CN107656305A - A kind of method for determining uranium enrichment - Google Patents
A kind of method for determining uranium enrichment Download PDFInfo
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- CN107656305A CN107656305A CN201710696336.XA CN201710696336A CN107656305A CN 107656305 A CN107656305 A CN 107656305A CN 201710696336 A CN201710696336 A CN 201710696336A CN 107656305 A CN107656305 A CN 107656305A
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Abstract
The invention belongs to radioactive substance field of measuring technique, is related to a kind of method for determining uranium enrichment.Described method utilizes gamma spectrum, carries out uranium enrichment measure from scale method by relative detection efficiency, comprises the following steps：(1) basis235U and238U is fitted to obtain relative detection efficiency curve function f (E) in the relative detection efficiency RE and ENERGY E of the intermediate energy region of power spectrum and high energy region relation respectively；(2) calculated according to f (E)235U uranium enrichments.Using the method for the measure uranium enrichment of the present invention, standard source can not be needed, does not consider the uranium enrichment in the determination sample of sample geometry, density, form, and be more suitable for measuring the sample that outer packing or container have certain gamma ray shielding.
Description
Technical field
The invention belongs to radiogen field of measuring technique, is related to a kind of method for determining uranium enrichment.
Background technology
Uranium enrichment is defined as isotope235The ratio between U quality and the gross mass of uranium, are generally represented with percentage.Determine uranium
Enrichment, nuclear safeguards field tool be of great significance.
The analysis of uranium enrichment can be divided into two classes from the property angle of measuring method.
One kind is destructive analysis (DA).This alanysis usually requires to sample and prepare sample, then measures analysis,
With the isotopics of element in determination sample and content, such as mass spectrography.Although such analysis method has very high precision,
But its process of measurement is complicated, specialized laboratories need to be sent to be analyzed, can not meet the needs of on-site rapid measurement.
Another kind of is non-destructive analysis (NDA), the gamma activity correlation based on isotope, does not change measurement object
Physical chemistry form, and the isotope abundance of determination sample.NDA technologies have it is simple and quick, do not destroy sample, without sampling and
Sample preparation, analysis cost is low, does not produce many advantages, such as secondary waste, has been widely used and has been verified in nuclear material production and nuclear safeguards
Among.
Gamma ray spectrometry method is to ensure one of non-destructive analysis method commonly used in verification, is incided by measurement
The gamma-ray power spectrum and intensity of detector, analyze contributive isotope and determine its enrichment.The method for analyzing enrichment
Main efficient scale method, abundance meter principle method, relative efficiency are from the heavy peak analytic method of scale method and Low Energy Region.
Efficiency calibration method be using known activity standard source (such as152Eu efficiency calibration) is carried out, by calculating standard source
The efficiency of each characteristic peak, then fit efficiency curve by these efficient points.After efficiency calibration, you can pass through unknown sample
The analysis of the characteristic peak of each isotopes of U determines respective activity in power spectrum, so as to obtain235U enrichments.
The principle of abundance meter principle method is as follows.When sample reaches saturated absorption thickness, what detector can detect
185.7keV gamma intensity only is from the gamma-rays launched in a part of volume of sample, and other positions are launched in sample
The energy gamma-rays because the reasons such as self-absorption are without into detector.Now, the 185.7keV that detector detects is penetrated
The intensity (net peak area at the energy peak) of line is just and in sample235U quality is linear.With one or more uranium enrichments
After sample known to known, uranium gross mass carries out scale, it is possible to by the gross mass of uranium in the linear relationship and testing sample
Draw the uranium enrichment of testing sample.
The advantages of efficiency calibration method and abundance meter principle method be if scale do it is accurate, its measure analysis result can reach
To very high precision.But the shortcomings that both approaches, is either to be carved with the sample of standard source or known enrichment
Degree, require that they and testing sample are as far as possible identical (form, density etc.), to ensure the accuracy of scale；And after scale,
It is consistent when also requiring the measuring condition (being mainly geometrical condition) during measurement unknown sample with scale.In most cases, exist
Ensure and be both needed to carry out Blind Test to items in verifying, i.e., can not know the information such as its profile, density, therefore both the above method has
Certain limitation.
The heavy peak analytic method of Low Energy Region (0-140keV, but do not include 140keV) be by uranium sample power spectrum about
In 80-105keV energy sections235U、238The γ of the separate sources such as U, X ray mixing power spectrum carry out accurate Analysis to determine uranium enrichment.
