Statistical and physical combined evaluation method for (n, alpha) reaction cross section experimental data

Abstract

The present application relates to a kind of statistical and physical combination (n, alpha) reaction cross section experimental data evaluation method, belong to nuclear data evaluation technical field, the method includes the following steps: investigation and collection existing (n, alpha) reaction cross section experimental data, and collect the relevant information of experimental data, determine the experimental method of experimental data, experimental purpose, detector information, to experimental data is mathematically and physically analyzed, understand the distribution law of experimental data, find implicit variable;According to implicit variable, experimental data is classified and analyzed to obtain experimental data evaluation result;And with the experimental data after evaluation as the basis, obtain recommended excitation function by mathematical fitting etc..The method of the present application starts from two aspects of mathematics and physics, finds the "implicit variable" that influences the accuracy of data in Simpson paradox, from the angle of experimental data evaluation, can effectively avoid the occurrence of PPP problem, effectively improve the accuracy of evaluation data and the efficiency of evaluation work.

Description

Technical Field

[0001] This invention belongs to the field of nuclear data evaluation technology, specifically a method for evaluating experimental data of (n,α) reaction cross sections that combines statistics and physics. Background Technology

[0002] Neutron-induced emission of light charged particles into the nucleus is called an (n,lcp) reaction (where lcp is an abbreviation for light-charged particle, including p, d, t, ...). 3 The helium production cross section induced by neutrons (e.g., helium, alpha particles) is sometimes referred to as the (n,x) reaction or (n,cp) reaction in other literature. Research on the (n,lcp) reaction is of great significance for refining the standard cross section of neutron nuclear reactions, neutron detection and protection, nuclear engineering applications, electronic safety, nuclear medicine development, nuclear astrophysics research, and the close integration of experimental measurement and evaluation of nuclear reactions with theoretical analysis. The neutron-induced helium production cross section ((n,α) reaction cross section) is an important light charged particle emission reaction and one of the charged particle emission cross sections of key interest in nuclear data; the accuracy and reliability of its data are closely related to the quality of nuclear data.

[0003] The main methods for measuring (n,α) reaction cross sections are activation and radiochemical separation, with activation accounting for a larger proportion. Research has revealed that experimental data on the (n,α) reaction cross sections of multiple nuclides are characterized by wide coverage of years, numerous measurements, and inconsistencies across countries, laboratories, facilities, neutron sources, detectors, standard cross sections, sample quantification, data correction, and processing. Experimental data values ​​often differ to varying degrees, even significantly, and the uncertainty sources given by different years and laboratories also vary. Furthermore, there are discrepancies in the (n,α) cross section evaluation data provided by various international evaluation databases. Conducting evaluation work on (n,α) cross section experimental data, clarifying discrepancies, recommending highly reliable excitation function data based on the evaluation results, and summarizing the physical evaluation methods for this type of experimental data are all of great significance for (n,α) cross section data evaluation, the calculation of related complete neutron data theoretical models, and the research on cross section experimental data evaluation methods.

[0004] Several evaluation systems have been established both domestically and internationally for evaluating experimental measurements of nuclear reaction cross-sections. The basic idea behind most of these methods is based on mathematical statistics, treating experimental measurements as random events. They assume the distribution of experimental data follows a mathematically normal distribution or other types of distributions, with the true value considered the mathematical expectation of that distribution. The experimental measurement system, including experimental instruments, samples, measurement environment, measurement methods, data corrections, etc., is divided into macroscopic and microscopic systems. Errors within each microscopic system and between independent microscopic systems are analyzed separately. Probabilistic and statistical methods, typically least squares and Bayesian methods, are used to mathematically process the experimental data, resulting in evaluation curves and associated error and covariance information.

[0005] In practical applications, especially when using mathematical methods to process abundant experimental data, this type of method can encounter physical problems, particularly with divergent experimental data or when experimental data values ​​are widely dispersed. This leads to Peelle's Pertinent Puzzle, a well-known problem in experimental data fitting. The PPP problem manifests itself in the fact that the fitted data cannot completely reproduce the experimental data, especially with divergent experimental data, where the fitted values ​​may deviate entirely from the experimental data. Since its discovery, the PPP problem has plagued nuclear data evaluation. To address these problems, various mathematical methods have been developed for data evaluation, including the arithmetic mean, median method, weighted average method, improved Bayesian method, limited-weighted average method, standard remainder method, Rajeval method, quadratic average method, systematic error assessment method, and off-diagonal element evaluation method of the covariance matrix, among others.

[0006] These processing methods inevitably involve uncertainty evaluation and correlation assessment to some extent. However, evaluating experimental data and assessing uncertainties and correlations presents other challenges. Experimental data often spans a wide range of years, and the neutron sources, detectors, and standard cross-sections used in measurements vary. Correcting and analyzing experimental data, and analyzing errors within and between microscopic systems, consumes significant time, effort, and research resources. Careful reading of the original experimental data measurement literature is necessary, further increasing time and research costs. Regarding data correction, data with provided original standard cross-sections are relatively easy to correct. However, without provided standard cross-sections, correction, especially the re-evaluation of uncertainties, requires analyzing experimental data from various sources and introduces numerous subjective factors, lacking strong persuasiveness.

