Method for making slow-light-emitting sub-ACE format database

Abstract

The invention discloses a method for making a slow luminescence sub-ACE format database. The method comprises the following steps: firstly, calculating a slow luminescence sub-generation section based on a fission yield sub-library and a decay sub-library of an evaluation kernel database; the decay photon energy spectrum is processed into an equal probability energy bond form, so that slow-emission photon energy distribution can be obtained; in order to ensure that the average energy of the slow luminophors obtained through calculation is the same as the average energy of the slow luminophors given in the evaluation kernel database, a slow luminophor generation cross section is corrected; and finally, storing the slow luminescence quantum generation cross section and slow luminescence quantum energy angle distribution information in an ACE format database. The invention provides a manufacturing method of a slow luminescence sub-ACE format database. The slow luminescence sub-ACE format database is considered in a Monte Carlo program, and the method has the advantages of being high in calculation precision and high in calculation speed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photon nuclear data processing calculation, and particularly relates to a method for manufacturing a delayed photon ACE (A Compact ENDF) format database. BACKGROUND

[0002] In the process of neutron-photon coupled transport calculation by the Monte Carlo program, the related data of the photons generated after the nuclear reaction of neutrons are needed. In addition to the prompt photons released by radiation capture, inelastic scattering and fission reaction, the excited fission products generated by the fission reaction will also release photons in the process of decay, and the photons are delayed photons. The delayed photons have an important influence on the power distribution of the nuclear reactor and the photon irradiation damage.

[0003] At present, the processing of the delayed photons in the Monte Carlo program includes that the OpenMC program assumes that the energy spectrum of the prompt photons generated by the fission in the equilibrium state is similar to that of the delayed photons, and the yield of the prompt photons generated by each fission is enlarged according to the energy proportion of the delayed photons to consider the influence of the delayed photons, but there is a large difference between the energy spectrum of the delayed photons and that of the prompt photons, and thus a certain error is introduced by directly modifying the yield of the prompt photons. The MCNP program considers the influence of the delayed photons by using the decay database provided by itself, the decay database stores the decay relationship between the radioactive nuclides, and 25 energy bands are used to describe the energy spectrum of the delayed photons, and the method has the disadvantages of low calculation accuracy and slow speed.

[0004] To solve the above problems, the present application provides a method for manufacturing a delayed photon ACE format database, which has the advantages of fast calculation speed and high calculation accuracy. SUMMARY

[0005] To solve the above problems in the prior art, the present application provides a method for manufacturing a delayed photon ACE format database, and the method has the advantages of fast calculation speed and high calculation accuracy when the delayed photons are considered in the Monte Carlo program.

[0006] To achieve the above object, the present application adopts the following technical scheme:

[0007] A method for manufacturing a delayed photon ACE format database, comprising the following steps:

[0008] Step 1: calculating the delayed photon production cross section based on the fission yield sub-database and the decay sub-database of the evaluation nuclear database;

[0009] During the long-term steady-state operation of a nuclear reactor, the production and decay rates of fission products and their decay products are approximately equal, i.e., decay equilibrium. Therefore, the production of slow-emitting electrons is independent of time. The yield of slow-emitting electrons at any given time is the total number of slow-emitting electrons released by fission products and their decay products when they return to the ground state. That is, fission products immediately complete the decay process after the fission reaction occurs. Based on the above decay equilibrium concept, the slow-emitting electron production cross-section is calculated using the following formula:

[0010] σ delay,i (E)=σ f,i (E)Y i (E) Formula (1)

[0011] In the formula:

[0012] σ delay,i (E)——Slow photon production cross section of fission nuclide i, unit: number·barn;

[0013] σ f,i (E)——Fission cross section of fission nuclide i, unit: barn;

[0014] Y i (E)—— Slow-light photon yield of fission nuclide i, in units of: particles;

[0015] E – Incident neutron energy, unit: MeV;

[0016] The fission cross section was obtained from the evaluation nuclear database after resonance reconstruction and linearization. The slow-emitting electron yield of fission nuclide i was calculated using the following formula:

[0017]

[0018] In the formula:

[0019] y i→p (E)——Independent fission yield of fission product p produced by fission nuclide i, in units of: p;

[0020] —The decay branching ratio of nuclide p to daughter nucleus p1;

[0021] D p — Decay photon yield of nuclide p, in units of photons;

[0022] — Decay photon yield of nuclide p1, in units of photons;

