RU2746412C1 - Method for the identification of beta-emitting radionuclides in samples using a liquid scintillation counter - Google Patents

Abstract

FIELD: radioecological monitoring.

SUBSTANCE: invention relates to the field of radioecological monitoring and is intended for the identification of beta-emitting radionuclides. The method for identifying beta-emitting radionuclides includes a preliminary one-time creation of a background library, the creation of a library for a given liquid scintillation counter and a given cocktail for all beta-emitting radionuclides, model spectra of the SRS sample at different levels of quenching in the form of a system of third-degree polynomials of the parameters of the sum of piecewise combined functions and the measurement efficiency as a function of quenching as an exponential function, measuring and recording the spectrum of the sample and the measurement parameters of the sample using the quenching parameter obtained by measuring the sample, determine the coefficients of the contribution of each library spectrum of the isotope to the spectrum of the measured sample. The method for identifying beta-emitting radionuclides in a sample is carried out using a liquid scintillation counter with automatic quenching detection, while using the entire energy scale. The activity of beta-emitting radionuclides is calculated from the obtained coefficients of the contribution of radionuclides and the library efficiencies of measuring radionuclides, depending on the quenching.

EFFECT: increased sensitivity of spectrometric analysis.

1 cl, 1 dwg

Description

The invention relates to the field of radioecological monitoring, environmental protection, individual dosimetric control of workers and is intended to determine beta-emitting radionuclides in environmental samples, in samples of biosubstrates, in technological samples, in particular for beta-spectrometric determination of the activity of radionuclides: H-3 (tritium ), K-40 (potassium-40), Sr-90 + Y-90 (strontium-90 + yttrium-90).

A known method for the identification of alpha-emitting radionuclides in samples using a liquid scintillation counter [1]. The method includes taking environmental and technological samples, processing samples, preparing samples for measurement on a liquid scintillation counter, measuring and recording the spectrum of the sample and measurement parameters, creating a model spectrum of the sample, minimizing the deviation of the model spectrum from the spectrum of the sample and determining the content of alpha-emitting radionuclides in the sample. When preparing a sample, the total activity of the analyzed sample and the energy range of alpha-emitting radionuclides in the sample are preliminarily determined, and then a radionuclide solution is introduced into the sample as an internal standard with a certain energy and a given activity of alpha radiation, the spectrum of alpha radiation of the sample is measured and recorded on Based on the results of measuring the spectrum of the sample, minimizing the deviation of the model spectrum from the spectrum of the sample in the region of the internal standard, the parameters of the asymmetric Gaussian distribution describing the peak of the internal standard are determined, according to these parameters, using the empirical formulas for the dependences of the parameters on the quenching for the alpha radiation energy of the internal standard, determine the value and the type of quenching of the analyzed sample, according to the obtained values of the magnitude and type of quenching of the sample, using the formulas for the dependence of the parameters of the asymmetric Gaussian distribution on energy and quenching and reference data on alpha-emitting radionuclides, are useful spectrum. The known method is intended for alpha-emitting radionuclides, uses a limited part of the energy scale, requires the introduction of a radionuclide into the solution as an internal standard, requires preliminary determination of the total activity of the analyzed sample and preliminary determination of the energy interval of alpha-emitting radionuclides in the sample, minimizes the functionality, repeating the minimization in Several stages, which take significantly more time in comparison with solving a system of linear equations, uses an asymmetric Gaussian distribution, which is computationally more complicated than a piecewise combined function in which there is no square root of the variables.

