A(n, p) cross section evaluation method combining experimental data and nuclear reaction mechanism analysis

Abstract

The application discloses a(n, p) cross section evaluation method combining experimental data and nuclear reaction mechanism analysis, and relates to the technical field of nuclear reaction. The method comprises the following steps: S1, collecting existing experimental data and evaluation data; S2, for the energy region covered by the experimental data, using a difference weight analysis method based on Simpson's paradox to group, physically evaluate and weight analyze the experimental data, and giving an evaluation result of the experimental data; S3, for the energy region not covered by the experimental data, using the physical conditions of the (n, p) reaction nuclear reaction mechanism to constrain and supplement the data evaluation, and obtaining the excitation function curve range conforming to the nuclear reaction mechanism; S4, respectively processing the energy regions covered and not covered by the experimental data, reasonably connecting the excitation function curves, comparing and analyzing the evaluation data, and determining the excitation function data center value and the evaluation uncertainty. The method provided by the application can improve the accuracy of data, clarify data differences, and realize accurate and rapid evaluation of the (n, p) reaction cross section.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reaction technology, specifically relating to a (n,p) cross-sectional evaluation method that combines experimental data and nuclear reaction mechanism analysis. Background Technology

[0002] The (n,p) reaction cross section refers to the probability that a neutron will produce a neutron and a proton after colliding with an atomic nucleus. It is an important charged particle emission data in neutron data and is an important parameter that affects the selection of nuclear materials, reaction rate and energy release. Its data quality is very important for nuclear reactor design, neutron detection and protection, nuclear astrophysics research, nuclear medicine development and nuclear energy generation.

[0003] A survey of the EXFOR (Experimental Nuclear Reaction Data) database and other data sources reveals varying degrees of discrepancy in experimental data on the (n,p) reaction cross sections of multiple nuclides. For the same nuclide, (n,p) reaction cross section measurements, aside from the central value, differ across data sources in terms of age, apparatus, neutron source, detector, sample quantification, data correction and processing, uncertainty level, and other aspects. Even among mainstream international databases, such as the US ENDF / B-VIII.0 database, the Japanese JENDL-5.0 database, the European JEFF-3.3 database, TENDL-2021, and the Chinese CENDL-3.2 database, as well as proprietary international databases such as the reactor dose database IRDFF-II and the European activation database EAF-2010, some differences exist in the evaluation data. For nuclides and energy regions with abundant experimental data, if the experimental data exhibits significant dispersion, the evaluation data will generally also show some discrepancies. For nuclides and energy regions lacking experimental data, the evaluation data may show differences in peak positions and data trends. Such data discrepancies pose significant challenges to data applications, necessitating data evaluation efforts to resolve these disagreements and recommend more accurate and reliable evaluation data.

[0004] Research on the evaluation method of (n,p) reaction cross section data is of great significance for clarifying data discrepancies, improving the accuracy and reliability of (n,p) cross section evaluation data, calculating related complete neutron data theoretical models, and researching other cross section evaluation methods.

[0005] The use of Simpson's paradox as a solution for evaluating divergent experimental data has made some progress, effectively avoiding the PPP problem and improving the accuracy and efficiency of data evaluation.

[0006] The solution to Simpson's paradox is primarily for situations involving large and discrete datasets. Sometimes, evaluations encounter situations where experimental data frequently fails to cover the entire target energy range. For energy ranges with missing data, or where the accuracy of the experimental data is poor, the difficulty of correction and the resulting uncertainty are significant. This necessitates supplementing the evaluation with other methods. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention aims to provide a method for evaluating (n,p) cross sections by combining experimental data and nuclear reaction mechanisms. This method can improve the accuracy of data, clarify data discrepancies, and achieve accurate and rapid evaluation of (n,p) reaction cross sections.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for evaluating (n,p) cross-sections by combining experimental data and nuclear reaction mechanisms includes the following steps:

[0010] S1. Collect existing experimental and evaluation data;

[0011] S2. For the energy range covered by the experimental data, the difference weighting method based on Simpson's paradox is used to group, physically evaluate and weight the experimental data, and give the evaluation results of the experimental data.

[0012] S3. For energy regions not covered by experimental data, the physical conditions of the (n,p) reaction nuclear reaction mechanism are used to constrain and supplement the data evaluation, so as to obtain the range of excitation function curves that conform to the nuclear reaction mechanism.

[0013] S4. Process the covered and uncovered energy regions of the experimental data separately to obtain the excitation function curves, and compare and analyze them with the evaluation data to determine the data center value of the excitation function and the evaluation uncertainty.

[0014] Furthermore, in the (n,p) cross-section evaluation method that combines experimental data and nuclear reaction mechanisms as described above, the influencing factors considered in step S2 for the energy region covered by the experimental data include: experimental purpose, experimental method, neutron source, neutron flux determination method, detector resolution level, standard cross-section selection, and other implicit variables.