[0007] Some domestic and international studies have focused primarily on physics, clarifying discrepancies in experimental data based on measurement conditions, and recommending only a few experimental data points as the most important basis for evaluation, while using the majority of other experimental data as references. This evaluation method has been used in the evaluation of abundant experimental data reaction cross-sections for certain nuclides in the US ENDF / B-VIII.0 library, the Chinese CENDL-3.2 library, and the CENDL-3.1 library. However, this method lacks sufficient mathematical basis and systematic reporting. Generally, in evaluations, unless there is a clear indication of serious problems or omissions in the measurement of experimental data points, there is no sufficient reason to discard the experimental data from that institution.

[0008] There's a well-known paradox in statistics, Simpson's paradox, which describes the phenomenon where, when data is broken down and examined closely, the details reveal a completely different trend from the overall picture. This bears many similarities to the PPP problem we encounter in data processing. Further research shows that since its introduction in 1951 by British statistician E.H. Simpson, Simpson's paradox has received considerable attention in various fields related to data analysis and statistics, including economics, medicine, and population studies. After years of detailed research, analysis, and validation in various fields, relatively mature solutions have been developed, and detailed explanations are available on websites such as the Encyclopedia Britannica, Baidu Encyclopedia, JianShu, Wikipedia, and related literature.

[0009] In the field of nuclear data evaluation, there have been no reports focusing on Simpson's paradox and its solutions.

[0010] By referencing analyses of Simpson's Paradox in other fields related to data analysis and statistics, we can hopefully solve the PPP problem in data evaluation. The key to avoiding Simpson's Paradox is to consider the complete picture of the facts across different data sets. This requires accurate cluster analysis to identify the "latent variables" (or "hidden variables") in the statistical data, carefully considering the weights of individual groups, and using appropriate coefficients to eliminate the impact of differences in the baseline data between groups. It is also essential to understand whether there are other underlying factors in the situation and consider them comprehensively. Generalized data is not very meaningful; comparisons are only valuable when broken down to specific categories.

[0011] For abundant and divergent experimental data, how to make sufficient reasons for selecting and discarding experimental data, and how to determine evaluation center values ​​with high accuracy and precision, how to avoid the PPP problem, and how to reduce evaluation costs and improve evaluation efficiency have always been very important issues in data evaluation. Summary of the Invention

[0012] To address the shortcomings of existing technologies, the present invention aims to provide a statistical and physical method for evaluating experimental data of (n,α) reaction cross sections. This method approaches the problem from both mathematical and physical perspectives, seeking the "hidden variables" in Simpson's paradox that affect the accuracy of the data. From the perspective of experimental data evaluation, it can effectively avoid the occurrence of the PPP problem.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A statistical and physical method for evaluating experimental data of (n,α) reaction cross sections includes the following steps:

[0015] S1. Collect relevant information on existing (n, α) reaction cross section experimental data. If the abundance of energy points and number of units measured by the experimental data meets the requirements of statistical processing, it is determined to be abundant experimental data.

[0016] S2. Perform mathematical classification analysis on the experimental data according to the relevant information of the experimental data, understand the non-normal distribution law of the experimental data from the perspective of mathematical statistics, and thus obtain the statistical latent variables;

[0017] S3. Based on the (n,α) reaction cross section experimental measurement method, analyze from a physical perspective the factors that have the greatest impact on the accuracy and precision of the experimental data, seek the reasons for the statistical non-normal distribution, and thus obtain the physical latent variables;

[0018] S4. Classify and analyze the experimental data of the physical latent variables, and evaluate the weights of different categories to obtain the experimental data evaluation results.

[0019] S5. Based on the evaluation results of the experimental data, a recommended activation function is obtained through a set method.

[0020] Furthermore, in the statistical and physical combined (n,α) reaction cross section experimental data evaluation method described above, the relevant information of the experimental data in step S1 includes the experimental measurement year, author, institution, literature title, apparatus, detector, neutron source, neutron flux measurement method, sample preparation details, measurement energy region, energy point, and uncertainty.

[0021] Furthermore, in the (n,α) reaction cross section experimental data evaluation method combining statistics and physics as described above, in step S2, when the experimental data exhibits an unbalanced distribution after being classified according to the relevant information, and has a special distribution pattern that does not conform to the normal distribution, the corresponding information is determined to be the statistical latent variable.

[0022] Furthermore, in the statistical and physical combined experimental data evaluation method for (n,α) reaction cross section described above, step S3 determines the (n,α) reaction cross section experimental measurement method as the activation method, that is, the sample to be tested is placed in a specific neutron field and irradiated for a set time, and after being taken out and cooled, the radioactivity of the reaction product nuclei is measured.

[0023] Furthermore, in the statistical and physical combined experimental data evaluation method for (n,α) reaction cross sections described above, the physical latent variables that have the greatest impact on the accuracy and precision of the experimental data in the activation method in step S3 include the detector resolution of the experimental angle, the experimental purpose, and the shape of the nuclear reaction mechanism curve of the evaluation angle. The experimental purpose refers to whether the experiment is carried out for the measurement of the (n,α) reaction cross section, and the shape of the nuclear reaction mechanism curve refers to whether the data distribution according to energy conforms to the laws of nuclear reaction.

