Method for measuring activity of nuclide based on 4pi gamma well ionization chamber

Abstract

The application discloses a radionuclide activity measurement method based on a 4pi gamma well ionization chamber, which comprises the following steps: collecting a time sequence of an output current under the condition that a measurement link input end is short-circuited and no effective input signal is present, calculating a statistical average value of the current as a zero input correction parameter, measuring an environmental background current under the condition that no sample to be measured is present, and taking a statistical average value of the environmental background current as a background correction parameter; obtaining a measured current signal, correcting the measured current signal, obtaining a radionuclide calibration coefficient based on a ratio of the measured current signal to the known activity, and establishing a radionuclide calibration coefficient matrix according to the radionuclide calibration coefficient; obtaining a gamma ray energy spectrum of a sample of a radionuclide to be measured, performing initial screening of a radionuclide type according to the gamma ray energy spectrum, determining a radionuclide half-life, and determining the radionuclide type according to the radionuclide half-life; obtaining an impurity radionuclide prior constraint through gamma spectrum inversion; and obtaining an activity value according to the calibration coefficient, the measured current signal and the impurity radionuclide prior constraint.

Description

Technical Field

[0001] This invention relates to the field of ionizing radiation metrology, and in particular to a method for measuring nuclide activity based on a 4πγ well-type ionization chamber. Background Technology

[0002] The 4πγ well-type ionization chamber, with its near-4π solid angle geometry, is an important metrological instrument for measuring the activity of radionuclides, and is widely used in the determination of the activity of radiopharmaceuticals, environmental samples, and standard sources. Its output is a saturation ionization current proportional to the sample activity, with an amplitude typically in the picoampere to nanoampere range, requiring extremely high stability of the microcurrent measurement link.

[0003] Existing measurement methods have the following problems: The electronic zero-point drift and leakage current of the measurement link are superimposed on the sample ionization current along with the ambient radiation background. Current techniques often only perform single background subtraction without separating and correcting the electronic zero-point and ambient background in stages, leading to large measurement deviations for low-activity samples. The ionization chamber outputs the total ionization current of all gamma radiation emitted by the sample, making it impossible to distinguish nuclide types. When the sample contains impurity nuclides, the total activity can only be calculated using the calibration coefficient of a single nuclide. The current contribution of impurity nuclides is included in the main nuclide, resulting in a systematically higher activity result. The calibration coefficient depends on the gamma-ray energy, sample container, and volume. Existing single-point calibration methods are applicable to a limited number of nuclides and geometric conditions. Uncalibrated nuclides can only use similar nuclide coefficients, introducing additional errors. Although high-resolution gamma spectroscopy can identify nuclide types, in existing techniques, the spectral measurement and ionization chamber current measurement are independent. The spectral results are not used for constrained current component decomposition, and the two sets of data are not used for joint inversion.

[0004] Therefore, there is an urgent need for a nuclide activity measurement method that combines zero-input and background classification correction, multi-dimensional calibration coefficient matrix, prior constraints of γ-energy spectrum impurity nuclides, and total activity time spectrum half-life verification to improve the accuracy and reliability of activity measurement. Summary of the Invention

[0005] The purpose of this invention is to provide a method for measuring the activity of nuclides based on a 4πγ well-type ionization chamber.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention includes the following steps: Under the conditions of short circuit at the input end of the measurement link and no effective input signal, the time series of the output current is collected, and the statistical average value of the current is calculated as the zero input correction parameter. Under the condition of no sample to be tested, the environmental background current is measured, and the statistical average value of the environmental background current is used as the background correction parameter. A standard nuclide sample with known activity is placed in the central measuring well. The measured current signal is obtained by a femtoampere-level low-noise microcurrent measurement. The measured current signal is corrected using the zero-input correction parameter and the background correction parameter. The nuclide calibration coefficient is obtained based on the ratio of the measured current signal to the known activity. A radionuclide calibration coefficient matrix is ​​established based on the nuclide calibration coefficient. The radionuclide sample to be tested is placed in the central measuring well, and the gamma-ray energy spectrum of the radionuclide sample is obtained. The types of radionuclides are initially screened based on the gamma-ray energy spectrum. The time series of the measured current signal is collected, and the half-life of the radionuclide is determined based on the decay characteristics of the measured current signal within a set time. The results of the initial screening are verified based on the half-life of the radionuclide to determine the types of radionuclides. Prior constraints on impurity nuclides are obtained through gamma-ray spectroscopy inversion. The activity value of the sample to be tested is obtained based on the calibration coefficient of the radionuclide sample, the measured current signal, and the prior constraints on impurity nuclides.

[0007] Further, the ambient background current is measured: under conditions where there is no sample to be measured and the shielding conditions are consistent with the formal measurement, the high-voltage current is collected when the high voltage of the 4πγ well-type ionization chamber is turned on and there is no sample, and the pure dark current is collected when the high voltage of the 4πγ well-type ionization chamber is turned off and there is no sample. The difference between the high-voltage current and the pure dark current is output as the ambient background current; wherein the pure dark current includes the electronic zero-point offset and the measurement link leakage current; calibration is performed according to... Find the net ionization current. It is a pure dark current. The background current of the environment, This is the measured current signal.

[0008] Furthermore, the radionuclide calibration coefficient matrix is ​​established, including: Using nuclide type, container type, and sample volume as a three-dimensional index, a scale coefficient matrix is ​​established. The elements of the scale coefficient matrix are the activity current conversion coefficients of nuclides under container and volume classifications. For multiple characteristic gamma rays of the same nuclide, they are further subdivided and stored according to the main energy range. A standard source covering the main gamma-ray energy range of the nuclide under test was selected. The standard activity and steady-state ionization current of the standard source were measured under standard geometric conditions, and the activity-current conversion factor of the nuclide was calculated. The activity current conversion coefficient is modified by introducing energy-dependent wellbore effects and self-absorption. ;in Let be the stable ionization current of the i-th nuclide. Zero input correction parameters, The background current of the environment, Let i be the standard activity of the i-th nuclide. Let be the activity current conversion coefficient of the i-th nuclide. Energy-dependent transmission correction of gamma rays to wellbore materials at gamma ray energy E. For gamma ray energy E, volume Self-absorption correction of the sample matrix. For the z-th volume, is the activity current conversion factor of the i-th nuclide at the j-th container and z-th individual integral level when the gamma ray energy is E; For nuclides not directly scaled in the matrix, their characteristic gamma-ray energies are used. Piecewise spline interpolation is performed between the energy response curves of calibrated nuclides and the nuclide to predict the calibration coefficients of the nuclides. Once the energy spectrum is initially screened and the main characteristic peak energy of the nuclide is determined, the calibrated nuclide with the highest energy matching degree in the matrix is ​​automatically retrieved, and the calibration coefficient is directly called; if it is identified as an uncalibrated nuclide, piecewise spline interpolation is triggered to automatically generate the predicted calibration coefficient; the updated calibration coefficient matrix is ​​output.