[0015] Furthermore, in the (n,p) cross-sectional evaluation method combining experimental data and nuclear reaction mechanisms as described above, in step S2: when using the difference-weighted analysis method based on Simpson's paradox to group, physically evaluate, and weight the experimental data, the data given larger weights include:

[0016] Experimental data with the target reaction cross section as the experimental objective; cross-sectional data measured using the activation method for (n, p); experimental data obtained by measuring the energy region using a neutron source with good monochromaticity; experimental data using coincidence measurement and adjoint particle method for calibrated neutron flux; experimental data using detectors with high resolution; measurement data with more reasonable monitoring cross sections; experimental data with good sample quantification; data with comprehensive and complete consideration of data correction; and data with thorough uncertainty consideration and detailed analysis.

[0017] Furthermore, in the (n,p) cross-section evaluation method based on the experimental data and nuclear reaction mechanism analysis described above, in step S2: the monitoring cross-section and the cross-section to be tested should satisfy the following relationships as much as possible: ① similar threshold energies; ② similar cross-section sizes; ③ the monitoring cross-section is relatively smooth in the test area; ④ the trend of the monitoring cross-section is consistent with that of the cross-section to be tested, and they do not form orthogonality; ⑤ the monitoring cross-section has been internationally standardized, and the first and second level standard cross-sections are more reliable.

[0018] Furthermore, in the (n,p) cross-section evaluation method that combines experimental data and nuclear reaction mechanisms as described above, step S2 includes sample preparation factors such as sample purity, sample abundance, geometry, sample properties, and other factors.

[0019] Furthermore, in the (n,p) cross-section evaluation method that combines experimental data and nuclear reaction mechanisms as described above, step S2 involves: standard cross-section correction for experimental data with relatively large weights, and no data correction is required for data with small weights, especially divergent data.

[0020] Furthermore, in the (n,p) cross-section evaluation method described above, which combines experimental data and nuclear reaction mechanisms for analysis, step S3 specifically includes the following for energy regions not covered by experimental data:

[0021] The shape of the excitation function curve is estimated and evaluated based on the curve shape obtained from the theoretical calculation.

[0022] The threshold energy of the (n,p) cross section is rigorously calculated based on the atomic nucleus mass and binding energy.

[0023] Calculate the position of the highest energy point of the excitation function curve based on the influence of particle emission competition;

[0024] Excitation function curves of reference and neighboring nuclei of the nucleus to be evaluated.

[0025] Furthermore, based on the experimental data and nuclear reaction mechanism analysis described above, the (n,p) cross-section evaluation method, considering the influence of particle emission competition, calculates the specific location of the highest point energy point on the excitation function curve as follows:

[0026] The energy condition for a secondary particle to emit a neutron is:

[0027]

[0028] In equation (1), E is the energy of the center-of-mass frame of the incident particle, and Q... n,np Let Q be the reaction Q value (n, np), Δ be the reaction correction parameter, and E1 and E2 be the center-of-mass energies of the first and second ejected particles, respectively.

[0029] Since E1 is greater than the Coulomb barrier of p, the energy corresponding to the peak value of the reaction cross section at (n,p) is:

[0030]

[0031] In equation (2), B represents the energy of the center-of-mass system corresponding to the peak value of the reaction cross section. Cp This represents the Coulomb barrier of the proton; the corresponding laboratory frame energy is:

[0032]

[0033] In equation (3), m is the laboratory system energy corresponding to the peak value of the reaction cross section. a and M A These correspond to the mass of the incident particle and the mass of the target nucleus, respectively.

[0034] Furthermore, in the (n,p) cross-section evaluation method based on the combined analysis of experimental data and nuclear reaction mechanisms as described above, step S4 specifically involves processing the covered and uncovered energy regions of the experimental data as follows:

[0035] For the energy range covered by the experimental data, the least squares method was used to fit the data to all evaluated experimental data.

[0036] For energy regions not covered by experimental data or not considered reliable, the nuclear reaction mechanism evaluation method is used.

[0037] By properly connecting the data results, the excitation function curve is obtained.

[0038] Furthermore, in the (n,p) cross-section evaluation method described above, which combines experimental data and nuclear reaction mechanisms for analysis, step S4 involves comparing and analyzing the data with the evaluation data to determine the data center value of the excitation function and the evaluation uncertainty. Specifically:

[0039] The experimental data and evaluation data are plotted and compared to analyze the discrepancies between the existing experimental data and evaluation data, and the rationality of the recommended data is discussed.

[0040] The data that has been mathematically processed and physically evaluated reasonably is used as the data center value for the evaluation excitation function;

[0041] Based on the measurement uncertainty and data dispersion of the experimental data, and combined with the analysis of nuclear reactions, the evaluation uncertainty is given.