[0024] Furthermore, in the statistical and physical combined (n,α) reaction cross section experimental data evaluation method described above, the detector's resolving power includes the detector's intrinsic energy resolution and temporal resolution.

[0025] Furthermore, in the statistical and physical combined (n,α) reaction cross-section experimental data evaluation method described above, in step S4, experimental data whose accuracy and precision do not meet the requirements in the classification experimental data of the physical latent variables are given a weight of less than 1 / 20. In the case that there are still discrepancies in the experimental data, the contribution of the higher-order small data classes is omitted in the fitting.

[0026] Furthermore, regarding the statistical and physical combined experimental data evaluation method for (n,α) reaction cross sections as described above, the specific analysis steps in step S4 are as follows:

[0027] Based on the resolution of the detector, the experimental data of the (n,α) reaction cross section are screened and recommended in the first round to obtain the distribution of the experimental data after the first round of screening and recommendation. If the experimental data have good consistency and cover the target energy region, then proceed to step S5.

[0028] Otherwise, if the experimental data still meet the statistical processing requirements, based on the experimental objective, a second round of screening and recommendation is carried out on the (n,α) reaction cross-section experimental data after the first round of screening and recommendation to obtain the distribution of the experimental data after the second round of screening and recommendation. If the experimental data have good consistency and cover the target energy region, then proceed to step S5.

[0029] Otherwise, if the experimental data still meet the statistical processing requirements, based on the shape of the nuclear reaction mechanism curve, a third round of screening and recommendation is carried out on the (n,α) reaction cross-section experimental data after the second round of screening and recommendation to obtain the distribution of the experimental data after the third round of screening and recommendation. If the experimental data have good consistency and cover the target energy region, then proceed to step S5.

[0030] Furthermore, in the statistical and physical combined experimental data evaluation method for the (n,α) reaction cross section described above, step S5 uses the least squares method to fit the experimental data to obtain the recommended excitation function for the (n,α) reaction cross section.

[0031] Furthermore, in the (n,α) reaction cross section experimental data evaluation method combining statistics and physics as described above, if the experimental data in step S1 does not meet the conditions required for statistical processing, other evaluation methods are used to evaluate the data and obtain the excitation function.

[0032] The method for evaluating experimental data of (n,α) reaction cross sections, which combines statistical and physical methods as described in this invention, has the following significant technical advantages:

[0033] This invention, based on the solution to Simpson's paradox, addresses the problem of evaluating cross-sectional data (n, α) of abundant experimental data. It identifies "latent variables" affecting the quality of data from activation method measurements of (n, α) nuclear reaction cross-sections. The experimental data is categorized and evaluated according to these latent variables, and the weights of each category are discussed to obtain evaluation results suitable for equal-weighted fitting. Based on these results, data fitting and cross-sectional data recommendations are performed. This method helps clarify discrepancies in experimental data, rationally select and recommend experimental data, and determine evaluation center values ​​with high accuracy and precision. It provides a practical route for the screening, recommendation, and evaluation of experimental data for activation method measurements of abundant (n, α) nuclear reaction cross-sections, saving time and improving evaluation efficiency. Attached Figure Description

[0034] Figure 1 This is a flowchart of the (n,α) reaction cross section experimental data evaluation method that combines statistics and physics provided by the present invention;

[0035] Figure 2 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Distribution diagram of experimental data for the Na section;

[0036] Figure 3 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Chronological classification diagram of Na-section experimental data;

[0037] Figure 4 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Chronological distribution map of experimental data from the Na section;

[0038] Figure 5 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Age distribution map of detectors used in Na cross section experimental data;

[0039] Figure 6 This is a specific embodiment of the present invention. 27 Al(n,α) 24 The Na cross section uses experimental data from different detectors;

[0040] Figure 7 This is a comparison chart of the intrinsic energy resolution and temporal resolution of detectors from different eras;

[0041] Figure 8 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Distribution map of Na cross-section experimental data after the first round of screening and recommendation;

[0042] Figure 9 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Distribution map of Na cross-section experimental data after the second round of screening and recommendation;

[0043] Figure 10 yes 27 Al(n,α) 24 Theoretical calculation curve of Na section;

[0044] Figure 11 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Distribution map of Na cross-section experimental data after the third round of screening and recommendation;

[0045] Figure 12 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Na cross-section reaction excitation function curve;

[0046] Figure 13 This is a specific embodiment of the present invention. 27 Al(n,α) 24 Comparison of the recommended results for the Na section with the international standard section;

[0047] Figure 14 This is a flowchart of the (n,α) reaction cross section experimental data evaluation method that combines statistics and physics, provided in a specific embodiment of the present invention.