[0009] Furthermore, the method for identifying the type of nuclide includes: The gamma spectrum of the sample is obtained, and the characteristic gamma-ray energy and net peak area are extracted by the peak position identification algorithm. The data are then matched with the nuclide database, and a candidate set is constructed based on the matching results. At the same time, impurity nuclides are determined based on the presence of characteristic peaks and their relative intensity ratios, forming an initial classification of the main nuclide and impurity nuclides. The total activity time spectrum half-life was verified for the initial classification: the total current of the ionization chamber was continuously collected at set intervals within a fixed time window, and a discrete sequence of total activity over time was constructed after zero input and background correction. Single nuclide scenario verification: The discrete sequence is fitted with a single exponential decay to obtain the decay constant, which is compared with the theoretical half-life of the candidate nuclide. If the deviation is within ±3%, the nuclide identity is confirmed, and the initial activity is obtained simultaneously to confirm that the sample is a single nuclide. Multi-nucleoside scenario verification: The theoretical decay model of each candidate nuclide combination is fitted with the measured discrete sequence by minimizing the residual, and the combination with the highest goodness of fit is selected as the final identification result; The search space is limited by the energy spectrum candidate set. The identity of the nuclide is locked by discrete sequence verification. The cross-confirmation is performed by single nuclide scenario verification and multi-nuclide scenario verification, and the nuclide type is output.

[0010] Furthermore, the method for obtaining the prior constraints of the impurity nuclides includes: The energy and net peak area of ​​the main nuclide are extracted by the second derivative method or Gaussian fitting method, and the energy and net peak area of ​​the impurity nuclide are identified at the same time. Nonlinear least squares decomposition is used for overlapping peaks. Using the emission branching ratios of characteristic gamma rays from the nuclide database and the calibration coefficients of the ionization chamber for the corresponding nuclides, the relative activity ratios of impurity nuclides to the host nuclide are calculated. ;in Main nuclides in energy The emission branching ratio of gamma rays at that location, For impurity nuclides in energy The emission branching ratio of gamma rays at that location, The calibration coefficients of the main nuclide in the 4πγ ionization chamber These are the calibration coefficients for impurity nuclides in the 4πγ ionization chamber. The activity of the impurity nuclide. The activity of the main nuclide, The energy of the characteristic gamma-ray peak of the main nuclide. The energy of the characteristic gamma-ray peak of the impurity nuclide; Based on the relative activity ratio combined with the upper limit of impurity nuclide activity. Construct the impurity nuclide prior constraint vector The objective function for optimizing the decomposition of current components in the ionization chamber incorporates prior constraints on impurity nuclides.

[0011] Furthermore, the method for obtaining the activity value includes: Acquire the measured current signal of the sample. Based on the activity of the main nuclide and the activity of impurity nuclides To optimize the variables, a joint objective function integrating ionization chamber current measurement and energy spectrum prior constraints is constructed. The constraints are: , ; ; in This is a matrix of radionuclide calibration coefficients. Let be the activity vector to be determined. This is the measured ionization current vector after zero-input correction and background correction. The regularization coefficient is . represents the prior confidence weight of impurity nuclide c. These are the weighting coefficients for the relative activity ratio constraint term in energy spectrum inversion; The activity of the main nuclide and the impurity activity were obtained by using a nonlinear least squares algorithm with boundary constraints, based on the time difference between the sample calibration time and the measurement time. ,according to Corrected to a unified reference time, Output the activity value and provide the expanded uncertainty. ;in The decay constant of the main nuclide As a inclusion factor, This represents the combined standard uncertainty.

[0012] The second aspect is a nuclide activity measurement device based on a 4πγ well-type ionization chamber, including an ionization chamber semiconductor combined detector, a femtoampere-level low-noise microcurrent module, a multichannel analyzer, a γ energy spectrum inversion module, a total activity time spectrum method, and a joint activity inversion unit. The ionization chamber semiconductor combined detector includes a 4πγ well-type ionization chamber and a zinc-cadmium telluride semiconductor detector. The 4πγ well-type ionization chamber is a sealed cylindrical cavity with a central measuring well, filled with a high-pressure working gas, with the sample placed at the geometric center, and outputting a saturated ionization current proportional to the activity. The zinc-cadmium telluride semiconductor detector is embedded in the well wall or arranged in parallel, receives the characteristic γ-rays of the sample, and outputs a pulse signal for high-resolution energy dispersive spectroscopy measurement. Flight safety-grade low-noise microcurrent module: The front end uses a transimpedance amplifier, is configured with a three-stage feedback network, and is equipped with a reed relay for automatic range switching; after an eighth-order Butterworth low-pass filter, it is connected to a 32-bit Σ-Δ analog-to-digital converter; the high-impedance node is equipped with a protection ring, overhead wiring and a nickel silver shield. Multichannel analyzer: Receives the charge pulses output from the cadmium zinc telluride detector, performs pulse amplification, shaping, peak holding and A / D conversion, accumulates and counts according to energy channel address, and forms gamma spectrum data; γ-ray spectrum inversion module: Input γ-ray spectrum data, extract the characteristic peaks of the main nuclide and the characteristic peaks of the impurity nuclide through the peak position recognition algorithm; call the branch ratio of the nuclide database and combine it with the calibration coefficient of the ionization chamber to calculate the relative activity ratio and upper limit of the impurity, and output the prior constraint vector of the impurity nuclide. Total Activity Time Spectrum Method Module: The current time series data output by the femtoampere-level module is continuously collected at a set sampling interval. After zero-input correction and background correction, a discrete sequence of total activity changing with time is constructed. The half-life is obtained by performing exponential decay fitting for single-nuctopus scenarios. For multi-nuctopus scenarios, the total activity time spectrum method is used as a residual test condition to verify the initial energy spectrum screening results and obtain the nuctopus identity. Joint Activity Inversion Unit: Integrates the calibration coefficient matrix, receives the impurity nuclide prior constraint vector provided by the nuclide identity and γ-ray spectrum inversion module, constructs a constrained optimization objective function, solves for the main nuclide activity and impurity activity, and outputs the final activity value after decay correction.