[0042] Compared with existing technologies, the (n,p) cross-section evaluation method provided by this invention, which combines experimental data and nuclear reaction mechanism analysis, has the following beneficial effects:

[0043] 1. This invention provides a tree-structured evaluation method for (n,p) reaction cross sections, combining experimental data analysis and nuclear reaction mechanism calculation. For energy regions covered by experimental data, a mathematical statistical method based on the solution of Simpson's paradox is used to analyze the implicit variables affecting the accuracy of experimental data from the perspective of the measured physical conditions, and to evaluate the experimental data. For energy regions without experimental data or with large experimental data uncertainty, the physical conditions of (n,p) reaction nuclear reaction mechanisms are used to constrain and supplement the data evaluation, realize the evaluation of excitation function curves and uncertainties, further improve the accuracy of cross-sectional data, clarify cross-sectional data discrepancies, and achieve accurate and rapid evaluation of (n,p) reaction cross sections.

[0044] 2. This invention standardizes the evaluation process, saves evaluation time, and improves evaluation efficiency;

[0045] 3. This invention can provide a methodological reference for the evaluation of other cross sections. Attached Figure Description

[0046] Figure 1 A flowchart of an (n,p) cross-sectional evaluation method for combining experimental data and nuclear reaction mechanism analysis provided in an embodiment of the present invention;

[0047] Figure 2 Experimental and evaluation data for the 14-Si-29(n,p) cross section;

[0048] Figure 3 Experimental and evaluation data for the 16-S-34(n,p) cross section;

[0049] Figure 4 Experimental and evaluation data for the 17-Cl-37(n,p) cross section;

[0050] Figure 5 Experimental and evaluation data for the 22-Ti-48(n,p) cross section;

[0051] Figure 6 Experimental and evaluation data for the 39-Y-89(n,p) cross section;

[0052] Figure 7 Experimental and evaluation data for the 42-Mo-92(n,p) cross section;

[0053] Figure 8Experimental and evaluation data for the 54-Xe-124(n,p) cross section. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0055] Figure 1 This invention provides a flowchart of a (n,p) cross-sectional evaluation method that combines experimental data and nuclear reaction mechanism analysis, comprising the following steps:

[0056] S1. Data Collection: Collect existing experimental data and evaluation data, and organize relevant charts.

[0057] S2. Experimental Data Analysis and Evaluation

[0058] Based on the experimental objectives, methods, neutron source, neutron flux determination method, detector resolution, standard cross-section selection, and other latent variables, a difference-weighted analysis method based on Simpson's paradox was used to group, physically evaluate, and perform weighted analysis of the experimental data, providing evaluation results. The weighting factors can be adjusted according to actual circumstances, with the principle of eliminating data discrepancies caused by grouping.

[0059] The specific evaluation methods for each influencing factor are as follows:

[0060] 2.1 Evaluation of Experimental Objectives

[0061] Based on the experimental objectives given in the experimental data information list, the experimental data from each institution are weighted and evaluated, with experimental data that take the target reaction cross section as the experimental objective being given a higher weight.

[0062] 2.2 Evaluation of Experimental Methods

[0063] The vast majority of experimental methods for measuring (n,p) reactions employ the activation method, with a very small number of data obtained using other methods. Cross-sectional data from (n,p) measurements obtained using the activation method are given significant weight in the evaluation.

[0064] 2.3 Neutron Source Evaluation

[0065] Activation methods for measuring (n,p) reactions generally utilize monoenergetic or quasi-monoenergetic neutron sources. The monochromaticity of a neutron source is a crucial indicator of neutron mass. Each monoenergetic neutron source exhibits a relatively good range of neutron monochromaticity. For experimental measurements near 14 MeV, the DT neutron source offers the best monochromaticity; for measurements near 2.5 MeV, the DD neutron source offers the best monochromaticity. Other neutron sources exhibit poorer monochromaticity than DD and DT sources; for example, the P-LI7 neutron source has good monochromaticity in the approximately 0.4–1 MeV range, but is inferior to the DD neutron source. Experimental data obtained using neutron sources with good monochromaticity should be given greater weight in the energy range measured.

[0066] 2.4 Evaluation of Neutron Flux Determination Methods

[0067] For monoenergetic neutron sources, there are a series of methods for determining neutron flux. Generally speaking, for monochromatic neutron sources, the most accurate method for determining neutron flux is the COIN method (coincidence measurement method), followed by the ASSOP method (adjoint particle method). Experimental data from these two methods for determining neutron flux are given greater weight.

[0068] 2.5 Evaluation of Detector Resolution

[0069] The resolution levels of different detectors vary greatly, and the resolution level directly affects the accuracy and precision of the measurement. The HPGe detector has the best resolution level, followed by other Ge-containing detectors, which are given greater weight in the evaluation.