[0048] Figure 15 This is in Embodiment 1 of the present invention 51 V(n,α)48 Distribution of experimental data for the Sc section;

[0049] Figure 16 This is in Embodiment 1 of the present invention 51 V(n,α) 48 Distribution of experimental data for the Sc section after the first round of screening and recommendation;

[0050] Figure 17 This is in Embodiment 1 of the present invention 51 V(n,α) 48 Distribution of experimental data for the Sc section after the second round of screening and recommendation;

[0051] Figure 18 This is in Embodiment 2 of the present invention 54 Cr(n,α) 51 Distribution of experimental data for Ti cross section;

[0052] Figure 19 This is in Embodiment 2 of the present invention 54 Cr(n,α) 51 Distribution diagram of Ti cross-section experimental data after the first round of screening and recommendation;

[0053] Figure 20 This is in Embodiment 2 of the present invention 54 Cr(n,α) 51 Distribution diagram of Ti cross-section experimental data after the second round of screening and recommendation;

[0054] Figure 21 This is in Embodiment 3 of the present invention 55 Mn(n,α) 52 V-section experimental data distribution diagram;

[0055] Figure 22 This is in Embodiment 3 of the present invention 55 Mn(n,α) 52 Distribution diagram of V-section experimental data after the first round of screening and recommendation;

[0056] Figure 23 This is in Embodiment 3 of the present invention 55 Mn(n,α) 52 Distribution diagram of V-section experimental data after the second round of screening and recommendation;

[0057] Figure 24 This is in Embodiment 4 of the present invention 63 Cu(n,α) 60 Distribution diagram of experimental data for Co cross section;

[0058] Figure 25 This is in Embodiment 4 of the present invention 63 Cu(n,α) 60Distribution map of Co cross-section experimental data after the first round of screening and recommendation;

[0059] Figure 26 This is in Embodiment 4 of the present invention 63 Cu(n,α) 60 Distribution map of Co section experimental data after the second round of screening and recommendation;

[0060] Figure 27 This is in Embodiment 5 of the present invention 115 In(n,α) 112 Distribution diagram of experimental data for Ag cross section;

[0061] Figure 28 This is in Embodiment 5 of the present invention 115 In(n,α) 112 Distribution map of Ag cross-section experimental data after the first round of screening and recommendation;

[0062] Figure 29 This is in Embodiment 5 of the present invention 115 In(n,α) 112 Distribution map of Ag cross-section experimental data after the second round of screening and recommendation;

[0063] Figure 30 This is in Embodiment 5 of the present invention 115 In(n,α) 112 Distribution map of Ag cross-section experimental data after the third round of screening and recommendation. Detailed Implementation

[0064] The present invention will now be further described with reference to specific embodiments and the accompanying drawings.

[0065] The experimental data measurement is relatively abundant 27 Al(n,α) 24 Taking the Na section evaluation as an example, we start from both mathematical and physical aspects to find the "hidden variables" that affect the accuracy of data in Simpson's paradox, and effectively avoid the occurrence of PPP problems from the perspective of experimental data evaluation.

[0066] Figure 1 The flowchart of the (n,α) reaction cross section experimental data evaluation method combining statistics and physics provided in a specific embodiment of the present invention is shown. The method includes the following steps:

[0067] S1. Collect relevant information on existing (n, α) reaction cross-section experimental data. If the abundance of energy points and number of units measured in the experimental data meets the requirements of statistical processing, it is determined to be abundant experimental data.

[0068] by 27 Al(n,α) 24Taking the evaluation of the Na section as an example, the results that can be retrieved from the EXFOR database are... 27 Al(n,α) 24 The experimental data on Na reaction cross sections are abundant and diverse, spanning from 1952 to 2009, and include data from 83 institutions. Detailed information on each institution's experimental data, including the measurement date, author, institution, publication title, apparatus, detector, neutron source, neutron flux measurement method, sample preparation, measurement energy region, energy point, and uncertainty, is presented in a table. Figure 2 Give 27 Al(n,α) 24 Experimental data for the Na section, from... Figure 2 As can be seen, 7 Al(n,α) 24 The experimental data from the Na cross section exhibit significant dispersion; even statistically consistent data points show considerable differences in their central values. This distribution pattern is a general characteristic of experimental data distribution across the Na cross section.

[0069] S2. Perform mathematical classification and analysis on the experimental data according to the relevant information of the experimental data, understand the non-normal distribution pattern of the experimental data from the perspective of mathematical statistics, and thus obtain the statistical latent variables.

[0070] right 27 Al(n,α) 24 The Na cross-section data were analyzed, and the experimental data from various institutions were carefully classified and analyzed based on factors such as age, measurement method, laboratory, neutron source, and detector.

[0071] 1) Classified by era

[0072] Figure 3 The approximate distribution of experimental data by year is given. Figure 4 The distribution relationship between the measured energy points and dates is given. From these two figures, it is clear that the data exhibits a significantly non-uniform distribution by date, with the following characteristics:

[0073] a) Earlier data, with more measurement data below 10MeV and around 14MeV, have relatively large error bars, and the energy dispersion of the data is large, with poor longitudinal consistency;

[0074] b) Data from 80 years later, especially from 90 years later, began to cover the energy range of 10-14 MeV and above 14 MeV, and the energy points of the data measurements became relatively denser, the continuity improved, the error bars were smaller, and the consistency improved.

[0075] c) Experimental data below 10MeV showed good consistency.

[0076] As can be seen, the experimental data are unevenly distributed according to the measurement period and do not conform to a normal distribution. The measurement period may be the latent variable we are looking for.