[0013] The beneficial effects of this invention are: This invention relates to a method for measuring the activity of nuclides based on a 4πγ well-type ionization chamber. Compared with existing technologies, this invention has the following technical advantages: This invention employs a tiered approach of zero-input correction and background correction, separating and subtracting electronic zero-point drift, dark current, and ambient radiation background to improve the accuracy of picoampere-level ionization current measurements and reduce measurement bias in low-activity samples. A calibration coefficient matrix is ​​established using nuclide type, container type, and sample volume as indices. Combined with wellbore effect and self-absorption correction, along with piecewise spline interpolation, this expands the range of measurable nuclides and their geometric applicability. Initial screening using gamma spectroscopy and verification using the half-life of the total activity time spectrum cross-confirm nuclide identity, avoiding misjudgment by a single method. The relative activity ratio and upper limit of impurity nuclides obtained from gamma spectroscopy inversion are embedded as prior constraints into the joint objective function, quantitatively decomposing the current contribution of impurity nuclides from the total ionization current, overcoming the defect of existing technologies that systematically overestimate activity based on single nuclide conversion. The invention outputs a unified reference time activity value with decay correction and provides expanded uncertainty, ensuring traceability of the results. Attached Figure Description

[0014] Figure 1 This is a flowchart of the steps of the radionuclide activity measurement method based on the 4πγ well-type ionization chamber of the present invention; Figure 2 This is a block diagram of the 4πγ ionization chamber activity measurement device system in an embodiment of the present invention; Figure 3 This is a circuit diagram of an eighth-order Butterworth low-pass filter in an embodiment of the present invention; Figure 4 This is a flowchart of the weak current and energy spectrum measurement unit in an embodiment of the present invention; Figure 5 This is a time-domain waveform diagram of a 0.1Hz sine wave input in an embodiment of the present invention; Figure 6 This is the time-domain waveform when the input is grounded in an embodiment of the present invention; Figure 7 This invention relates to the task state switching relationship and related functions of the main control host in this embodiment. Figure 8 The linear fitting and deviation of the activity measurement results in the embodiments of the present invention are shown. Detailed Implementation

[0015] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0016] The present invention provides a method for measuring the activity of nuclides based on a 4πγ well-type ionization chamber, comprising the following steps: like Figure 1 As shown, this embodiment includes the following steps: Under the conditions of short circuit at the input end of the measurement link and no effective input signal, the time series of the output current is collected, and the statistical average value of the current is calculated as the zero input correction parameter. Under the condition of no sample to be tested, the environmental background current is measured, and the statistical average value of the environmental background current is used as the background correction parameter. In the actual evaluation, the sample was obtained by rinsing a molybdenum technetium generator. 99m Tc eluent, packaged in standard ampoules, 5 mL in volume, calibrated at 08:00, nominal activity approximately 30 MBq; measured at 14:00. Apparatus: 4πγ well-type ionization chamber: sealed cylindrical cavity (height 45cm, diameter 13cm, well pipe diameter 65mm, inner cavity wall thickness 1mm, polytetrafluoroethylene insulation, insulation resistance >10 ohms) 14 Ω, with a 5mm stainless steel shield on the outer shell, filled with 99.99% high-purity argon gas to 1.2MPa, and a polarization voltage of +400V; Cadmium zinc telluride (CZT) detector: effective volume 5mm×5mm×5mm, embedded in the bottom of the measuring well, energy resolution FWHM≤6.0keV@140.5keV, connected to a 4096-channel multichannel analyzer (gain approximately 0.5keV / channel). Fly-safe microcurrent module: ADA4530-1 transimpedance amplifier, 100GΩ / 1GΩ / 10MΩ three-range feedback network (Ohmite Mini-MOX 1% high impedance), reed relay automatic range switching with hysteresis range setting (100GΩ range upper cut-off threshold 24pA, lower cut-off threshold 20pA), eighth-order Butterworth low-pass (cut-off 1Hz), ADS1262 32-bit Σ-Δ ADC (reference voltage 2.5V, 10SPS output rejection at 50Hz power frequency); Control host: Built-in nuclide database (branch ratio and half-life taken from LNHB / DDEP), calibration coefficient matrix library, γ energy spectrum inversion module, total activity time spectrum module and joint activity inversion unit; Zero-input measurement: The measurement link input terminal is short-circuited (the standard source Keithley 6430 provides 0A input), and three ranges are continuously sampled for 5 hours each. The time series statistical average values ​​are taken as follows: I0(100GΩ)=1.0594fA, I0(1GΩ)=103.36fA, I0(10MΩ)=948.4fA, and stored in the on-chip Flash. Pure dark current measurement: With the ionization chamber connected, high voltage off, and no sample, the pure dark current was measured to be 1.13 fA (including the electronic zero-point offset and the leakage current of the measurement link, which is in good agreement with the zero input value; the difference is due to the leakage current of the ionization chamber cable). Environmental background measurement: High voltage +400V turned on, no sample, shielding conditions consistent with the formal measurement, continuous for 3 hours, the high voltage current was measured to be 51.76fA, and the environmental background current was 50.63fA (high voltage current - pure dark current); Using standard nuclide solutions, and under standard geometry in 5mL standard ampoules, the ionization chamber was calibrated according to the activity-current conversion coefficient. Energy-dependent wellbore transmission correction τ(E) and self-absorption correction η(E,V) were introduced. The self-absorption correction was calculated using the Monte Carlo method to model the ionization chamber geometry, establishing a three-dimensional index matrix of nuclide-container-volume. Part of this matrix contains: nuclide... 57 Co characteristics, characteristic γ energy 122.06keV, container 5mL national standard ampoule, activity current conversion coefficient 1.5 pA / MBq; Initial screening using energy dispersive spectroscopy (EDS): After sample placement, CZT cumulative measurements were performed for 1800 s (count rate approximately 1.6 kcps, corrected for lifetime). Peak finding was performed using the second derivative method combined with Gaussian fitting, yielding a main peak of 140.5 ± 0.3 keV (compared to...). 99 The Tc characteristic peak at 140.51 keV matched, and a candidate set of main nuclides was constructed. Weak peaks at 739.5 keV and 777.9 keV were also detected (corresponding to...). 99 Mo feature peak matching), determination 99 Mo is an impurity nuclide; Half-life verification: The total current of the ionization chamber was continuously collected at 10-minute intervals for 6 hours (36 points). After zero-input and background correction, a discrete sequence of total activity was constructed: a single exponential fit of ln I_net(t)-t was obtained. It is 6.03h, and 99 The theoretical value of Tc is 6.007h with a deviation of +0.4%, within the ±3% criterion; the search space is limited by the energy spectrum candidate set, and the multi-nucleus residual is minimized for fitting. 99 ᵐTc+ 99 The Mo} combination showed the highest goodness of fit and did not produce non-physical negative amplitude values, which was confirmed by cross-validation with the initial energy spectrum screening: the main nuclide 99 ᵐTc, impurity nuclide 99 Mo; Net peak area extracted: S(140.5keV) = 2.84 × 10⁻⁶ 6 Count, S(739.5keV)=136 counts (peak significance approximately 9σ after Compton continuous background subtraction); CZT relative efficiency 152 Eu / 241 Am standard point source scale: ε(739.5) / ε(140.5)=0.429; Checking the database, the branch ratios are P(140.5)=0.8906 and P(739.5)=0.1213; The relative activity ratio is: [S(739.5) / S(140.5)]×[P(140.5) / P(739.5)]×[ε(140.5) / ε(739.5)]=8.2×10 -4 Statistical uncertainty ±1.8×10 -4 ; Converted to the priori proportion of ionization chamber current: =r×k_Mo / k_Tc=8.2×10 -4 ×0.586 / 1.253=3.84×10 -4 Take the upper limit of 3σ for the peak area. 1.25×10 -3 Construct a joint objective function by embedding prior constraint vectors; The measured total current was 19.080 pA, and the net current was 19.080 - 0.00113 - 0.05063 = 19.028 pA. An objective function with boundary constraints was constructed using 6-hour time-series data to solve for the activity of the main nuclide. The activity of impurity nuclides is (30.5 ± 0.5) MBq (k = 2, reference time 08:00). for 99 Mo impurity content 13.3 kBq (4.3 × 10⁻⁶) -4 ); Uncertainty: calibration factor 0.8%, current repeatability 0.2%, zero-point and background correction 0.03%, prior weight 0.05%, decay correction 0.21%, combined The uncertainty is 0.86%, and the expanded uncertainty is 1.7% (k=2). Uncalibrated nuclides: If the sample is identified as 123 I (159.0 keV), matrix has no directly scaled elements, triggering piecewise spline interpolation of energy response (anchor points 122.06 / 140.51 / 364.49 / 661.66 keV), predicting k( 123 I)≈1.29pA / MBq, and an interpolation component of 2.5% is added to the uncertainty budget; subsequent... 123 The matrix is ​​automatically updated after standard source scaling; For a single pure nuclide: if there are no impurity peaks in the energy spectrum, the upper limit of impurity activity is constrained by the detection limit, and the joint inversion degenerates into a single nuclide for direct conversion. The result is output once the half-life single exponent verification is passed.