[0070] 2.6 Evaluation of Monitoring Section Selection

[0071] In experimental measurements, the selection of the monitoring section is also a crucial factor affecting the accuracy of the measurements. Generally, the monitoring section and the section to be measured should, as far as possible, satisfy the following relationships: ① similar threshold energies; ② similar section sizes; ③ the monitoring section is relatively smooth in the measurement area; ④ the monitoring section's trend is consistent with the section to be measured, and they do not form orthogonals; ⑤ the monitoring section has been internationally standardized, and first- or second-order standard sections are more reliable. During data evaluation, the above relationships can be used as a reference to ensure the reasonableness of the selected monitoring section, and measurement data from more reasonably selected monitoring sections should be given greater weight.

[0072] 2.7 Quantitative Evaluation of Samples

[0073] Sample purity, abundance, geometry, properties, and other factors can all affect measurement accuracy. In the evaluation, sample preparation factors need to be considered, and experimental data with better sample quantification should be given greater weight.

[0074] 2.8 Data Correction Evaluation

[0075] Evaluators need to pay attention to the experimenter's corrections to the data, and data with more comprehensive and complete corrections should be given greater weight.

[0076] 2.9 Uncertainty Evaluation

[0077] The experimenter's analysis of data uncertainty is also a factor in assessing the quality of experimental data. Data with well-considered and detailed uncertainty analysis should be given greater weight in the evaluation.

[0078] 2.10 Evaluation of other factors

[0079] Decay data, data post-processing, and other factors should also be included in the evaluation.

[0080] Based on the above factors, and according to the solution to Simpson's paradox, the experimental data were grouped and weighted to obtain the evaluation results of the experimental data.

[0081] In this method, standard cross-section correction is performed on experimental data with relatively large weights. For data with small weights, especially divergent data, this data correction step can be omitted because its contribution to data processing and recommendation is small and can be ignored.

[0082] S3, Analysis and Evaluation of Nuclear Reaction Mechanism

[0083] The influencing factors related to the nuclear reaction mechanism are calculated, evaluated, and physically analyzed to obtain the range of excitation function curves consistent with the nuclear reaction mechanism. The energy uncertainties corresponding to the starting point and peak of the excitation function curves are relatively small. Supplementary data constraints are then implemented based on experimental data evaluation. The specific calculation and evaluation of the influencing factors related to the nuclear reaction mechanism includes:

[0084] 3.1 Theoretical calculation of curve shape

[0085] The most commonly used theoretical systems for nuclear reaction calculations mainly include optical models, equilibrium and pre-equilibrium reaction mechanisms. Internationally, there is a lot of experience in calculating (n,p) cross sections, and the shape of the excitation function curve can be estimated and evaluated based on the curve shape obtained from theoretical calculations.

[0086] 3.2 Calculate the threshold energy of the (n,p) section.

[0087] The threshold energy of the (n,p) cross section is rigorously calculated based on the atomic nucleus mass and binding energy. The threshold energy is the starting point of the excitation function curve.

[0088] 3.3 Calculation of the influence of Coulomb potential

[0089] Near the threshold, the cross-section is small, resulting in lower accuracy and greater uncertainty in experimental data measurement, and experimental data is also scarce. For the exit cross-section of charged particles, due to the influence of the Coulomb potential, the energy point at which the actual cross-section begins to rise rapidly is not the theoretically calculated threshold, but rather a region of energy above the threshold. The same problem exists for the no-threshold case, where the probability of barrier penetration is very small. The influence of the Coulomb potential can be obtained through theoretical calculations, providing better data support and constraints for evaluating near-threshold or no-threshold (n,p) reaction cross-sections, supplementing the lack of or inaccurate experimental data.

[0090] 3.4 Calculate the impact of particle emission competition

[0091] Due to the competition mechanism of nuclear reactions, competition arises between different cross sections. The later-opened reaction channel affects the earlier-opened cross section, and secondary particle emission has a significant impact. After a channel with a higher threshold energy opens and shows an upward trend, the curve of the previously competed cross section (i.e., the one with the lower threshold energy) will show a downward trend. The position of the highest point energy of the excitation function curve can be analyzed and calculated from this, providing excellent data support and constraints for the excitation function curve. It offers data evaluation references for situations where experimental measurements are lacking, highly divergent, or the trend is unclear, effectively reducing the uncertainty of recommended data.

[0092] The energy condition for a secondary particle to emit a neutron is:

[0093]

[0094] In equation (1), E is the energy of the center-of-mass frame of the incident particle, and Q... n,np Let Q be the reaction Q value (n, np), Δ be the reaction correction parameter, and E1 and E2 be the center-of-mass energies of the first and second ejected particles, respectively.

