bethe-Bloch formula.

[0063] For ease of calculation, a free parameter λ (or figure of merit) is introduced. λ refers to the ratio between the effective energy of particle deposition (after ionization quenching correction) and the average number of photoelectrons reaching the first darad electrode.

[0064]

[0065] in, This represents the average number of photoelectrons detected at the first damper of the PMT. Typically, the liquid scintillator records a count as soon as a photoelectron is received at the first damper of the PMT. Whether each scintillator photon generates an electron that can reach the first damper is completely independent; therefore, the total number is... Photons The probability of producing an electron that can reach the first stage follows a parameter of: The Poisson distribution is given. Therefore, the detection efficiency of a single PMT for a single monoenergetic electron is...

[0066]

[0067] That is, beta particles of different energies have different probabilities of being detected by the first photomultiplier tube. Assuming the optical chamber is perfectly designed so that all scintillation light can be received by the photomultiplier tube, the probabilities of T and D being detected as a function of energy distribution can be calculated as follows:

[0068]

[0069]

[0070] Due to the use of a three-tube composite liquid scintillation device, free parameters It needs to be multiplied by a factor of 3.

[0071] Steps 2-4: Convert the x-axis from energy to channel.

[0072] The decaying β particles interact with the scintillating fluid, emitting a certain number of photons. After signal processing by photomultiplier tubes, amplifiers, and other means, the energy spectrum is recorded by a multichannel pulse analyzer. The amplification process and the sampling process of the ADC are basically linear. However, the intensity of the light emitted by the liquid scintillator has a nonlinear relationship with the energy of the β particles. That is, the "effective energy" is basically linearly related to the number of channels, rather than the energy of the β particles.

[0073] As can be seen from the calculation process of detection efficiency, the actual energy used for luminescence is... Therefore, the relationship between energy and Tao can be expressed by the following formula.

[0074]

[0075] in, The energy of the β particle. For the energy spectrum channels, , , The fitting coefficients are used. Although this formula cannot be compared with... and The analytical expression can be solved directly, but this does not affect the use of nonlinear fitting methods to obtain the fitting results.

[0076] Step 3: Use a nonlinear fitting method to jointly solve the energy spectra of T-tubes and D-tubes.

[0077] Based on the characteristics of liquid scintillation instruments, the energy spectra of T-tubes and D-tubes can be determined. , The conversion of the x-axis from energy to channel is consistent, as shown in the following system of equations:

[0078]

[0079] in, The energy deposition spectrum of nuclide 1, The energy deposition spectrum of nuclide 2. The total energy spectrum of the T-tube was collected in the experiment. The total energy spectrum of tube D collected in the experiment is given by λ, which is a free parameter, a is the quadratic coefficient of the energy scale, b is the linear coefficient of the energy scale, c is the constant term of the energy scale, AT is the energy spectrum height of tube T, AD is the energy spectrum height of tube D, and r is the ratio coefficient of the two nuclides. Since the energy spectra of the two nuclides are not normalized, they are not equal to the activity ratio or the count ratio.

[0080] Therefore, the objects to be solved by the nonlinear fitting method include: λ is the free parameter; a is the quadratic coefficient of the energy scale; b is the linear coefficient of the energy scale; c is the constant term of the energy scale; AT is the energy spectrum height of the T tube; AD is the energy spectrum height of the D tube; and r is the ratio coefficient of the two nuclides. Since the energy spectra of the two nuclides are not normalized, they are not equal to the activity ratio or the count ratio.

[0081] The above parameters can be solved using nonlinear fitting methods (such as Levenberg-Marquardt).

[0082] Step 4: After solving, substitute the calculated unknowns into the formulas in steps 2-3 and 2-4 to calculate the T and D energy spectra of the two nuclides respectively:

[0083]

[0084]

[0085]

[0086]

[0087] in, To determine the T-tube energy spectrum contribution of nuclide 1, To determine the energy spectrum contribution of nuclide 1 in the D tube, To determine the T-tube energy spectrum contribution of nuclide 2, To determine the contribution of the D-tube energy spectrum of nuclide 2, subscripts are used to distinguish between the T and D spectra and the nuclide. Based on... Convert the above four energy spectra to , , , This allows the single-nucleus energy spectrum collected by the instrument to be reconstructed. The area of ​​the reconstructed energy spectrum is the T and D count values ​​of the two nuclides respectively, and the T and D count rates can then be calculated.

[0088] Step 5: Based on the T and D count rates of each nuclide in the previous step, the count rate and TDCR value can be obtained. Using the TDCR method (Triple to Double Coincidence Ratio), the detection efficiency can be calculated from the TDCR value, thereby calculating the activity of each nuclide.

[0089] In this embodiment, step 1: A dual-nucleon mixture sample containing H-3 and C-14 was prepared, and measurements were obtained using a three-tube coincidence liquid scintillation system as shown below. Figure 3 The energy spectra of the T and D tubes are shown, and the live time is recorded. .

[0090] The total count for the T-tube was 4,625,858, and the total count for the D-tube was 5,926,777. The total measurement time was 1,800.0740 seconds, and the active time was 1,149.8659 seconds.