[0017] A standard nuclide sample with known activity is placed in the central measuring well. The measured current signal is obtained by a femtoampere-level low-noise microcurrent measurement. The measured current signal is corrected using the zero-input correction parameter and the background correction parameter. The nuclide calibration coefficient is obtained based on the ratio of the measured current signal to the known activity. A radionuclide calibration coefficient matrix is ​​established based on the nuclide calibration coefficient. The radionuclide sample to be tested is placed in the central measuring well, and the gamma-ray energy spectrum of the radionuclide sample is obtained. The types of radionuclides are initially screened based on the gamma-ray energy spectrum. The time series of the measured current signal is collected, and the half-life of the radionuclide is determined based on the decay characteristics of the measured current signal within a set time. The results of the initial screening are verified based on the half-life of the radionuclide to determine the types of radionuclides. Prior constraints on impurity nuclides are obtained through gamma-ray spectroscopy inversion. The activity value of the sample to be tested is obtained based on the calibration coefficient of the radionuclide sample, the measured current signal, and the prior constraints on impurity nuclides.

[0018] In this embodiment, the ambient background current is measured as follows: Under conditions where there is no sample to be measured and the shielding conditions are consistent with the formal measurement, the high-voltage current is collected when the 4πγ well-type ionization chamber is powered on and there is no sample; the pure dark current is collected when the 4πγ well-type ionization chamber is powered off and there is no sample. The difference between the high-voltage current and the pure dark current is output as the ambient background current. The pure dark current includes electronic zero-point offset and measurement link leakage current. Calibration is performed according to... Find the net ionization current. It is a pure dark current. The background current of the environment, This is the measured current signal.