The problem of heavy peak analytic method of Low Energy Region avoids scale, it is not necessary to which standard source carries out efficiency calibration, to sample
Geometry, density and form do not have particular/special requirement yet.But there is also many shortcomings for the heavy peak analytic method of Low Energy Region：By
Smaller in the energy section of analysis, ray height is overlapping, it is desirable to which detector has higher energy resolution；Shielding is lower inapplicable again,
In verification, sample may carry out Blind Test verification in container, because γ/X-ray energy positioned at Low Energy Region is relatively low, penetrate
Power is poor.
The content of the invention
It is an object of the invention to provide a kind of method for determining uranium enrichment, so that standard source can not needed, sample is not considered
Uranium enrichment in product geometry, density, the determination sample of form.
In order to achieve this, in the embodiment on basis, the present invention provides a kind of method for determining uranium enrichment, described
Method utilize gamma spectrum, by relative detection efficiency from scale method carry out uranium enrichment measure, comprise the following steps：
(1) basis235U and238U is respectively in the intermediate energy region of power spectrum (140-570keV, including 140keV but do not include
570keV) and high energy region (570-1001keV, including 570keV but do not include 1001keV) relative detection efficiency RE and ENERGY E
Relation be fitted to obtain relative detection efficiency curve function f (E)；
(2) calculated according to f (E)235U uranium enrichments.
The relative efficiency of the present invention belongs to NDA technologies from scale method, and it can area by analyzing the 143-1001keV of uranium power spectrum
In the range of a plurality of come from235U、238U gamma-rays carries out relative efficiency from scale, and the detection for analyzing each isotope of uranium is imitated
Rate ratio, and then corresponding atomicity ratio is calculated, draw uranium enrichment.
The relative efficiency of the present invention not only has the various advantages of the heavy peak analytic method of foregoing Low Energy Region from scale method, and
And its shortcoming is overcome, and have without standard source scale, the advantages of limitation sample geometry, density and form, and
And it is more suitable for measuring the sample that outer packing or container have certain gamma ray shielding.
In a preferred embodiment, the present invention provides a kind of method for determining uranium enrichment, wherein step (1)
In, for238U is in the high energy region of power spectrum, ln (A238ε)=ln (Area238/BR238)=f (E),
Wherein：
Area238For238The peak area at U net feature γ energy peak；
BR238For238The branching ratio at U net feature γ energy peak；
A238For238U activity；
ε is full energy peak detection efficient.
In a kind of more preferred embodiment, the present invention provides a kind of method for determining uranium enrichment, wherein step
(1) in, for235U is in the intermediate energy region of power spectrum, ln (A235ε)=ln (Area235/BR235)=f (E)+ln k,
Wherein：
Area235For235The peak area at U net feature γ energy peak；
BR235For235The branching ratio at U net feature γ energy peak；
ε is full energy peak detection efficient；
Wherein A235For235U activity；A238For238U activity；T235For235U half-life period；T238For238U half-life period；
Enr is uranium enrichment.
In a preferred embodiment, the present invention provides a kind of method for determining uranium enrichment, wherein in step (2)
The calculation formula of described uranium enrichment is：
Wherein：
NiFor isotope i atom number；
NkFor isotope k atom number；
It is E by the isotope i energy sentjγ can peak j peak area；
It is E by the isotope k energy sentlγ can peak l peak area；
λiFor isotope i decay coefficient；
λkFor isotope k decay coefficient；
γ energy peak j branching ratio is sent by isotope i；
γ energy peak l branching ratio is sent by isotope k；
RE(El) it is ENERGY ElThe relative detection efficiency at place；
RE(Ej) it is ENERGY EjThe relative detection efficiency at place.
The term " fitting " used in the present invention refers to the physical significance according to relative detection efficiency curve, is pushed away by mathematics
Lead and interative computation, by this respective representative not on same curve235U and238U data points are incorporated into same by translation
On curve, that is, on the relative detection efficiency curve that obtains.And " fitting " if typically refer to certain known function in the prior art
Dry discrete function value { f1, f2..., fn, by adjusting some undetermined coefficient f (λ in the function1, λ2..., λn) so that the letter
The difference (least square meaning) of number and known point set is minimum.
The beneficial effects of the present invention are, using the method for the measure uranium enrichment of the present invention, standard source can not be needed,
The uranium enrichment in the determination sample of sample geometry, density, form is not considered, and is more suitable for measuring outer packing or appearance
The sample of certain gamma ray shielding be present in device.