[0077] 2) Classified by measurement method

[0078] All experimental data were measured using the activation method.

[0079] 3) Classified by laboratory

[0080] right 27 Al(n,α) 24 The experimental data of the Na section were plotted according to the laboratories in the Americas, Europe, and Asia, and further subdivided to the countries and even laboratories. No special distribution pattern was found in the experimental data, indicating that the laboratories are not a latent variable.

[0081] 4) Classification by neutron source

[0082] for 27 Al(n,α) 24 For the Na reaction cross section, based on the collected experimental data, the neutron sources used were almost all monoenergetic or quasi-monoenergetic neutron sources, and there was no data measured by white light sources.

[0083] 5) Classification by detector

[0084] right 27 Al(n,α) 24 The experimental data for the Na cross section were categorized and analyzed according to the detectors used in the experimental reports. Figure 5 The distribution of detectors used over time is shown, and it is clear that Ge-related detectors appear more frequently in later periods. Figure 6 The number of experimental data sources using different detection methods is given, showing that NAICR is the most prevalent. The experimental data exhibits a distinct and unusual distribution based on era and detector, deviating from a normal distribution. Measurements prior to the 1980s primarily used NaI detectors or other scintillator detectors, while measurements after the 1980s mostly employed germanium-containing detectors such as GeLi and HPGe. The detector may be a latent variable we are searching for.

[0085] S3. Based on the experimental measurement method of (n,α) reaction cross section, analyze the factors that have the greatest impact on the accuracy and precision of experimental data from a physical perspective, seek the reasons for the statistical non-normal distribution, and thus obtain the physical latent variables.

[0086] 27 Residual nuclei from the Al(n,α) reaction 24 Na has a half-life of 14.951 hours, which is very beneficial for measuring cross-sectional experimental data using the activation method.

[0087] The activation method involves irradiating the sample in a specific neutron field for a period of time, then removing and cooling it before measuring the radioactivity of the reaction product nuclei. Specifically, a detector measures the gamma-ray spectrum, processes the spectrum to obtain the characteristic gamma-ray full-energy peak counts of the activated products, and then calculates the number of product nuclei generated per unit time in the nuclear reaction according to radioactive decay laws. Simultaneously, the neutron fluence rate is measured, and the nuclear reaction cross-section is obtained using the formula N2 = N1φnσ. The activation cross-section measurement mainly measures two physical quantities: the measured full-energy peak count and the incident neutron fluence.

[0088] Detector efficiency is a major reason for the non-normal distribution of experimental data over time, and it is also the factor that has the greatest impact on the accuracy and precision of the experimental data. In addition, the experimental objective is also a significant factor; the objective refers to whether the experiment is conducted specifically for measuring the (n, α) reaction cross section. Experimental data aimed at cross section measurement are much more accurate than data from other motivations. Furthermore, factors such as the neutron source, background radiation, and data processing also affect the accuracy of the experimental data.

[0089] Table 1 and Figure 7 The intrinsic energy resolution and temporal resolution of detectors from different eras are given, revealing a significant difference in resolution between the detectors. This resolution directly affects the accuracy and precision of the measurements.

[0090] Table 1 Typical energy resolution and time resolution of commonly used detectors

[0091]

[0092] From an evaluation perspective, evaluators use the shape of the systematic curve (or the shape of the nuclear reaction mechanism curve) to roughly screen experimental data. The shape of the nuclear reaction mechanism curve refers to whether the energy distribution of the data conforms to the laws of nuclear reactions. This invention adopts this rough screening principle when necessary.

[0093] It should be noted that only a few factors with significant impact have been considered here; other factors have not yet been taken into account, and the logical rationality and rigor of the shape of the nuclear reaction mechanism curve are still not mature enough.

[0094] S4. Classify and analyze the experimental data of the physical latent variables, and evaluate the weights of different categories to obtain the experimental data evaluation results.

[0095] The latent variables we identified include: detector resolution, experimental objective, and the shape of the (n,α) cross-section phylogenetic curve (or nuclear reaction mechanism curve). Other factors, such as the neutron source, have not yet been considered. Based on the solution to Simpson's paradox, we need to classify the data and use appropriate weighting coefficients to eliminate the influence of cardinality in grouping.

[0096] From Table 1 andFigure 7 It can be seen that for germanium-containing detectors, there is an order of magnitude difference in their resolving power and counting accuracy. The data accuracy resulting from the two implicit variables—experimental objective and curve shape—cannot be quantified. We determine that experimental data with poor accuracy and precision should be assigned a weight of at least less than 1 / 20. When experimental data is abundant, a mathematical approach of discarding poorly accurate experimental data is adopted; that is, when discrepancies still exist in the experimental data, the contribution of smaller, higher-order weights is omitted during fitting.

[0097] In this embodiment, based on the detector, experimental objective, and the shape of the nuclear reaction mechanism curve, [the following is determined]: 27 Al(n,α) 24 The experimental data for the Na section were selected and recommended in three rounds.

[0098] The first round of screening and recommendations was based on detector quality. The detector types selected for the data were germanium-containing detectors such as HPGE, GE-IN, and GELI, and 28 out of 83 items were chosen. Figure 8 The experimental data after the recommended selection is presented. Figure 4 The comparison shows that the consistency of the experimental data has significantly improved after the detector level screening recommendation.