[0019] In this embodiment, establishing the radionuclide calibration coefficient matrix includes: Using nuclide type, container type, and sample volume as a three-dimensional index, a scale coefficient matrix is ​​established. The elements of the scale coefficient matrix are the activity current conversion coefficients of nuclides under container and volume classifications. For multiple characteristic gamma rays of the same nuclide, they are further subdivided and stored according to the main energy range. A standard source covering the main gamma-ray energy range of the nuclide under test was selected. The standard activity and steady-state ionization current of the standard source were measured under standard geometric conditions, and the activity-current conversion factor of the nuclide was calculated. The activity current conversion coefficient is modified by introducing energy-dependent wellbore effects and self-absorption. ;in Let be the stable ionization current of the i-th nuclide. Zero input correction parameters, The background current of the environment, Let i be the standard activity of the i-th nuclide. Let be the activity current conversion coefficient of the i-th nuclide. Energy-dependent transmission correction of gamma rays to wellbore materials at gamma ray energy E. For gamma ray energy E, volume Self-absorption correction of the sample matrix. For the z-th volume, is the activity current conversion factor of the i-th nuclide at the j-th container and z-th individual integral level when the gamma ray energy is E; For nuclides not directly scaled in the matrix, their characteristic gamma-ray energies are used. Piecewise spline interpolation is performed between the energy response curves of calibrated nuclides and the nuclide to predict the calibration coefficients of the nuclides. Once the energy spectrum is initially screened and the main characteristic peak energy of the nuclide is determined, the system automatically retrieves the calibrated nuclide with the highest energy matching degree in the matrix and directly calls the calibration coefficient; if it is identified as an uncalibrated nuclide, it triggers piecewise spline interpolation to automatically generate the predicted calibration coefficient; and outputs the updated calibration coefficient matrix. In practical evaluation, the energy anchor point selection rules for piecewise spline interpolation are as follows: the characteristic gamma-ray energy of the calibrated nuclide with an emission branching ratio greater than 5% is used as the anchor point energy; in the low-energy region (<200keV), the energy interval between adjacent anchor points does not exceed 50keV; in the medium-energy region (200keV–1000keV), the energy interval between adjacent anchor points does not exceed 150keV; and in the high-energy region (>1000keV), the energy interval between adjacent anchor points does not exceed 300keV. For the nuclide to be interpolated, at least one anchor point is guaranteed to exist on both sides of the characteristic gamma-ray energy. When the energy to be interpolated is within the anchor point coverage area, cubic spline interpolation is used; when it exceeds the outermost anchor point, linear extrapolation is used, and the extrapolation component is added to the uncertainty budget. If the energy to be interpolated happens to coincide with an anchor point, the calibration coefficient of that anchor point is directly called, and interpolation is not triggered. When the laboratory obtains new standard source calibration data, if the minimum interval between the characteristic γ energy of the new calibration nuclide and the existing anchor point is less than the above interval density threshold, then the nuclide is included in the anchor point set, the spline coefficients are recalculated, and the calibration coefficient matrix library is updated.

[0020] In this embodiment, the method for identifying the type of nuclide includes: The gamma spectrum of the sample is obtained, and the characteristic gamma-ray energy and net peak area are extracted by the peak position identification algorithm. The data are then matched with the nuclide database, and a candidate set is constructed based on the matching results. At the same time, impurity nuclides are determined based on the presence of characteristic peaks and their relative intensity ratios, forming an initial classification of the main nuclide and impurity nuclides. The total activity time spectrum half-life was verified for the initial classification: the total current of the ionization chamber was continuously collected at set intervals within a fixed time window, and a discrete sequence of total activity over time was constructed after zero input and background correction. Single nuclide scenario verification: The discrete sequence is fitted with a single exponential decay to obtain the decay constant, which is compared with the theoretical half-life of the candidate nuclide. If the deviation is within ±3%, the nuclide identity is confirmed, and the initial activity is obtained simultaneously to confirm that the sample is a single nuclide. Multi-nucleoside scenario verification: The theoretical decay model of each candidate nuclide combination is fitted with the measured discrete sequence by minimizing the residual, and the combination with the highest goodness of fit is selected as the final identification result; The search space is limited by the energy spectrum candidate set. The identity of the nuclide is locked by discrete sequence verification. The cross-confirmation is performed by single nuclide scenario verification and multi-nuclide scenario verification, and the nuclide type is output.

[0021] In this embodiment, the method for obtaining the prior constraints of the impurity nuclide includes: The energy and net peak area of ​​the main nuclide are extracted by the second derivative method or Gaussian fitting method, and the energy and net peak area of ​​the impurity nuclide are identified at the same time. Nonlinear least squares decomposition is used for overlapping peaks. Using the emission branching ratios of characteristic gamma rays from the nuclide database and the calibration coefficients of the ionization chamber for the corresponding nuclides, the relative activity ratios of impurity nuclides to the host nuclide are calculated. ;in Main nuclides in energy The emission branching ratio of gamma rays at that location, For impurity nuclides in energy The emission branching ratio of gamma rays at that location, The calibration coefficients of the main nuclide in the 4πγ ionization chamber These are the calibration coefficients for impurity nuclides in the 4πγ ionization chamber. The activity of the impurity nuclide. The activity of the main nuclide, The energy of the characteristic gamma-ray peak of the main nuclide. The energy of the characteristic gamma-ray peak of the impurity nuclide; Based on the relative activity ratio combined with the upper limit of impurity nuclide activity. Construct the impurity nuclide prior constraint vector The objective function for optimizing the decomposition of current components in the ionization chamber incorporates prior constraints on impurity nuclides. In practical evaluation, the relative activity ratio and upper limit of the impurity nuclides obtained by γ-ray spectrum inversion are used as prior constraint vectors and embedded into a boundary-constrained optimization model with the goal of decomposing the current components of the ionization chamber to solve the activity distribution between the main nuclide and the impurity nuclide.

[0022] In this embodiment, the method for obtaining the activity value includes: Acquire the measured current signal of the sample. Based on the activity of the main nuclide and the activity of impurity nuclides To optimize the variables, a joint objective function integrating ionization chamber current measurement and energy spectrum prior constraints is constructed. The constraints are: , ; ; in This is a matrix of radionuclide calibration coefficients. Let be the activity vector to be determined. This is the measured ionization current vector after zero-input correction and background correction. The regularization coefficient is . The prior confidence weights for impurity nuclide c are given. These are the weighting coefficients for the relative activity ratio constraint term in energy spectrum inversion; The activity of the main nuclide and the impurity activity were obtained by using a nonlinear least squares algorithm with boundary constraints, based on the time difference between the sample calibration time and the measurement time. ,according to Corrected to a unified reference time, Output the activity value and provide the expanded uncertainty. ;in The decay constant of the main nuclide As a inclusion factor, This represents the combined standard uncertainty. In actual assessment, , Calibration experiments or adaptive selection strategies: Prepare a series of mixed standard sources of main nuclide and impurity nuclide, covering the relative activity ratio of impurity nuclides. From 10 -4 Up to 10 -1 The range of magnitudes; performing a complete measurement procedure for each standard source, with current fitting difference. The horizontal axis represents the degree of violation of the energy spectrum prior constraints. Plot the L-curve with the vertical axis as the ordinate, and select the inflection points of the L-curve corresponding to... The combination is used as the optimal parameter; the signal-to-noise ratio based on impurity characteristic peaks is adopted. The adaptive grading strategy, when hour, , ;when hour, , ;when , , ,Will , Treating these as hyperparameters, a Bayesian approach is introduced into the joint objective function to automatically optimize the hyperparameters through evidence maximization; where... , This represents the net peak area of ​​the characteristic peaks of the impurity nuclides. The background area below the peak; Mapping relationship with statistical significance of energy spectrum peak area: Statistical significance of characteristic peaks of impurity nuclides in γ-ray spectra Establish a deterministic mapping using the Sigmoid function. to Smooth mapping ,when , For high confidence, close to 1; when , This represents a medium confidence level; when , The confidence level is low, close to 0; among which For statistical significance, The net peak area after deducting the background. The background area within the peak boundary. The half-value significance threshold; If an impurity nuclide has multiple identifiable characteristic peaks, the prior confidence weight of each peak is calculated separately, and the overall prior confidence weight of the impurity nuclide is obtained by weighting the peaks according to the emission branching ratio. Substituting directly into the regularization term of the joint objective function, when When this term degenerates to zero, the joint inversion no longer enforces the upper limit of the activity of the impurity nuclide, and only retains the current fitting residual term and the relative activity ratio constraint term.