[0095] Since E1 is greater than the Coulomb barrier of p, the energy corresponding to the peak value of the reaction cross section at (n,p) is:

[0096]

[0097] In equation (2), B represents the energy of the center-of-mass system corresponding to the peak value of the reaction cross section. Cp This represents the Coulomb barrier of the proton. The corresponding laboratory frame energy is:

[0098]

[0099] In equation (3), m is the laboratory system energy corresponding to the peak value of the reaction cross section. a and M A These correspond to the mass of the incident particle and the mass of the target nucleus, respectively.

[0100] 3.5. Refer to the excitation function curve of the nearest nucleus

[0101] The excitation function curves of nuclei adjacent to the nucleus to be evaluated have reference and constraint value for the excitation function to be evaluated.

[0102] By calculating and evaluating the above factors and conducting physical analysis, the range of the excitation function curve that conforms to the nuclear reaction mechanism can be obtained. The energy uncertainty of the starting point and peak point of the curve is relatively small. Data supplementation and constraints are then carried out based on the evaluation of experimental data.

[0103] S4. Process experimental data and recommend data.

[0104] Specifically, the following steps are included:

[0105] S41, Data Processing

[0106] The energy regions covered and uncovered by the experimental data were processed separately. Least squares was used to mathematically process all evaluated experimental data, with spline fitting programs such as SPCC and other data processing programs available for fitting. For energy regions not covered or unreliable by the experimental data, nuclear reaction mechanisms were used for evaluation. The data results were then reasonably connected to obtain the excitation function curves.

[0107] S42. Comparison Analysis

[0108] Compare and plot the experimental and evaluation data. Analyze the discrepancies between the existing experimental and evaluation data, and discuss the rationality of the recommended data. Repeated evaluation and comparative discussions may be necessary.

[0109] S43, Data Recommendation

[0110] The data that has been mathematically processed and physically evaluated reasonably is used as the data center value for the evaluation excitation function;

[0111] Based on the measurement uncertainty and data dispersion of the experimental data, and combined with the analysis of nuclear reactions, the evaluation uncertainty is given.

[0112] Example 1: 14-Si-29(n,p) cross section

[0113] A total of 21 experimental data points and 77 energy points were retrieved for the 14-Si-29(n,p) cross section. Due to space limitations, Table 1 provides partial information from the experimental measurements. In specific work, all experimental data mentioned in the technical solution should be listed, and the same applies below.

[0114] Table 1. Experimental data list for 14-Si-29(n,p) cross-section

[0115]

[0116]

[0117] Figure 2 The paper presents a comparison of existing experimental data and evaluation data. The experimental data covers the entire energy range but exhibits some structure, with significant discrepancies in measurements near 14 MeV. Based on factors such as experimental setup, neutron source, detector level, and standard cross-section selection, the paper strongly recommends [specific methods / initiatives]. Figure 2 The experimental data are displayed in 1.3x increments and labeled with the authors and dates. Based on the key recommended experimental data and nuclear reaction mechanism analysis, the evaluation results of the excitation function (thick black line) in the figure are obtained. The uncertainty is estimated based on the dispersion and uncertainty of the experimental data.

[0118] Example 2 16-S-34(n,p) cross section

[0119] A total of 7 experimental data points were retrieved from the 16-S-34(n,p) cross section, covering 17 energy points. Table 2 provides some information on the experimental measurements.

[0120] Table 2. Experimental data list for the 16-S-34(n,p) cross section.

[0121] YEAR AUTHOR SOURCE METHOD DETECTOR ENERGY POINTS 2001 [[ID=..]]Y.Kasugai D-T ACTIV HPGE 13.36～14.94 6 1985 J.P.Gupta D-T ACTIV SCIN,PROPC 14.8 1 1980 P.N.Ngoc D-T ACTIV,MOMIX GELI 14.6 1 1970 W.Schantl D-T ACTIV GELI,GEMUC,SCIN 14.7 1 1966 M.Bormann D-T ACTIV NAICR 14.～16.65 6 1966 R.Prasad D-T ACTIV ,SCIN 14.8 1 1953 E.B.Paul D-T ACTIV - 14.5 1

[0122] Figure 3 The paper presents a comparison of existing experimental and evaluation data plots. The experimental data are concentrated around 14 MeV, with no reference data available for the 4-12 MeV range. Based on factors such as experimental setup, neutron source, detector level, and standard cross-section selection, this work provides a key recommendation. Figure 3 Experimental data with 1.3x larger icons and annotations of authors and years are presented. Based on the key recommended experimental data and nuclear reaction mechanism analysis, the following calculations are obtained: Figure 3 The evaluation results of the excitation function (thick black solid line) are given, and the evaluation uncertainty is given based on the experimental conditions, the degree of data dispersion, and the evaluation process.