[0023] p—Identifier for fission products;

[0024] p1—Identifier of decay products of fission products;

[0025] D - decay photon yield of nuclide x, unit: number; x The calculation is performed by using the following formula, formula (3) is used for the case of discrete photon energy spectrum, and formula (4) is used for the case of continuous photon energy spectrum:

[0026]

[0027] In the formula:

[0028] D x - decay photon yield of nuclide x, unit: number;

[0029] k - decay reaction channel number of released photons;

[0030] NSP - number of reaction channels producing decay photons;

[0031] A k - normalization coefficient of decay reaction channel k releasing photons;

[0032] m - discrete photon energy point identifier;

[0033] NER - number of discrete photon energy points;

[0034] γ k,m (E γ ) - decay photon yield of the kth decay reaction channel at the mth discrete energy point, unit: number;

[0035] γ k (E γ ) - continuous decay photon energy spectrum of the kth decay reaction channel, unit: number / MeV;

[0036] E γ - decay photon energy, unit: MeV;

[0037] Step 2: Calculate the delayed photon energy distribution in the form of equal probability energy bins;

[0038] Equal probability energy bins are to divide the delayed photon energy range into N energy intervals, and the probability of the delayed photon falling in each energy interval is equal. The N intervals are N energy bins. When storing the delayed photon energy distribution data in the form of equal probability energy bins, N+1 boundary point energies need to be obtained. The boundary point energy is calculated by using the following formula:

[0039]

[0040] In the formula:

[0041] E bound,i - energy of the ith energy point, unit: MeV;

[0042] P(E) — Decay photon energy spectrum, unit: number / MeV;

[0043] i — Energy point identifier;

[0044] N — Number of energy points;

[0045] Although the energy of decay photons in the decay sub-library of the evaluated nuclear database JEF-2.2 can reach 12.7 MeV, in fact, the energy of delayed photons is mostly concentrated in [4.7 MeV-6 MeV], and if the energy of the last energy point is set to 12.7 MeV, the delayed photon energy will be overestimated, so the energy of the last energy point is set to 6 MeV, that is, the delayed photons above 6 MeV are ignored;

[0046] Step 3: Correct the delayed photon production cross section using the average energy of delayed photons given in the evaluated nuclear database;

[0047] The average energy of delayed photons released after the fission of fissile nuclides is given in the evaluated nuclear database, and the total delayed photon production cross section of fissile nuclides is corrected to ensure that the average energy of delayed photons calculated using the fission yield and decay data is consistent with the average energy of delayed photons given in the evaluated nuclear database, and the corrected delayed photon production cross section is calculated using the following formula:

[0048]

[0049] In the formula:

[0050] — Corrected delayed photon production cross section, unit: barn;

[0051] Q delay — The average energy of delayed photons released after the fission of fissile nuclides given in the evaluated nuclear database, unit: MeV;

[0052] Q delay,cal — The average energy of delayed photons calculated using the fission yield and decay data, unit: MeV;

[0053] Step 4: Make an ACE database containing delayed photons by adding a photon production reaction channel in the ACE database;

[0054] The delayed photon production cross section is added to the instantaneous photon production cross section and stored in the GPD (Photon production data) array of the ACE database; the delayed photon energy distribution is stored in the DLWP (Photon production energy distributions) array of the ACE database; since the decay photons are isotropic, the delayed photon angle distribution is stored in the ANDP (Photon production angular distributions) array of the ACE database according to the isotropic distribution; finally, the processed data is output in the ACE format to obtain the delayed photon ACE format database.

[0055] Compared with the prior art, the present application has the following advantages:

[0056] (1) The prior art uses direct amplification of the instantaneous photon yield or uses 25-group delayed photon yield to consider the influence of the delayed photons, and cannot accurately describe the delayed photon energy spectrum, and has the problem of low calculation precision. The present application describes the delayed photon energy spectrum in the form of equal-probability energy bins, and since the number of equal-probability energy bins is large, the delayed photon energy spectrum can be accurately described, and therefore the calculation precision is higher than that of the traditional method.

[0057] (2) Compared with using a decay particle database, the database prepared by the present application does not need to traverse the decay chain of each fission product when performing Monte Carlo calculation, and can save calculation time and improve calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 is a flow chart of the method of the present application.

[0059] Figure 2 is a photon flux comparison chart of the spherical shell filling 233 U.