[0023] The second aspect is a nuclide activity measurement device based on a 4πγ well-type ionization chamber, including an ionization chamber semiconductor combined detector, a femtoampere-level low-noise microcurrent module, a multichannel analyzer, a γ energy spectrum inversion module, a total activity time spectrum method, and a joint activity inversion unit. The ionization chamber semiconductor combined detector includes a 4πγ well-type ionization chamber and a zinc-cadmium telluride semiconductor detector. The 4πγ well-type ionization chamber is a sealed cylindrical cavity with a central measuring well filled with high-pressure inert gas. The sample is placed at the geometric center, and the output is a saturated ionization current proportional to the activity. The zinc-cadmium telluride semiconductor detector is embedded in the well wall or arranged in parallel, receives the characteristic γ-rays of the sample, and outputs a pulse signal for high-resolution energy dispersive spectroscopy measurement. Flight safety-grade low-noise microcurrent module: The front end uses a transimpedance amplifier, is configured with a three-stage feedback network, and is equipped with a reed relay for automatic range switching; after an eighth-order Butterworth low-pass filter, it is connected to a 32-bit Σ-Δ analog-to-digital converter; the high-impedance node is equipped with a protection ring, overhead wiring and a nickel silver shield. Multichannel analyzer: Receives the charge pulses output from the cadmium zinc telluride detector, performs pulse amplification, shaping, peak holding and A / D conversion, accumulates and counts according to energy channel address, and forms gamma spectrum data; γ-ray spectrum inversion module: Input γ-ray spectrum data, extract the characteristic peaks of the main nuclide and the characteristic peaks of the impurity nuclide through the peak position recognition algorithm; call the branch ratio of the nuclide database and combine it with the calibration coefficient of the ionization chamber to calculate the relative activity ratio and upper limit of the impurity, and output the prior constraint vector of the impurity nuclide. Total Activity Time Spectrum Method Module: The current time series data output by the femtoampere-level module is continuously collected at a set sampling interval. After zero-input correction and background correction, a discrete sequence of total activity changing with time is constructed. The half-life is obtained by performing exponential decay fitting for single-nuctopus scenarios. For multi-nuctopus scenarios, the total activity time spectrum method is used as a residual test condition to verify the initial energy spectrum screening results and obtain the nuctopus identity. Joint Activity Inversion Unit: Integrates the calibration coefficient matrix, receives the impurity nuclide prior constraint vector provided by the nuclide identity and γ-ray spectrum inversion module, constructs a constrained optimization objective function, solves for the main nuclide activity and impurity activity, and outputs the final activity value after decay correction.

[0024] like Figure 2 As shown, the activity program is divided into three parts: a 4πγ ionization chamber, a weak current measurement unit, and a control host. These components respectively handle radioactive sample detection, front-end weak current signal measurement, and back-end integrated control and management. Based on hardware and software design, an integrated architecture combining measurement, control, display, and data management is formed. The two parts are connected via cables for power supply and RS-485 communication. The weak current measurement unit is integrated at the bottom of the 4πγ ionization chamber and connected via three coaxial cables with the shortest possible current transmission path to reduce signal attenuation and external interference, ensuring the accuracy and stability of the front-end measurement. In terms of hardware design, the front-end uses a high-value resistor IV-to-voltage conversion method to achieve weak current detection, and combines this with a multi-range high-value resistor feedback network to broaden the measurement range and meet the needs of different activity levels. Measurement requirements are met; simultaneously, necessary shielding, filtering, and isolation measures are used to reduce noise interference and improve the reliability of measurement results; the embedded program works in conjunction with hardware functions to complete data acquisition, status control, communication processing, and storage management; the control host, as the core of the whole machine's control and management, undertakes data communication, task scheduling, interface driving, parameter management, and file management functions; the hardware integrates display touch, communication, storage, and power supply modules to form a control and display terminal that works with the measurement unit; the software is ported to FreeRTOS, and the graphical interface program is written based on LVGL. Through multi-task collaboration, it realizes measurement process control, interface interaction, parameter management, nuclide database management, and file management functions, thereby constructing a complete activity measurement and management system; An eighth-order Butterworth low-pass filter is used to further process the transimpedance amplified voltage signal. This is achieved through cascading based on a Sallen-Key active filter unit structure, as shown in the circuit diagram. Figure 3The cutoff frequency of the filter circuit is set to 1Hz. This cutoff frequency balances the requirements of effective signal transmission and noise suppression, ensuring the complete preservation of weak DC signals and their slowly changing components while effectively reducing interference components exceeding the measurement bandwidth. The filter parameters were designed and optimized using the filter design software Filter Solutions. Operational amplifiers with low offset, low temperature drift, low noise, and strong anti-interference capabilities were selected to ensure the accuracy, stability, and reliability of the filter circuit. like Figure 4 After the system powers on, the program first initializes the underlying runtime resources, and then sequentially configures the peripheral interfaces such as SPI, UART, and SDMMC, as well as sets the initial parameters of the ADC registers. It then mounts the FATFS file system and reads the configuration parameters stored in the on-chip Flash, such as the local address, background value, calibration time, and buffer width. After establishing the runtime environment, it sets the ADC to start continuous sampling, putting the entire program into the normal radionuclide activity measurement mode. The main loop will enter the measurement and communication modules according to the status flags to execute the corresponding processing flow. Specifically, when a new data flag is detected, the program enters the measurement module to complete data conversion, calibration, and range adjustment. The system switches between judgment and result storage; when a reception completion flag is detected, it enters the communication module, completes data parsing, and enters the corresponding functional branch to execute operations; the update of the status flag is achieved through interrupt response. The measurement module uses the ADC data ready pin of the digital-to-analog converter to trigger an external interrupt, reads the conversion result and writes it to the measurement buffer in the interrupt service function, and sets the new data flag; in the communication module, the serial communication receive interrupt, based on the completion of byte data buffering, combines the timeout method to determine the end of a frame of data reception and sets the reception completion flag; in addition, the timer interrupt program provides a unified time base for functions such as delay control, timeout timing, and status monitoring involved in the program operation. Sampling performance under dynamic input conditions was tested by directly applying a 0.1Hz sinusoidal signal with a peak-to-peak value of 5V to the input of the low-pass filter circuit. The sampling results are as follows: Figure 5 The output time-domain waveform is consistent with the input sine wave, indicating that the designed analog-to-digital converter interface circuit and its initialization configuration can well meet the acquisition requirements of low-frequency dynamic signals. A continuous 1-hour data acquisition test was conducted under grounded input conditions, and time-frequency domain analysis was performed on the test results. The results are as follows: Figure 6 The test results show that the overall output fluctuation of the analog-to-digital converter is small. The standard deviation is 0.1078 in the configured Sinc4 filter mode, and the dynamic range reaches 146.33dB. This indicates that under the hardware interface design and software configuration conditions in this paper, the sampling link has good static stability and a wide effective dynamic range. Figure 7This demonstrates the task state transition relationships and related functions. The running state indicates that the task is currently occupying the processor for execution; the ready state indicates that the task is ready to run, but is temporarily waiting for scheduling because the processor is executing other tasks; the blocked state indicates that the task cannot run temporarily due to waiting for events such as delays, semaphores, or message queues; and the suspended state indicates that the task is explicitly suspended and does not participate in system scheduling. During system operation, tasks will transition between the above states based on external events, system calls, and scheduling results, thus forming the dynamic operation process of a multitasking system. like Figure 8 As shown, the overall trend of the measured results over time is consistent with the theoretical decay law, and the maximum relative deviation between the two is 1.55%, which proves that the activity meter can accurately reflect the decay process of sample activity. At the same time, no obvious abnormal drift was observed in the measurement results during the entire test process, indicating that the activity meter has good measurement accuracy and long-term stability under continuous operation conditions.