[0091] Step 2: Based on the content of Step 2 above, write the function code. The function's purpose is to take the parameters from Step 3 as input and output the mixed energy spectrum expressed by the formula in Step 2.

[0092] Step 3: Solve for the optimal result of the parameters in Step 3 using a nonlinear fitting method, such as... Figure 4 As shown: the parameters are as follows:

[0093]

[0094] Step 4: Figure 5 As shown, based on the solution results, substituting them into the energy spectrum expressions for the two nuclides respectively, we obtain the following energy spectra:

[0095] And extract the count from the energy spectrum:

[0096]

[0097]

[0098] In this example, the detection efficiency of the D-tube is... , The calculations were performed using the software tdcr07c (the URL for tdcr07c is: http: / / www.lnhb.fr / home / conferences-publications / icrm_lsc_wg / icrm_lsc_software / ). In this example, the steps are as follows: First, open the tdcr07c software. In the efficiency calculation step, select "From Free Parameters". λ In the "Calculate Detection Efficiency" working mode, input the free parameters obtained from the fitting. λ Record the calculated efficiency. After obtaining the efficiency, the activities of the two nuclides are:

[0099]

[0100]

[0101] For this example, the result is as follows:

[0102]

[0103] The above description is merely an example and illustration of the structure of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

Claims

1. A method for simultaneous quantitative measurement of two liquid scintillation nuclides based on mixed spectrum interpretation, characterized in that, The dual-nucleoside activity is simultaneously measured using liquid scintillation and resolved via mixed spectra, achieving simultaneous absolute activity measurement. This includes the following steps: Step 1: Prepare a dual-nucleoside mixed sample; Step 2: Establish a spectral theory description model for single nuclides; Step 3: Use a nonlinear fitting method to jointly solve the energy spectra of the T-tube and D-tube; Step 4: Deconstruct the energy spectra of the T-tube and D-tube based on the theoretical description model to obtain the count values ​​of the T-tube and D-tube; Step 5: The activity of each nuclide is calculated from the statistically obtained count values ​​of the T-tubes and D-tubes using the triple coincidence ratio method; Step 2, the method for establishing a spectral theory description model for a single nuclide specifically includes: 2-1 Calculate the emission spectrum of a nuclide and construct a functional expression for the emission energy spectrum of β particles for β-decayed nuclides; 2-2 Calculate the energy deposition spectrum. For low-energy pure β nuclides, the emission spectrum of the nuclide is used as the energy deposition spectrum. For high-energy β nuclides or nuclides with other decay branches, the energy deposition spectrum is calculated by Monte Carlo method, and then the function expression is obtained by interpolation. 2-3 Calculate the energy spectrum after ionization quenching, based on the Birks ionization quenching function to describe the conversion of electron energy into effective energy for luminescence; 2-4 Convert the energy x-axis to a channel, establish the relationship between energy and channel through a scale formula, and solve using nonlinear fitting.

2. The method for simultaneous quantitative measurement of two liquid scintillation nuclides based on mixed spectrum interpretation according to claim 1, characterized in that, In step 2-1, the emission spectrum of the nuclide is calculated. The energy spectrum of the β particle emitted during β decay is expressed as: in, , where is the total energy of the β particles. For the kinetic energy of the β particle, Let be the rest mass of the β particle. Let be the momentum of the β particle. , where represents the energy of the corresponding neutrino. This represents the maximum total energy of β particles, corresponding to the maximum energy of the β energy spectrum. , Let be the shape factor, denoted as . ; The Fermi function, used to correct energy spectrum distortions caused by the electric field of the atomic nucleus, is expressed as: in, , It is the atomic number. For fine structure constants, , , where is the radius of the atomic nucleus. The mass number of the atomic nucleus. For the gamma function, the complex gamma function in the above equation is calculated as: in .

3. The method for simultaneous quantitative measurement of two liquid scintillation nuclides based on mixed spectrum interpretation according to claim 1, characterized in that, The equations for jointly solving the energy spectra of the T-tube and D-tube are shown below: in, For energy, The energy deposition spectrum of nuclide 1, The energy deposition spectrum of nuclide 2. The total energy spectrum of the T-tube was collected in the experiment. The total energy spectrum of the D tube collected in the experiment; λ is the free parameter; a is the coefficient of the quadratic term of the energy scale; b is the coefficient of the linear term of the energy scale; c is the constant term of the energy scale. The energy spectrum height of the T-tube; denoted as the height of the D-tube energy spectrum; r is the ratio coefficient between the two nuclides. Since the energy spectra of the two nuclides are not normalized, they are not equal to the activity ratio or count ratio.

4. The method for simultaneous quantitative measurement of two liquid scintillator nuclides based on mixed spectrum interpretation according to claim 1, characterized in that, The formulas for calculating the T and D energy spectra are: in, To determine the T-tube energy spectrum contribution of nuclide 1, To determine the energy spectrum contribution of nuclide 1 in the D tube, To determine the T-tube energy spectrum contribution of nuclide 2, To determine the D-tube energy spectrum contribution of nuclide 2, the four energy spectra mentioned above are converted according to the calibration formula. , , , The restored energy spectrum area is the T and D count values ​​of the two nuclides respectively, and the count rates of T and D can then be calculated.

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