[0099] The second round of selection and recommendation was based on the experimental objective, and the experimental objective for selecting the data was: to target... 27 Al(n,α) 24 For the activation measurement of Na, 15 out of 28 items were selected without considering the results of integral experiments and other measurements. Figure 9 The experimental data after the selection and recommendation process is presented. It can be seen that the consistency of the experimental data improved further after the selection and recommendation process based on the experimental objectives.

[0100] The third round of screening and recommendation was based on the theoretical mechanism of nuclear reaction. According to the cross-sectional shape and trend calculated by the theoretical model of nuclear reaction, the experimental data with a bulging segment in the high-energy trend was removed. Figure 10 Given 27 Al(n,α) 24 Theoretical calculation curve of Na section Figure 11 The experimental data after screening and recommendation are presented. It can be seen that, after nuclear reaction theoretical calculations and screening and recommendation based on the shape of the evaluation curves, the trend of the experimental data is physically more reasonable.

[0101] The experimental data after screening and recommendation showed good consistency, and the uncertainty level was also significantly improved.

[0102] S5. Based on the evaluation results of the experimental data, a recommended activation function is obtained through a set method.

[0103] In this embodiment, based on the evaluation results of the experimental data, mathematical fitting methods, such as the least squares method, are used to fit the data to obtain... Figure 12 shown 27 Al(n,α) 24 The recommended excitation function can also be obtained using other methods, based on the excitation function curve results for the Na reaction.

[0104] Figure 13 The recommended results are compared with the international standard cross section. It can be seen that the evaluation curve is almost completely consistent with the international standard cross section below 16 MeV, while the agreement is even stronger with experimental data of higher measurement accuracy above 16 MeV.

[0105] Figure 14 This invention illustrates a flowchart of a statistical and physical method for evaluating experimental data of (n,α) reaction cross sections, as provided in a specific embodiment. The invention first surveys and collects existing experimental data, listing information such as the measurement date, author, institution, apparatus, detector, neutron source, and neutron flux measurement method for each experimental data source. It analyzes the distribution characteristics of the experimental data, determines whether the measurement method is an activation method, and then determines whether the experimental data is abundant, discrete, or discrepancies. If so, it uses detector efficiency level as the screening and recommendation criterion for the first round of screening and recommendation, analyzing the consistency of the experimental data before and after screening and recommendation. If the data consistency is good and covers the target energy region, it performs mathematical fitting to obtain the recommended excitation function; otherwise, it uses the experimental purpose as the screening and recommendation criterion for the second round of screening and recommendation, analyzing the consistency of the experimental data before and after screening and recommendation. If necessary, it uses nuclear reaction theory mechanisms as the screening and recommendation criterion for the third round of screening and recommendation, analyzing the consistency of the experimental data before and after screening and recommendation. Based on the consistency of the experimental data after screening and recommendation, it uses mathematical methods to fit the data to obtain the recommended excitation function.

[0106] The key issue of this invention lies in the evaluation and recommendation of experimental data. Here are some examples of experimental data (n, α) cross-sections before and after data screening and recommendation. It can be seen that after screening and recommendation through "latent variable" analysis, the consistency of experimental data is significantly improved.

[0107] Example 1: 51 V(n,α) 48 Sc reaction cross section

[0108] Retrieved from the EXFOR database 51 V(n,α) 48 The Sc reaction cross section is based on experimental data from 42 institutions, spanning from 1953 to 2020, with an energy range of 2.96-29.1 MeV. Figure 15The experimental data presented are abundant but also contain some discrepancies. All experimental methods used were activation methods to measure the data.

[0109] Figure 16 The results show that after the first round of detector screening and recommendation, only experimental data from 20 companies using germanium-containing detectors were selected, demonstrating a significant improvement in data consistency.

[0110] 51 V(n,α) 48 The experimental purpose of all measurements of the Sc reaction cross section was to measure this cross section, and there were no abnormal data that did not conform to the shape of the systematic curve. Therefore, we further screened and recommended detectors, selecting experimental data from 5 sources measured with high-purity germanium detectors. Figure 17 These experimental data are presented, along with a comparison of the evaluations from IRDFF-II and the US ENDF / B-VIII.0. It can be seen that after the second screening and recommendation, the consistency of the experimental data further improved, and these experimental data were also adopted in the evaluation of the standard cross-section. At this point, the energy range coverage is no longer complete, but the center values ​​are relatively accurate. Excitation function curves need to be provided in conjunction with the experimental data before the second screening and recommendation.

[0111] Example 2: 54 Cr(n,α) 51 Ti reaction cross section

[0112] Retrieved from the EXFOR database 54 Cr(n,α) 51 A total of 14 experimental data sources were collected on the Ti reaction cross section, spanning from 1967 to 2003, with an energy range of 14.0-20.24 MeV. Figure 18 All experimental data are presented. There are no experimental measurements between the threshold energy and 14 MeV, while experimental data are more abundant and show significant discrepancies above 14 MeV. All experiments were conducted using the activation method.