[0123] Example 3 17-Cl-37(n,p) cross section

[0124] A total of 17 experimental data points and 43 energy points were retrieved from the 17-Cl-37(n,p) cross section. Table 3 provides some information on the experimental measurements.

[0125] List of experimental data for the 74-W-186(n,p)73-Ta-186 cross section near 14 MeV

[0126] YEAR AUTHOR SOURCE METHOD [[ID=..]]DETECTOR ENERGY POINTS 2000 [[ID=..]]A.Fessler D-T ACTIV,TOF,GSPEC HPGE,SCIN,STANK 16.124～20.45 5 1998 Y.Kasugai D-T ACTIV HPGE 13.4～14.87 6 1992 M.Belgaid D-T ACTIV HPGE 14.73 1 1985 J.P.Gupta D-T ACTIV SCIN,PROPC 14.8 1 1980 P.N.Ngoc D-T ACTIV,MOMIX GELI 14.6 1 1978 M.Hyvoenen-Dabek D-T ACTIV GELI 14.7 1 1971 R.Prasad D-T ACTIV ,NAICR 14.8 1 1970 W.Schantl D-T ACTIV GELI,GEMUC,SCIN 14.7 1 1967 A.Pasquarelli D-T ACTIV GEMUC,SOLST 14.7 1 1967 B.Mitra D-T ACTIV PROPC,NAICR,SCIN 14.1～14.8 2 1966 S.C.Mathur D-T ACTIV TELES,NAICR 13.1～22. 12 1965 C.S.Khurana D-T ACTIV GEMUC,SCIN 14.8 1 1960 G.S.Mani - ACTIV NAICR 17.5 1 1959 C.S.Khurana D-T ACTIV ,GEMUC 14 1 1958 R.S.Scalan - ACTIV - 14.8 1 1956 A.V.Cohen D-T ACTIV GEMUC,PROPC 13.1～16.1 6 1953 E.B.Paul D-T ACTIV - 14.5 1

[0127] Figure 4The paper presents a comparison of existing experimental data and evaluation data. While the experimental data is relatively abundant, no reference data is available for the 4-12 MeV range. Significant discrepancies exist in the experimental data near 14 MeV. Based on factors such as experimental setup, neutron source, detector level, and standard cross-section selection, the experimental data represented by the 1.3x scale icon in the figure, along with the authors and dates, are highly recommended. Even after evaluation, some discrepancies remain in the experimental data. Based on the recommended experimental data and nuclear reaction mechanism analysis, the following results are obtained: Figure 4 The evaluation results of the excitation function (thick black solid line) are given, and the evaluation uncertainty is given based on the experimental conditions, the degree of data dispersion, and the evaluation process.

[0128] Example 4: 22-Ti-48(n,p) cross section

[0129] A total of 49 experimental data points and 176 energy points were retrieved from the 22-Ti-48(n,p) cross section. Table 4 provides some information on the experimental measurements.

[0130] Table 3. Experimental data list for 22-Ti-48(n,p) cross-section

[0131]

[0132]

[0133] Figure 5 The paper presents a comparison of existing experimental data and evaluation data. The experimental data is relatively abundant, covering the entire energy range, and the data consistency is relatively good, but the distribution is also somewhat wide. This work considers factors such as the monoenergeticity of the neutron source, the resolving power of the detector used in the experiment, the selection of the standard cross section, and the stability of the beam generated by the device. The experimental data marked with the 1.3x icon in the figure and labeled with the author and year are highly recommended. The Lu Han-Lin (1989) experiment used the NAICR detector with poor resolving power, but according to our laboratory's understanding, methods such as COIN are generally used to determine the neutron flux, so it is also highly recommended. Based on the experimental data highly recommended and the analysis and calculation of the nuclear reaction mechanism, the evaluation results of the excitation function of the thick black solid line are obtained, and the uncertainty of the recommended data is obtained based on the uncertainty of the experimental measurement and the evaluation process.

[0134] Example 5 39-Y-89(n,p) cross section

[0135] A total of 7 experimental data points were retrieved from the 39-Y-89(n,p) cross section, covering 42 energy points. Table 5 provides some information on the experimental measurements.