In addition, there is a known method for the identification of alpha-emitting radionuclides [2]. The method includes sampling the environment and technological samples, processing samples, preparing samples for measurement, measuring and recording the spectrum of the sample and measurement parameters, creating a model spectrum of the sample, minimizing the deviation of the model spectrum from the spectrum of the sample, and determining the content of alpha-emitting radionuclides in the sample. When preparing a sample, the total activity of the analyzed sample is preliminarily determined, then a radionuclide solution is introduced into the sample as an internal standard with a certain energy and a given activity of alpha radiation, the spectrum of alpha radiation of the sample is measured and recorded. Based on the results of measuring the spectrum of the sample, minimizing the deviation of the model spectrum from the spectrum of the sample in the area of the internal standard, the parameters of the asymmetric Gaussian distribution, describing the peak of the internal standard, are determined. The method for identifying alpha-emitting radionuclides is carried out using a semiconductor spectrometer and the entire energy scale of the spectrometer is used. The known method is intended for alpha-emitting radionuclides, requires the introduction of a radionuclide into the solution as an internal standard, requires preliminary determination of the total activity of the analyzed sample, uses an asymmetric Gaussian distribution, which is computationally more complicated than a piecewise combined function in which there is no square root of the variables.

The closest to the proposed method in technical essence and the achieved effect is a method for identifying radionuclides in a liquid scintillation sample [3], in which the spectrum of the test sample is measured, after which, for the appropriate level of quenching from the library of basic spectra of individual radionuclides for different levels of quenching by interpolation and extrapolation determine the normalized model spectra of individual radionuclides. Next, the least squares method minimizes the difference between the spectrum of the sample P _i and the sum of the model spectra of individual radionuclides M _{i, j} , multiplied by the coefficients c _j , which determine the activity of individual radionuclides. The expression to be minimized looks like this:

where i is the channel number of the analyzer, j is the radionuclide index. However, the known method does not regulate either the storage, retrieval, or spectral interpolation of the spectrum sample stored in the library, which, if the choice of storage or retrieval or interpolation is unsuccessful, may complicate the task of finding the radionuclide activities in the sample and increase its execution time. Also, the known method does not indicate the rules for processing the background spectrum.

The objective of the invention is the correct construction of a library of model spectra, and as a consequence, a potential increase in the sensitivity of spectrometric analysis. The use of a system of third degree polynomials of the parameters of the sum of piecewise combined functions and a library of measurement efficiencies depending on quenching and the use of the background spectrum improved the accuracy of determining the activity of radionuclides in the sample. The replacement of minimization, when solving the least squares method, with a system of linear equations and the direct solution of the system of linear equations, significantly accelerated the calculations and improved the accuracy of calculating the activity of radionuclides, since the proposed system of linear equations is an exact solution to the problem of finding coefficients by the least squares method, unlike any method of minimization ...

To accomplish the task, a method for the identification of beta-emitting radionuclides is proposed, including a preliminary one-time creation of a library of rates for a set of background samples, a preliminary one-time creation of a library for a given liquid scintillation counter and a given cocktail for all beta-emitting radionuclides found in measured samples, model spectra of samples of reference radioactive solutions (OPR) at different levels of quenching in the form of a system of third-degree polynomials of the parameters of the sum of piecewise-combined functions and measurement efficiency depending on quenching in the form of an exponential function, measuring and recording the spectrum of the sample and measuring parameters of the sample, minimizing the deviation of all model spectra from the spectrum of the sample, Using the quenching parameter obtained by measuring the sample, the coefficients of the contribution of each library spectrum of the radionuclide to the spectrum of the measured sample are determined. The method for identifying beta-emitting radionuclides in a sample is carried out using a liquid scintillation counter with automatic quenching detection, whereby the entire energy scale is used. The activity of beta-emitting radionuclides is calculated from the obtained coefficients of the contribution of radionuclides and the library efficiencies of measuring radionuclides, depending on the quenching.

Distinctive features of the claimed method are the use of a liquid scintillation counter with automatic determination of quenching, the use of the entire energy scale, storage of model spectra in the form of a system of third-degree polynomials of parameters of the sum of piecewise combined functions from quenching and parameters of the measurement efficiency function from quenching, replacement of minimization, when solving by the method least squares, a system of linear equations and a direct solution to a system of linear equations.