[0113] We first use the detector efficiency comparison 54 Cr(n,α) 51 The first round of screening and recommendation was conducted using experimental data on the Ti reaction cross-section. The energy range of the experimental data is relatively concentrated, but the data center values ​​show significant discrepancies. There are 12 experimental data sources using measurements with GE detectors; we selected data from 6 sources using HPGE detectors. Other data using SCIN, NAICR, GE-IN, etc., detectors were given less weight and temporarily disregarded. It can be seen that compared to… Figure 18 , Figure 19 The consistency of the experimental data presented has improved significantly, but there are still considerable discrepancies.

[0114] We also considered... 54 Cr(n,α)51 Experimental data on the Ti reaction cross section were used to screen and recommend experimental objectives, eliminating those not related to the intended purpose. 54 Cr(n,α) 51 Experimental data obtained for the purpose of measuring the Ti cross section were as follows: Figure 20 The experimental data from the four studies with good consistency are shown. We compared them with the evaluation data from the European Activation Library Association (EAF-2010). It can be seen that these data are also the experimental data that the EAF-2010 evaluation focuses on.

[0115] Example 3: 55 Mn(n,α) 52 V reaction cross section

[0116] Retrieved from the EXFOR database 55 Mn(n,α) 52 A total of 24 experimental data on the V reaction cross section were collected, spanning from 1953 to 2016, covering an energy range of 2.96-20.313 MeV, with the activation method being the primary experimental method. Figure 21 The experimental data presented show that the data is relatively abundant and contains significant discrepancies.

[0117] Figure 22 The experimental data from 10 institutions using germanium-containing detectors are presented. It can be seen that the consistency of the data obtained after the first round of detector-level screening and recommendation has significantly improved.

[0118] Figure 23 The figure presents experimental data from six institutions using high-purity germanium detectors, showing that the consistency of the experimental data has further improved. Data from the European activation library EAF-2010 is also provided for comparison.

[0119] The experimental data, selected through two rounds of horizontal screening by the detectors, all aimed to achieve the following objectives: 55 Mn(n,α) 52 V-reaction cross-section measurement. The recommended data still differ somewhat from international evaluation results. Further research indicates significant discrepancies among the evaluation results for this cross-section provided by several popular international databases, suggesting that the data may require further evaluation.

[0120] Example 4: 63 Cu(n,α) 60 Co reaction cross section

[0121] Retrieved from the EXFOR database 63 Cu(n,α) 60 A total of 25 experimental data on Co reaction cross sections were collected, spanning from 1960 to 2016, covering an energy range of 3.56-19.97 MeV, with the activation method being the primary experimental method. Figure 24The experimental data presented are abundant and show significant discrepancies.

[0122] Figure 25 Data from 15 experiments using germanium-containing detectors are presented. It is evident that after the first round of screening and recommendation, the consistency of experimental data in the energy ranges below 14 MeV and above 15 MeV has significantly improved and can be used to evaluate the fit. However, significant discrepancies remain in the experimental data near 14 MeV.

[0123] Figure 26 We present experimental data from four institutions using high-purity germanium detectors. After a second round of screening and recommendation, the experimental data near 14 MeV showed excellent consistency. We used the IRDFF-II evaluation data as a comparison reference, indicating that these four experimental data were also key references in the IRDFF-II evaluation.

[0124] Figure 26 The obtained experimental data plus Figure 25 Experimental data in the energy range below 14 MeV can be directly fitted to obtain the excitation function results.

[0125] Example 5: 115 In(n,α) 112 Ag reaction cross section

[0126] Retrieved from the EXFOR database 115 In(n,α) 112 A total of 14 experimental data on Ag reaction cross sections were collected, spanning from 1955 to 2020, covering an energy range of 13.36-29.1 MeV, and all experimental methods were activation methods. Figure 27 The experimental data presented show that the data does not cover the entire energy range, but is relatively abundant and concentrated around 14 MeV, although there are still some differences in the center values.

[0127] Figure 28 The experimental data from 10 companies using germanium-containing detectors are presented, showing that the issue of differences in data values ​​near 14 MeV has been improved after the first round of screening and recommendation.

[0128] Figure 29 Five experimental data points measured using a high-purity germanium detector are presented. It can be seen that after the second round of screening and recommendation, the consistency of data center values ​​near 14MeV has further improved.

[0129] Figure 30 The purpose of the experiment is to target 115 In(n,α) 112 We used data from four sources for Ag reaction cross-section measurements, and we also used the US evaluation ENDF / B-VIII.0 as a reference.

[0130] In energy regions where experimental data is unavailable, excitation function curves should be evaluated using alternative methods. Evaluation based on experimental data is helpful in determining the center value of the curve near 14 MeV.

[0131] This invention provides a statistical and physical method for evaluating experimental data on (n,α) reaction cross sections. Based on the solution to Simpson's paradox, it addresses the evaluation problem of abundant (n,α) nuclear reaction cross sections by identifying "latent variables" affecting the quality of data from activation method measurements of (n,α) nuclear reaction cross sections. The method categorizes and evaluates experimental data according to these latent variables, discusses the weights of each category, and obtains evaluation results suitable for equal-weighted fitting. Based on these results, data fitting and cross-section data recommendations are performed. This method helps clarify discrepancies in experimental data, rationally select and recommend experimental data, and determine evaluation center values ​​with high accuracy and precision. It provides a practical route for the screening, recommendation, and evaluation of experimental data on abundant (n,α) nuclear reaction cross sections measured by activation method, saving time and improving evaluation efficiency.