[0136] Table 4. List of experimental data for the 39-Y-89(n,p) cross section

[0137] YEAR AUTHOR SOURCE METHOD DETECTOR ENERGY POINTS 2016 Luo Junhua D-T ACTIV HPGE,SIBAR 13.5～14.8 3 1998 N.I.Molla D-T ACTIV,RCHEM - 14.41～14.71 3 1997 R.M.Klopries D-D,D-T ACTIV,BGCT GELI,HPGE 7.81～14.67 11 1969 V.N.Levkovskii - ACTIV,CHSEP - 14.8 1 1967 J.Csikai D-T ACTIV GEMUC,LONGC 14.7 1 1961 B.P.Bayhurst - ACTIV - 7.～19.76 18 1960 H.A.Tewes D-D ACTIV TELES 9.35～14. 5

[0138] Figure 6 The paper presents a comparison of existing experimental data and evaluation data. There is a large amount of experimental data, with significant dispersion in the 8-15 MeV energy range. Two measurement data sources utilize the DD neutron source. Based on factors such as experimental setup and detector resolution, this work primarily recommends RMKlopries (1997) data near 8 MeV. Four measurement data sources utilize the DT neutron source. Based on factors such as experimental setup, neutron source, detector level, and standard cross-section selection, this work primarily recommends Luo Junhua (2016) measurements near 14 MeV, with NIMolla (1998) measurements as a secondary recommendation. Experimental information for BP Baihurst (1961) data is unavailable. Due to its wide energy range (7–19.76 MeV), it is used as an evaluation reference in the absence of other experimental data. The excitation function is derived based on the recommended experimental data, the calculated Coulomb potential, and the influence of secondary particle emission mechanisms, among other factors. Figure 6 As shown by the thick black solid line, the uncertainty is estimated based on the dispersion of the experimental data, the measurement uncertainty, and the evaluation process.

[0139] Example 6: 42-Mo-92(n,p) cross section

[0140] Two experimental data points were retrieved for the 42-Mo-92(n,p) cross section, with two energy points. Table 6 provides some information from the experimental measurements.

[0141] Table 5. Experimental data list for 42-Mo-92 (n,p) cross-section

[0142] YEAR AUTHOR SOURCE METHOD DETECTOR ENERGY POINTS 1966 A.Fabry REAC ACTIV NAICR 1 1 1964 JW Boldeman REAC ACTIV NAICR 1 1

[0143] Figure 7 This paper presents a comparison of existing experimental and evaluation data for the 42-Mo-92(n,p) cross section. The collected experimental data are FIS high-energy fission cross section data, using a reactor neutron source, with all measured energies at 1 MeV. Therefore, the data has limited reference value for evaluating the 42-Mo-92(n,p) cross section. The excitation function is determined based on factors such as the influence of the theoretically calculated Coulomb potential and the secondary particle emission mechanism, and with reference to other evaluation results. Figure 7 As shown by the thick black solid line, the uncertainty is assessed at 20%, and the uncertainty of the Coulomb potential range is considered to be relatively small, with an evaluation of 10-15%.

[0144] Example 7 54-Xe-124(n,p) cross section

[0145] One experimental data point was retrieved from the 54-Xe-124(n,p) cross section. Table 7 provides some information about the experimental measurements.

[0146] Table 6. List of experimental data for the 54-Xe-124(n,p) cross section.

[0147] YEAR AUTHOR SOURCE METHOD DETECTOR ENERGY POINTS 1985 JHZaidi - ACTIV,CHSEP GELI,GE-IN 1.5 1

[0148] Figure 8 The paper presents a comparison of existing experimental and evaluation data plots. For the 54-Xe-124(n,p) cross section, there is only one experimental data measurement point with an energy of 1.5 MeV, which is FIS high-energy fission cross section data. The neutron source used is a reactor neutron source, resulting in significant data uncertainty and limited reference value for cross section evaluation. The excitation function in this work is based on factors such as the nuclear reaction mechanism, the influence of theoretically calculated Coulomb potential, and the influence of secondary particle emission mechanisms. Figure 8 As shown by the thick black solid line in the middle, and based on other evaluation results, the uncertainty is estimated to be 10-20%, and the uncertainty in the energy range affected by the Coulomb potential is considered to be relatively small.

[0149] This invention provides a method for evaluating (n,p) cross-sections by combining experimental data and nuclear reaction mechanism analysis. It employs a tree-structured evaluation approach that integrates experimental data analysis and nuclear reaction mechanism calculations. For energy regions covered by experimental data, a mathematical statistical method based on the solution of Simpson's paradox is used to analyze the latent variables affecting the accuracy of experimental data from the perspective of the measured physical conditions, thus evaluating the experimental data. For energy regions without experimental data or with high uncertainty, the physical conditions of (n,p) reaction nuclear reaction mechanisms are used to constrain and supplement the data evaluation, thereby enabling the evaluation of excitation function curves and uncertainties. This improves the accuracy of cross-section data, clarifies discrepancies in cross-section data, and achieves accurate and rapid evaluation of (n,p) reaction cross-sections. This invention standardizes the evaluation process, saves evaluation time, improves evaluation efficiency, and can provide a methodological reference for the evaluation of other cross-sections.

[0150] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention is also intended to include these modifications and variations.