[0060] Figure 3 is a photon flux comparison chart of the spherical shell filling 235 U.

[0061] Figure 4 is a photon flux comparison chart of the spherical shell filling 238 U.

[0062] Figure 5 is a photon flux comparison chart of the spherical shell filling 239 Pu. DETAILED DESCRIPTION

[0063] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0064] This invention discloses a method for creating a slow-photon ACE format database, which involves adding a photon generation reaction channel to the slow-photon data into the ACE (ACompact EndF) format database. Figure 1 As shown, the present invention includes the following steps:

[0065] Step 1: Calculate the slowed photon generation cross section based on the fission yield sub-library and decay sub-library of the evaluation kernel database;

[0066] During the long-term steady-state operation of a nuclear reactor, the production and decay rates of fission products and their decay products can be approximated as equal, i.e., decay equilibrium. Therefore, the production of slow-emitting electrons can be considered independent of time. The yield of slow-emitting electrons at any given time can be considered to be the total number of slow-emitting electrons released by fission products and their decay products when they return to the ground state. In other words, fission products are assumed to complete their decay process immediately after the fission reaction occurs. Based on this decay equilibrium concept, the slow-emitting electron production cross-section is calculated using the following formula:

[0067] σ delay,i (E)=σ f,i (E)Y i (E) Formula (1)

[0068] In the formula:

[0069] σ delay,i (E)——Slow photon production cross section of fission nuclide i, unit: number·barn;

[0070] σ f,i (E)——Fission cross section of fission nuclide i, unit: barn;

[0071] Y i (E)—— Slow-light photon yield of fission nuclide i, in units of: particles;

[0072] E – Incident neutron energy, unit: MeV;

[0073] The fission cross section can be obtained from the evaluation nuclear database after resonance reconstruction and linearization. The slow-light luminescence yield of fission nuclide i is calculated using the following formula:

[0074]

[0075] In the formula:

[0076] y i→p (E)——Independent fission yield of fission product p produced by fission nuclide i, in units of: p;

[0077] —The decay branching ratio of nuclide p to daughter nucleus p1;

[0078] D p — decay photon yield of nuclide p, unit: number;

[0079] — decay photon yield of nuclide p1, unit: number;

[0080] p — fission product identifier;

[0081] p1 — decay product identifier of fission product;

[0082] wherein the decay photon yield D of nuclide x is calculated by x The following formula is used for calculation, formula (3) is used for the case that the photon energy spectrum is discrete energy spectrum, and formula (4) is used for the case that the photon energy spectrum is continuous energy spectrum:

[0083]

[0084] In the formula:

[0085] D x — decay photon yield of nuclide x, unit: number;

[0086] k — decay reaction channel number releasing photons;

[0087] NSP — number of reaction channels producing decay photons;

[0088] A k — normalization coefficient of decay reaction channel k releasing photons;

[0089] m — discrete photon energy point identifier;

[0090] NER — number of discrete photon energy points;

[0091] γ k,m (E γ ) — decay photon yield of the kth decay reaction channel at the mth discrete energy point, unit: number;

[0092] γ k (E γ ) — continuous decay photon energy spectrum of the kth decay reaction channel, unit: number / MeV;

[0093] E γ — decay photon energy, unit: MeV;

[0094] Step 2: Calculate the delayed photon energy distribution in the form of equal probability energy bin;

[0095] Equal probability energy bin is to divide the delayed photon energy range into N energy intervals, the probability of the delayed photon falling in each energy interval is equal, the N intervals are N energy bins, when using the form of equal probability energy bin to store the delayed photon energy distribution data, N+1 boundary point energies need to be obtained, the boundary point energy is calculated by the following formula:

[0096]

[0097] In the formula:

[0098] E bound,i - the energy of the i th energy point, unit: MeV;

[0099] P(E) - the decay photon energy spectrum, unit: number / MeV;

[0100] i - energy point identifier;

[0101] N - the number of energy bins;

[0102] Although the energy of the decay photon in the decay sub-library of the evaluated nuclear database JEF-2.2 can be as high as 12.7 MeV, in fact, the energy of the delayed photon is mostly concentrated in [4.7 MeV-6 MeV], if the energy of the last energy point is set to 12.7 MeV, the delayed photon energy will be overestimated, therefore, the energy of the last energy point is set to 6 MeV, that is, the delayed photon above 6 MeV is ignored;