[0132] The above embodiments are merely illustrative examples of the present invention. The present invention may also be implemented in other specific ways or forms without departing from its spirit or essential characteristics. Therefore, the described embodiments should be considered illustrative rather than limiting in any respect. The scope of the present invention should be defined by the appended claims, and any variations equivalent to the intent and scope of the claims should also be included within the scope of the present invention.

Claims

1. A method for evaluating experimental data of (n,α) reaction cross sections that combines statistical and physical methods, comprising the following steps: S1. Collect existing experimental data on (n,α) reaction cross sections and collect relevant information about the experimental data. The relevant information about the experimental data includes the year of the experiment, author, institution, title of the literature, device, detector, neutron source, neutron flux measurement method, sample preparation, measurement energy region, energy point and uncertainty. If the abundance of energy points and number of institutions measured by the experimental data meets the requirements of statistical processing, it is determined as abundant experimental data. S2. Referring to the solution to Simpson's paradox, the experimental data is mathematically classified and analyzed according to relevant information to understand the non-normal distribution pattern of the experimental data from a mathematical statistical perspective, thereby obtaining the statistical latent variables; S3. Referring to the solution to Simpson's paradox, based on the experimental measurement method for the (n,α) reaction cross section, analyze from a physical perspective the factors that have the greatest impact on the accuracy and precision of the experimental data, seek the reasons for the statistical non-normal distribution, and thus obtain the physical latent variables. The experimental measurement method for the (n,α) reaction cross section is the activation method, that is, the sample to be tested is placed in a specific neutron field and irradiated for a set time, then taken out and cooled, and the radioactivity of the reaction product nuclei is measured. The physical latent variables that have the greatest impact on the accuracy and precision of the experimental data in the activation method include the detector resolution from the experimental perspective, the experimental purpose, and the shape of the nuclear reaction mechanism curve from the evaluation perspective. The experimental purpose refers to whether the experiment is carried out for the measurement of the (n,α) reaction cross section, and the shape of the nuclear reaction mechanism curve refers to whether the distribution of data according to energy conforms to the laws of nuclear reaction. S4. Referring to the solution to Simpson's paradox, perform physical classification analysis on the experimental data of the physical latent variables, and evaluate the weights of different categories to obtain the experimental data evaluation results. S5. Based on the evaluation results of the experimental data, a recommended activation function is obtained through a set method.

2. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to claim 1, characterized in that, In step S2, when the experimental data exhibits an unbalanced distribution and a special distribution pattern after being classified according to the relevant information, and does not conform to the normal distribution, the corresponding information is identified as a statistical latent variable by referring to the solution of Simpson's paradox.

3. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to claim 1, characterized in that, The detector's resolving power is a latent variable that conforms to the solution to Simpson's paradox, including the detector's intrinsic energy resolution and temporal resolution.

4. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to claim 1, characterized in that, In step S4, experimental data whose accuracy and precision do not meet the requirements in the classification experiment data of the physical latent variable are given a weight of less than 1 / 20. If there is still discrepancy in the experimental data, the contribution of the higher-order small data classes is omitted in the fitting process, referring to the solution of Simpson's paradox.

5. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to claim 1, characterized in that, The specific analysis steps for step S4 are as follows: Referring to the solution to Simpson's paradox, based on the detector's resolving ability, i.e. the first type of latent variable, the experimental data of the (n,α) reaction cross section are screened and recommended in the first round to obtain the distribution of the experimental data after the first round of screening and recommendation. If the experimental data has good consistency and covers the target energy region, then proceed to step S5. Otherwise, if the experimental data still meet the requirements of statistical processing, referring to the solution to Simpson's paradox, based on the experimental objective, i.e. the second type of latent variable, a second round of screening and recommendation is carried out on the (n,α) reaction cross-section experimental data after the first round of screening and recommendation to obtain the distribution of the experimental data after the second round of screening and recommendation. If the consistency of the experimental data is good and covers the target energy region, then proceed to step S5. Otherwise, if the experimental data still meet the requirements of statistical processing, referring to the solution to Simpson's paradox, based on the shape of the nuclear reaction mechanism curve, i.e. the third type of latent variable, a third round of screening and recommendation is carried out on the (n,α) reaction cross-section experimental data after the second round of screening and recommendation to obtain the distribution of the experimental data after the third round of screening and recommendation. If the consistency of the experimental data is good and covers the target energy region, then proceed to step S5.

6. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to claim 5, characterized in that, In step S5, the least squares method is used to fit the experimental data to obtain the recommended excitation function for the (n, α) reaction cross section.

7. The method for evaluating experimental data of (n,α) reaction cross sections combining statistics and physics according to any one of claims 1-6, characterized in that, If the experimental data in step S1 does not meet the requirements for statistical processing, other evaluation methods are used to evaluate the data and obtain the activation function.

Images