Claims

1. A method for evaluating (n,p) cross-sections by combining experimental data and nuclear reaction mechanisms, comprising the following steps: S1. Collect existing experimental and evaluation data; S2. For the energy range covered by the experimental data, the difference weighting method based on Simpson's paradox is used to group, physically evaluate and weight the experimental data, and give the evaluation results of the experimental data. S3. For energy regions not covered by experimental data, the physical conditions of the (n,p) reaction nuclear reaction mechanism are used to constrain and supplement the data evaluation, so as to obtain the range of excitation function curves that conform to the nuclear reaction mechanism. S4. Process the covered and uncovered energy regions of the experimental data separately, and reasonably connect them to obtain the excitation function curve. Compare and analyze the curve with the evaluation data, and determine the data center value of the excitation function and the evaluation uncertainty. In step S2, the influencing factors considered when evaluating the energy region covered by the experimental data include: experimental purpose, experimental method, neutron source, neutron flux determination method, detector resolution level, standard cross section selection, and other implicit variables. When using the differential weighting analysis method based on Simpson's paradox to group, physically evaluate, and weight experimental data, data with higher weights include: experimental data with the target reaction cross section as the experimental objective; cross-sectional data measured using the activation method (n, p); experimental data obtained using a neutron source with good monochromaticity to measure the energy range; experimental data using coincidence measurement and adjoint particle calibrated neutron flux; experimental data using detectors with high resolution; measurement data with more reasonable monitoring cross sections; experimental data with good sample quantification; data with comprehensive and complete data correction considerations; and data with thorough uncertainty considerations and detailed analysis. Standard cross-section correction is performed on experimental data with relatively large weights, while no data correction is required for data with small weights. Step S3, for the energy regions not covered by experimental data, specifically includes the following analysis and evaluation methods: The shape of the excitation function curve is estimated and evaluated based on the curve shape obtained from the theoretical calculation. The threshold energy of the (n,p) cross section is rigorously calculated based on the atomic nucleus mass and binding energy. Calculate the position of the highest energy point of the excitation function curve based on the influence of particle emission competition; Excitation function curves of reference and neighboring nuclei to be evaluated; The calculation of the highest energy point position of the excitation function curve based on the influence of particle emission competition is specifically as follows: The energy condition for a secondary particle to emit a neutron is: （1） In equation (1), E is the energy of the center-of-mass frame of the incident particle. Let Q be the reaction value for (n, np). E1 and E2 are the center-of-mass energies of the first and second ejected particles, respectively, and are the correction parameters for the reaction. Since E1 is greater than the Coulomb barrier of p, the energy corresponding to the peak value of the reaction cross section at (n,p) is: （2） In equation (2), B represents the energy of the center-of-mass system corresponding to the peak value of the reaction cross section. Cp This represents the Coulomb barrier of the proton; the corresponding laboratory frame energy is: （3） In equation (3), This represents the laboratory system energy corresponding to the peak value of the reaction cross section. and These correspond to the mass of the incident particle and the mass of the target nucleus, respectively.

2. The (n,p) cross-section evaluation method based on the combined analysis of experimental data and nuclear reaction mechanisms according to claim 1, characterized in that, In step S2: The monitoring section and the section to be measured should meet one or more of the following relationships: ① similar threshold energy; ② similar section size; ③ the monitoring section is relatively smooth in the area to be measured; ④ the trend of the monitoring section is consistent with that of the section to be measured and they do not form orthogonality; ⑤ the monitoring section has been internationally standardized and the first and second level standard sections are more reliable.

3. The (n,p) cross-section evaluation method based on the combined analysis of experimental data and nuclear reaction mechanisms according to claim 2, characterized in that, In step S2: Sample preparation factors include sample purity, sample abundance, geometry, sample properties and other factors.

4. The (n,p) cross-section evaluation method based on the combined analysis of experimental data and nuclear reaction mechanisms according to claim 3, characterized in that, In step S4: the energy regions covered and uncovered by the experimental data are processed separately as follows: For the energy range covered by the experimental data, the least squares method was used to fit the data to all evaluated experimental data. For energy regions not covered by experimental data or not considered reliable, the nuclear reaction mechanism evaluation method is used. By properly connecting the data results, the excitation function curve is obtained.

5. The (n,p) cross-section evaluation method based on the combined analysis of experimental data and nuclear reaction mechanisms according to claim 4, characterized in that, In step S4: A comparative analysis is performed with the evaluation data to determine the data center value of the activation function and the evaluation uncertainty, specifically: The experimental data and evaluation data are plotted and compared to analyze the discrepancies between the existing experimental data and evaluation data, and the rationality of the recommended data is discussed. The data that has been mathematically processed and physically evaluated reasonably is used as the data center value for the evaluation excitation function; Based on the measurement uncertainty and data dispersion of the experimental data, and combined with the analysis of nuclear reactions, the evaluation uncertainty is given.

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