[0103] Step 3: using the evaluated delayed photon average energy given in the evaluated nuclear database to correct the delayed photon production cross section;

[0104] The average energy of the delayed photon released after the fission of the fissile nuclide is given in the evaluated nuclear database, the total delayed photon production cross section of the fissile nuclide needs to be corrected, so as to ensure that the average energy of the delayed photon calculated using the fission yield and decay data is consistent with the average energy of the delayed photon given in the evaluated nuclear database, the corrected delayed photon production cross section is calculated by the following formula:

[0105]

[0106] In the formula:

[0107] - the corrected delayed photon production cross section, unit: barn;

[0108] Q delay - the average energy of the delayed photon released after the fission of the fissile nuclide given in the evaluated nuclear database, unit: MeV;

[0109] Q delay,cal—The average energy of slowed photons, calculated using fission yield and decay data, in MeV;

[0110] Step 4: Create an ACE database containing delayed photons by adding a photon generation reaction channel to the ACE (A Compact EndF) database; add the delayed photon generation cross section to the instantaneous photon generation cross section and store it in the GPD array of the ACE database; store the delayed photon energy distribution in the DLWP array; since all decaying photons are isotropic, store the delayed photon angular distribution in the ANDP array according to the isotropic distribution; finally, output the processed data in ACE format to obtain the delayed photon ACE format database.

[0111] The fission yield sub-library and decay sub-library in the evaluation kernel database used in steps 1 and 3 are only applicable to the method of creating the slow-luminescent ACE format database in this invention, and there are no restrictions on the source and use of the evaluation kernel database.

[0112] Validation of the ACE format database of slow-release phosphors

[0113] To verify the accuracy of the slow-photon ACE format database, the database was constructed using both the method of this invention and the multi-group form normalized slow-photon yield method. Neutron and photoatomic data were evaluated using the ENDF / B-VII.0 nuclear database, while fission and decay data were evaluated using the JEF-2.2 nuclear database. 233 U、 235 U、 238 U、 239 The ACE database of slow-emitting photons for the four common fissile nuclides (Pu) was used to calculate a one-dimensional spherical shell problem using a Monte Carlo program. The shell had an inner diameter of 10 cm and an outer diameter of 19.9 cm, and the materials were the four fissile nuclides mentioned above. The center of the shell was a 14.1 MeV isotropic neutron source. The flux of 123 photon groups in the energy range [0.3679 MeV, 10 MeV] at the shell was statistically analyzed, and the results were compared with those obtained using a conventional decay particle database. To ensure consistency with the evaluation nuclear database used, the slow-emitting photon yields of 25 groups for each radionuclide calculated using NECP-Atlas based on the JEF-2.2 evaluation nuclear database were used to replace the corresponding parts in the decay particle database. The calculation results are as follows: Figures 2-5 As shown:

[0114] from Figures 2-5It can be seen that the calculation results of using the multi-group form to describe the delayed photon energy distribution are in good agreement with the results calculated using the decay particle database, and the multi-group form database and the traditional decay particle database describe the energy distribution of the delayed photon by averaging the discrete photon yield in each group, which will smooth the fluctuations of the delayed photon energy distribution. The use of the database of the present application can more accurately describe the fluctuations of the delayed photon energy spectrum, and therefore the present application method has higher calculation accuracy than the traditional method.

[0115] The calculation time using the traditional decay particle database and the database of the present application is shown in Table 1,

[0116] Table 1 Comparison of calculation time

[0117]

[0118] Wherein, since the traditional decay particle database stores the delayed photon yield of each radionuclide, it needs to be traversed one by one according to the decay chain during the running of the Monte Carlo program, so the running time is long. The calculation time using the database of the present application is only about one fourth of that.

Claims

1. A method for creating a deferred light ACE format database, characterized by: The method comprises the following steps: Step 1: calculating the delayed photon production cross section based on the fission yield sub-base and the decay sub-base of the evaluation nuclear database; Step 2: calculating the delayed photon energy distribution in the form of equal-probability energy bands; Step 3: correcting the delayed photon production cross section using the average energy of delayed photons given in the evaluation nuclear database; Step 4: making an ACE database containing delayed photons by adding a photon production reaction channel in the ACE database.