[0025] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring nuclide activity based on a 4πγ well-type ionization chamber, characterized in that, Includes the following steps: Under the conditions of short circuit at the input end of the measurement link and no effective input signal, the time series of the output current is collected, and the statistical average value of the current is calculated as the zero input correction parameter. Under the condition of no sample to be tested, the environmental background current is measured, and the statistical average value of the environmental background current is used as the background correction parameter. A standard nuclide sample with known activity is placed in the central measuring well. The measured current signal is obtained by a femtoampere-level low-noise microcurrent measurement. The measured current signal is corrected using the zero-input correction parameter and the background correction parameter. The nuclide calibration coefficient is obtained based on the ratio of the measured current signal to the known activity. A radionuclide calibration coefficient matrix is ​​established based on the nuclide calibration coefficient. The radionuclide sample to be tested is placed in the central measuring well, and the gamma-ray energy spectrum of the radionuclide sample is obtained. The types of radionuclides are initially screened based on the gamma-ray energy spectrum. The time series of the measured current signal is collected, and the half-life of the radionuclide is determined based on the decay characteristics of the measured current signal within a set time. The results of the initial screening are verified based on the half-life of the radionuclide to determine the types of radionuclides. Prior constraints on impurity nuclides are obtained through gamma-ray spectroscopy inversion. The activity value of the sample to be tested is obtained based on the calibration coefficient of the radionuclide sample, the measured current signal, and the prior constraints on impurity nuclides.

2. The method for measuring nuclide activity based on a 4πγ well-type ionization chamber according to claim 1, characterized in that, The ambient background current was measured as follows: Under conditions where there was no sample to be measured and the shielding conditions were consistent with the formal measurement, the high-voltage current was collected when the 4πγ well-type ionization chamber was powered on and there was no sample; the pure dark current was collected when the 4πγ well-type ionization chamber was powered off and there was no sample. The difference between the high-voltage current and the pure dark current was output as the ambient background current. The pure dark current includes electronic zero-point offset and measurement link leakage current. Calibration was performed according to... Find the net ionization current. It is a pure dark current. The background current of the environment, This is the measured current signal.

3. The method for measuring nuclide activity based on a 4πγ well-type ionization chamber according to claim 1, characterized in that, Establishing the radionuclide calibration coefficient matrix includes: Using nuclide type, container type, and sample volume as a three-dimensional index, a scale coefficient matrix is ​​established. The elements of the scale coefficient matrix are the activity current conversion coefficients of nuclides under container and volume classifications. For multiple characteristic gamma rays of the same nuclide, they are further subdivided and stored according to the main energy range. A standard source covering the main gamma-ray energy range of the nuclide under test was selected. The standard activity and steady-state ionization current of the standard source were measured under standard geometric conditions, and the activity-current conversion factor of the nuclide was calculated. The activity current conversion coefficient is modified by introducing energy-dependent wellbore effects and self-absorption. ;in Let be the stable ionization current of the i-th nuclide. Zero input correction parameters, The background current of the environment, Let i be the standard activity of the i-th nuclide. Let be the activity current conversion coefficient of the i-th nuclide. Energy-dependent transmission correction of gamma rays to wellbore materials at gamma ray energy E. For gamma ray energy E, volume Self-absorption correction of the sample matrix. For the z-th volume, is the activity current conversion factor of the i-th nuclide at the j-th container and z-th individual integral level when the gamma ray energy is E; For nuclides not directly scaled in the matrix, their characteristic gamma-ray energies are used. Piecewise spline interpolation is performed between the energy response curves of calibrated nuclides and the nuclide to predict the calibration coefficients of the nuclides. Once the energy spectrum is initially screened and the main characteristic peak energy of the nuclide is determined, the calibrated nuclide with the highest energy matching degree in the matrix is ​​automatically retrieved, and the calibration coefficient is directly called; if it is identified as an uncalibrated nuclide, piecewise spline interpolation is triggered to automatically generate the predicted calibration coefficient; the updated calibration coefficient matrix is ​​output.