I. Creation of a library of model spectra

The model spectrum of a radionuclide is an approximation of the spectrum of a sample of a reference radioactive solution (ORR) of a given radionuclide by any function for a given liquid scintillation counter and a given cocktail. The library consists of functions for changing the model spectrum depending on the quenching, and the measurement efficiency depending on the quenching.

To create a library for the j-th radionuclide (j∈J), you need the following:

соответствующего k-му уровню гашения, строим модельный спектр j-го радионуклида M^k в виде суперпозиции кусочно-комбинированных функций

с параметрами

l∈L для каждой l-й энергетической линии j-го радионуклида (не путать с асимметричным распределением Гаусса):1. To enter the model spectrum of the j-th radionuclide (hereinafter in paragraphs 1, 2, 3, 4, the index j will be omitted, since all calculations are given for one radionuclide) into the library for a given liquid scintillation counter and a given cocktail, it is necessary to obtain the spectra of an exemplary radioactive solution of the radionuclide of interest for different levels of quenching g _k , k∈K. For the obtained spectrum

corresponding to the k-th level of quenching, we construct the model spectrum of the j-th radionuclide M ^k in the form of a superposition of piecewise-combined functions

with parameters

l∈L for each l-th energy line of the j-th radionuclide (not to be confused with the asymmetric Gaussian distribution):

Where

J is the set of all radionuclides;

I - the set of all channels of the liquid scintillation counter;

L is the set of all energy lines of the j-th radionuclide;

j is the number of the radionuclide;

i is the channel number of the liquid scintillation counter;

l is the number of the energy line of the j-th radionuclide;

k is the number of the quenching level;

- площадь пика, [имп.];

- peak area, [imp.];

- абсцисса центра пика;

is the abscissa of the center of the peak;

- параметры, определяющие форму пика;

- parameters that determine the shape of the peak;

M ^k - model spectrum, [imp.].

, l∈L кусочно-комбинированных функций

соответствующие k-му уровню гашения, вычисляются путем минимизации функционала:Parameters

, l∈L of piecewise combined functions

corresponding to the kth level of damping are calculated by minimizing the functional:

2. Construction of the function of changing the model spectrum from the quenching level in the form of a system of third-degree polynomials - formula (4) (stored in the library):

Where

g - quenching level: g≡SQP (E);

SQP (E) - quenching value, calculated automatically when measuring a sample by determining the Spectral Quench Parameter of External standard;

вычисляются путем минимизации функционалов:Polynomial parameters

are calculated by minimizing the functionals:

Where

g _k - k-th level of damping: g _k ≡SQP (E) | _k .

3. Construction of the measurement efficiency function depending on the damping, for this the efficiency is calculated for the k-th level of damping:

Where

t _k - spectrum acquisition time for the k-th level of quenching, [s];

S ^k - the area of the OPR spectrum for the k-th level of quenching, [imp.];

- активность ОРР введенная в пробу k-го уровня гашения, [Бк].

- OPP activity introduced into the sample of the k-th level of quenching, [Bq].

Equality should hold:

4. Construction of the function of changing the measurement efficiency from the level of quenching in the form of an exponential function (8) (stored in the library):

Where

a, b, c - approximation parameters,

approximation parameters a, b, c are calculated by minimizing the functional when constructing a spectrum library for an individual radionuclide:

5. When calling the model spectrum for the j-th radionuclide for the known quenching g = const from the library it follows:

Where

B _{i, j} (g) - the model spectrum updated by quenching g in the j-th channel for the j-th radionuclide (spectral interpolation of the spectrum sample), [imp.];

для l-й энергетической линии j-го радионуклида определены в (4), эффективность измерения E_j(g) для j-го радионуклида для известного гашения g=const определено в (8).

for the l-th energy line of the j-th radionuclide are determined in (4), the measurement efficiency E _j (g) for the j-th radionuclide for the known quenching g = const is determined in (8).