2. The method for making a delayed light sub-ACE format database according to claim 1, wherein: The specific process of step 1 is as follows: during the long-term steady operation of a nuclear reactor, the production rate and disappearance rate of fission products and their decay products are approximately considered to be equal, that is, the decay is balanced, therefore, the production of delayed photons is independent of time, and the yield of delayed photons at any time is the number of all delayed photons emitted by fission products and their decay products when returning to the ground state, that is, the fission product immediately completes the decay process after the fission reaction occurs, based on the above idea of decay balance, the delayed photon production cross section is calculated using the following formula: σ delay,i (E) = σ f,i (E) Y i (E) Equation (1) In the formula, E is the incident neutron energy, unit: MeV; wherein the fission cross section is obtained after resonance reconstruction and linearization processing of the evaluation nuclear database, and the delayed photon yield of the fission nuclide i is calculated using the following formula: σ delay,i (E) - Delayed photon production cross section of fissile nuclide i in units of individual barns; σ f,i (E) - fission cross section of fissile nuclide i, in barns; Y i (E) - delayed photon yield of fissile nuclide i in units of photons; In the formula, p is the fission product identifier; p1 is the decay product identifier of the fission product; wherein k is the decay reaction channel number of the released photon; NSP is the number of reaction channels producing decay photons; m is the discrete photon energy point identifier; NER is the number of discrete photon energy points; and P(E) is the decay photon energy spectrum, unit: number / MeV. The specific process of step 2 is as follows: the equal-probability energy band is to divide the delayed photon energy range into N energy intervals, and the probability of the delayed photon falling in each energy interval is equal, the N intervals are N energy bands, and N+1 boundary point energies are needed when using the form of equal-probability energy band to store the delayed photon energy distribution data, the boundary point energy is calculated using the following formula: In the formula, P(E) is the decay photon energy spectrum, unit: number / MeV; i is the energy point identifier; N is the number of energy bands; and E is the incident neutron energy, unit: MeV. y i→p (E) - independent fission yield of fissile nuclide i to produce fission product p, in units of individuals; - the decay branching ratio of the nuclide p decaying into the daughter nucleus p1; D p - decay photon yield of the nuclide p in units of photons; - the decay photon yield of the nuclide p1 in pieces; Although the energy of the decay photon in the decay sub-base of the JEF-2.2 evaluation nuclear database can reach 12.7 MeV, in fact, the energy of the delayed photon is mostly concentrated in [4.7 MeV-6 MeV], and if the energy of the last energy point is set to 12.7 MeV, the delayed photon energy will be overestimated, therefore, the energy of the last energy point is set to 6 MeV, that is, the delayed photon above 6 MeV is ignored. The specific process of step 3 is as follows: the average energy of the delayed photon released after the fission of the fission nuclide is given in the evaluation nuclear database, the total delayed photon production cross section of the fission nuclide is corrected to ensure that the average energy of the delayed photon calculated using the fission yield and decay data is consistent with the average energy of the delayed photon given in the evaluation nuclear database, and the corrected delayed photon production cross section is calculated using the following formula: where D is the decay photon yield of the nuclide x x The calculation is performed using the following equations, equation (3) for the case of a discrete photon spectrum and equation (4) for the case of a continuous photon spectrum: ​ D x - the decay photon yield of the nuclide x in units of photons; ​ ​ A k - the normalization coefficient of the decay reaction channel k releasing photons; ​ ​ gamma k,m (E γ ) — decay photon yield of the kth decay reaction channel at the mth discrete energy point, unit: pieces; gamma k (E γ ) — the continuous decay photon spectrum of the kth decay reaction channel, in units of photons / MeV; E γ Decay photon energy, in MeV.

3. The method of claim 1, wherein: ​ ​ ​ E bound,i - the energy of the i-th energy point, in MeV; ​ ​ ​ ​ 4. The method of claim 1, wherein: ​ ​ ​ - corrected delayed photon production cross section in barns; Q delay - evaluate the average energy of delayed photons released after fission of the fissile nuclide given in the nuclear database, in MeV; Q delay,cal Delayed photon average energy calculated using fission yield and decay data, in MeV.

5. The method of claim 1, wherein: The specific process of step 4 is: adding the delayed photon production cross section and the prompt photon production cross section and storing them in the GPD array of the ACE database; storing the delayed photon energy distribution into the DLWP array of the ACE database; since the decay photons are isotropic, the delayed photon angle distribution is stored into the ANDP array of the ACE database according to the isotropic distribution; finally, the processed data is output according to the ACE format, and the delayed photon ACE format database is obtained. ​

Images