4. The method for measuring nuclide activity based on a 4πγ well-type ionization chamber according to claim 1, characterized in that, Methods for identifying the types of nuclides include: The gamma spectrum of the sample is obtained, and the characteristic gamma-ray energy and net peak area are extracted by the peak position identification algorithm. The data are then matched with the nuclide database, and a candidate set is constructed based on the matching results. At the same time, impurity nuclides are determined based on the presence of characteristic peaks and their relative intensity ratios, forming an initial classification of the main nuclide and impurity nuclides. The total activity time spectrum half-life was verified for the initial classification: the total current of the ionization chamber was continuously collected at set intervals within a fixed time window, and a discrete sequence of total activity over time was constructed after zero input and background correction. Single nuclide scenario verification: The discrete sequence is fitted with a single exponential decay to obtain the decay constant, which is compared with the theoretical half-life of the candidate nuclide. If the deviation is within ±3%, the nuclide identity is confirmed, and the initial activity is obtained simultaneously to confirm that the sample is a single nuclide. Multi-nucleoside scenario verification: The theoretical decay model of each candidate nuclide combination is fitted with the measured discrete sequence by minimizing the residual, and the combination with the highest goodness of fit is selected as the final identification result; The search space is limited by the energy spectrum candidate set. The identity of the nuclide is locked by discrete sequence verification. The cross-confirmation is performed by single nuclide scenario verification and multi-nuclide scenario verification, and the nuclide type is output.

5. The method for measuring nuclide activity based on a 4πγ well-type ionization chamber according to claim 1, characterized in that, The method for obtaining the prior constraints of the impurity nuclides includes: The energy and net peak area of ​​the main nuclide are extracted by the second derivative method or Gaussian fitting method, and the energy and net peak area of ​​the impurity nuclide are identified at the same time. Nonlinear least squares decomposition is used for overlapping peaks. Using the emission branching ratios of characteristic gamma rays from the nuclide database and the calibration coefficients of the ionization chamber for the corresponding nuclides, the relative activity ratios of impurity nuclides to the host nuclide are calculated. ;in Main nuclides in energy The emission branching ratio of gamma rays at that location, For impurity nuclides in energy The emission branching ratio of gamma rays at that location, The calibration coefficients of the main nuclide in the 4πγ ionization chamber These are the calibration coefficients for impurity nuclides in the 4πγ ionization chamber. The activity of the impurity nuclide. The activity of the main nuclide, The energy of the characteristic gamma-ray peak of the main nuclide. The energy of the characteristic gamma-ray peak of the impurity nuclide; Based on the relative activity ratio combined with the upper limit of impurity nuclide activity. Construct the impurity nuclide prior constraint vector The objective function for optimizing the decomposition of current components in the ionization chamber incorporates prior constraints on impurity nuclides.

6. The method for measuring nuclide activity based on a 4πγ well-type ionization chamber according to claim 1, characterized in that, The method for obtaining the activity value includes: Acquire the measured current signal of the sample. Based on the activity of the main nuclide and the activity of impurity nuclides To optimize the variables, a joint objective function integrating ionization chamber current measurement and energy spectrum prior constraints is constructed. The constraints are: ， ； ； in This is a matrix of radionuclide calibration coefficients. Let be the activity vector to be determined. This is the measured ionization current vector after zero-input correction and background correction. The regularization coefficient is . represents the prior confidence weight of impurity nuclide c. These are the weighting coefficients for the relative activity ratio constraint term in energy spectrum inversion; The activity of the main nuclide and the impurity activity were obtained by using a nonlinear least squares algorithm with boundary constraints, based on the time difference between the sample calibration time and the measurement time. ,according to Corrected to a unified reference time, Output the activity value and provide the expanded uncertainty. ;in The decay constant of the main nuclide As a inclusion factor, This represents the combined standard uncertainty.

7. A radionuclide activity measuring device based on a 4πγ well-type ionization chamber, used to perform the method according to any one of claims 1-6, characterized in that, It includes an ionization chamber semiconductor combined detector, a femtoampere-level low-noise microcurrent module, a multichannel analyzer, a gamma-ray spectrum inversion module, a total activity time spectrum method, and a joint activity inversion unit; The ionization chamber semiconductor combined detector includes a 4πγ well-type ionization chamber and a zinc-cadmium telluride semiconductor detector. The 4πγ well-type ionization chamber is a sealed cylindrical cavity with a central measuring well, filled with a high-pressure working gas, with the sample placed at the geometric center, and outputting a saturated ionization current proportional to the activity. The zinc-cadmium telluride semiconductor detector is embedded in the well wall, the bottom of the well, or arranged in parallel, to receive the characteristic γ-rays of the sample and output a pulse signal for high-resolution energy dispersive spectroscopy measurement. Flight safety-grade low-noise microcurrent module: The front end uses a transimpedance amplifier, is configured with a three-stage feedback network, and is equipped with a reed relay for automatic range switching; after an eighth-order Butterworth low-pass filter, it is connected to a 32-bit Σ-Δ analog-to-digital converter; the high-impedance node is equipped with a protection ring, overhead wiring and a nickel silver shield. Multichannel analyzer: Receives the charge pulses output from the cadmium zinc telluride detector, performs pulse amplification, shaping, peak holding and A / D conversion, accumulates and counts according to energy channel address, and forms gamma spectrum data; γ-ray spectrum inversion module: Input γ-ray spectrum data, extract the characteristic peaks of the main nuclide and the characteristic peaks of the impurity nuclide through the peak position recognition algorithm; call the branch ratio of the nuclide database and combine it with the calibration coefficient of the ionization chamber to calculate the relative activity ratio and upper limit of the impurity, and output the prior constraint vector of the impurity nuclide. Total activity time spectrum method module: continuously collects the current time series data output by the femtoampere-level module at a set sampling interval, and after zero input correction and background correction, constructs a discrete sequence of total activity changing with time, and performs exponential decay fitting on a single nuclide scenario to obtain the half-life for verification. For multi-nucleoside scenarios, the total activity time spectrum method is used as the residual test condition to verify the initial screening results of the energy spectrum and obtain the nuclide identity. Joint Activity Inversion Unit: Integrates the calibration coefficient matrix, receives the impurity nuclide prior constraint vector provided by the nuclide identity and γ-ray spectrum inversion module, constructs a constrained optimization objective function, solves for the main nuclide activity and impurity activity, and outputs the final activity value after decay correction.

Images