II. Sample measurement

When measuring a sample: 1) the spectrum of the sample P _i , i∈I is measured, where i is the number of the analyzer channel; 2) the damping g≡SQP (E) = const is automatically measured.

From the measured spectrum of the sample P _i , i∈I, it is necessary to subtract the background spectrum corresponding to the cocktail (the rate of collection of the background F _i , i∈I from the library of rates of collection of background samples, multiplied by the time of collection of the sample):

In the present invention, a library of background sampling rates is used, but this library can be arranged identically to the library of OPP sample spectra at different quenching levels, therefore, a separate description of the library of background sampling rates is not provided.

Having model spectra of the j-th radionuclide B _{i, j} (g), i∈I, j∈J (9), and minimizing functional (13), we obtain the coefficients θ _j , j∈J of the contribution of the j-th radionuclide to the spectrum Р ' ...

уравнение минимизации функционала (13) тождественно преобразуется в систему линейных уравнений:after differentiation

the equation of minimization of functional (13) is identically transformed into a system of linear equations:

Let us write (14) in matrix form:

Solution (15) has the form:

The activity of the j-th radionuclide is calculated by the formula:

Where:

A _j - activity of the j-th radionuclide in the sample, [Bq];

t is the time of the spectrum acquisition of the sample, [s];

θ _j is the contribution of the j-th radionuclide to the spectrum P ';

E _j (g) - library efficiency of measurement of the j-th radionuclide depending on quenching g;

B _{i, j} (g) - model spectrum updated by quenching g in the i-th channel for the j-th radionuclide (spectral interpolation of the spectrum sample), [imp.].

An example of the implementation of the method

Example 1. The result of measuring the sample Q101004N.001 by the presented method is shown in FIG. 1. Shown: graph with a thin blue line - the original spectrum; the thin red line is the spectrum minus the background; thin yellow line - the contribution of Sr-90 + Y-90 to the spectrum of the sample; the thin green line is the contribution of K-40 to the spectrum of the sample; thick blue line - the sum of radionuclides Sr-90 + Y-90 + K-40, and in the right window numerical values: sample measurement time, sample quenching SQP (E) (Spectral Quench Parameter of External standard), total background activity for all channels , and for each radionuclide: counting rate, registration efficiency, activity in the sample, volumetric activity.

The technical efficiency of the proposed method in comparison with the prototype consists in improving the accuracy of determining the activity of radionuclides in the sample by taking into account the background spectrum, in increasing the rate of determining the activity of radionuclides in the sample by storing the model spectrum in the form of a system of third degree polynomials of the parameters of the sum of piecewise combined functions and the library measurement efficiencies depending on quenching and replacement of minimization when solving the least squares method for a system of linear equations and direct solution of a system of linear equations, since the proposed system of linear equations (14) is an exact solution to equation (13), in contrast to any minimization method.

List of used literature

1. Patent RU 2191409, G01T 1/204, 1/36.

2. Patent RU 2267800, G01T 1/24, 1/36.

3. WO 199110922 A, 25.07.91.

Claims (70)

A method for identifying beta-emitting radionuclides in samples using a liquid scintillation counter, including a preliminary one-time creation of a library of rates for a set of background samples, a preliminary one-time creation of a library for a given liquid scintillation counter and a given cocktail for all beta-emitting radionuclides found in the measured samples, model spectra OPP samples at different levels of quenching in the form of a system of third-degree polynomials of parameters of the sum of piecewise-combined functions and measurement efficiency depending on quenching in the form of an exponential function, measuring and recording the spectrum of the sample and sample measurement parameters, minimizing the deviation of all model spectra from the sample spectrum using the quenching parameter obtained during the measurement of the sample determines the coefficients of the contribution of each library spectrum of the radionuclide to the spectrum of the measured sample, according to the coefficient of contribution and measurement efficiency, depending on the quenching, calculate activity of beta-emitting radionuclides, characterized in that the method for identifying beta-emitting radionuclides in a sample is carried out using a liquid scintillation counter with automatic quenching detection, while using the entire energy scale, the library spectrum of an individual radionuclide is described using the formula:

Where

- the number of pulses in the i-th channel of the model spectrum for the k-th level of quenching of an individual radionuclide; i is the channel number of the liquid scintillation counter, i∈I; k is the number of the quenching level, k∈K; I - the set of all channels of the liquid scintillation counter; K - the set of all levels of damping, is selected for reasons of sufficiency for constructing third-order polynomials; l is the number of the power line of a separate radionuclide, l∈L; L is the set of all energy lines of an individual radionuclide;

- piecewise combined function:

Where g _k - k-th level of suppression: g _k ≡SQP (E) | _k ; SQP (E) - quenching value, calculated automatically when measuring OPP or sample by determining the Spectral Quench Parameter of External standard; S ^{k, l} - peak area, [imp.];

is the abscissa of the center of the peak;

- parameters that determine the shape of the peak, parameters

l∈L of piecewise combined functions

corresponding to the kth level of damping are calculated by minimizing the functional:

Where

- ORR spectrum of an individual radionuclide for the k-th quenching level g _k , in the library, the parameters of the piecewise-combined function of changing the model spectrum from the quenching level are stored as a system of third-degree polynomials:

Where

- the parameters of the third degree polynomials are calculated by minimizing the functionals:

the function of the measurement efficiency of an individual radionuclide, depending on the quenching, is stored in the library and has the form:

Where a, b, c - approximation parameters, approximation parameters a, b, c are calculated by minimizing the functional when constructing a spectrum library for an individual radionuclide:

Where E _k is the measured value of the efficiency for the k-th level of damping, k∈K, the spectrum of the background sample is measured, reduced to the background sample collection rate F (counting set in the i-th channel, divided by the background sample collection time) and saved in the background sample collection rate library: F _i , i∈I the spectrum of the sample P is measured: P _i , i∈I from the measured spectrum of sample P, the background spectrum corresponding to the cocktail is subtracted (the rate of background collection from the library of rates of collection of background samples, multiplied by the time of sample collection):

Where t - time of collection of the spectrum of the sample, [s], when measuring the sample or ORP, the quenching of the sample is automatically measured: g≡SQP (E) = const, with a known quenching of the sample, measured automatically when measuring the sample, spectral interpolation of the spectrum sample occurs in the form of updating the library for the measured sample for all radionuclides from the library, the number of pulses in the i-th channel of the model spectrum, updated by quenching g, for the j-th radionuclide is calculated as follows way:

Where B _{i, j} (g) is the model spectrum updated by quenching g in the i-th channel for the j-th radionuclide;

- piecewise combined function:

Where

- parameters updated by quenching g for the l-th energy line of the j-th radionuclide are determined from the system of third-degree polynomials stored in the library of model spectra, The estimation of the contribution coefficient of the model spectrum of the j-th radionuclide, updated by quenching g, is found by minimizing a functional of the form:

Where θ _j are the coefficients of the contribution of the model spectrum of the j-th radionuclide to the spectrum of the sample; B _{i, j} (g) - the number of pulses in the i-th channel of the model spectrum, updated by quenching g, for the j-th radionuclide, [imp.];

- the number of pulses in the i-th channel of the measured spectrum of the sample minus the background spectrum corresponding to the cocktail, [pulses], after differentiation

the functional minimization equation is identically transformed into a system of linear equations:

also in matrix form: B × θ = M the solution is in the form: θ = B ^-1 × M the activity of the j-th radionuclide is calculated by the formula:

Where A _j - activity of the j-th radionuclide in the sample, [Bq]; t is the time of the spectrum acquisition of the sample, [s];

- library efficiency of measurement of the j-th radionuclide depending on the quenching g.

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