Grasp and determined using gamma spectrum235The relative detection efficiency of U enrichments from the Key technique problem of scale method be as
What, which is fitted, covers the relative detection efficiency curve of whole intermediate and high energy.It can be seen that from uranium spectrum235U feature γ can peak master
The intermediate energy region of power spectrum is distributed in,238The feature γ energy peak of U daughters is mainly distributed on high energy region, positioned at relative detection efficiency curve
Flex point section have a bigger space, therefore accurately fitting relative detection efficiency curve has very big difficulty.This hair
It is bright mainly to solve the technological difficulties, fit the relative detection efficiency curve of covering intermediate and high energy and finally thereby determine that corresponding
Uranium enrichment.
Brief description of the drawings
Fig. 1 is the relative detection efficiency curve diagram of different uranium isotopes (nucleic) in embodiment.
Fig. 2 is the relative detection efficiency curve diagram (14.84wt% of slightly enriched uranium sample in embodiment235U)。
Fig. 3 is the relative detection efficiency curve diagram (90.20wt% of highly concentrated uranium sample in embodiment235U)。
Fig. 4 is the iterative fitting stream of relative detection efficiency curve in the exemplary method for determining uranium enrichment of the invention
Cheng Tu.
Embodiment
The embodiment of the present invention is further illustrated below in conjunction with accompanying drawing.
The measuring principle and applicating example of the method for exemplary measure uranium enrichment of the invention are as follows.
(1) Computing Principle of uranium enrichment
235U enrichments are represented by：
Enr is uranium enrichment in formula, N235, N238, N234, N236Respectively235U,238U,234U,236The respective atomicities of U.
Generally234U and236U contents seldom (such as234U contents in weapongrade high-enriched uranium are only possible to reach 1wt%), at this
After being ignored in invention,235U enrichments are solely dependent upon235U and238U atomicity ratio.
(2) the iterative fitting principle of relative detection efficiency curve
The HPGe gamma spectrums of uranium sample to be measured are analyzed first, by obtain to from235U、238U and228Th spy
Sign γ energy peak (including with235143.7keV, 163.3keV, 185.7keV, 205.3keV feature γ energy peak related U, with238U phases
258.3keV, 742.8keV, 766.4keV and 1001keV feature γ of pass can peak, with228The 238.6keV of Th correlations,
583.2keV, 727.3keV and 860.5keV feature γ energy peak) carry out the integral peak background processing, peak width scale, peak shape quarter
Degree and unimodal fitting, determine the net peak area at each feature γ energy peak, and covering 143-1001keV is fitted in combination with following technology
The relative detection efficiency curve in energy area.
The full energy peak net count for the Characteristic γ ray that specific isotope is launched is expressed as follows in the sample of arbitrary shape：
In above formula,It is E by the isotope i energy sentjγ can peak j peak area；λiFor isotope i
Decay coefficient；NiFor isotope i atomic nucleus number；γ energy peak j branching ratio is sent by isotope i；ε(Ej) be
Detector is E to energyjGamma-rays peak full energy peak detection efficient.
Then any two energy peak corresponds to the ratio between atom number of nucleic：
If by some energy point E0The detection efficient ε at place0As a reference value, by the full energy peak detection efficient of other energy with
Its ratio is defined as the relative detection efficiency after normalizing：
Difference between the corresponding full energy peak detection efficient of defined herein relative detection efficiency is only one often
Number factor ε0, the factor only it is relevant with energy.
Then (3) formula can be converted into：
Just only need to solve the relative detection efficiency ratio at its feature γ energy peak in the ratio between atomicity for being to solve for two nucleic,
Without knowing the occurrence of its full energy peak detection efficient.
Multiple energy peaks for coming from same nucleic, due to the decay coefficient λ in above formulakAnd λjIt is equal, atomicity Nj
And NkAlso it is equal, then：
I.e.：
It can be seen that the detection efficient ratio at two energy peaks of same nucleic can directly be obtained by power spectrum net count and branching ratio data
Go out.Assuming that the nucleic launches altogether m bar rays, and this m ray is all detected by detector, and these ray peaks each other compared with
For isolated (can peaks interference without other) and covering can area it is larger, then its corresponding net peak can be directly obtained from power spectrum and is counted.If
Choose wherein certain ray, such as kth bar ray detection efficient be used as a reference value, calculate other m-1 energy peak it is relative
Detection efficient, then RE~E curves are made, and fit the functional expression for describing the curve.
It should be noted that although the relative detection efficiency curve is made by a plurality of ray of some nucleic, but its
Reaction is variation relation of the detection efficient with energy, and unrelated with nucleic species.Therefore relative detection efficiency curve is solved
Function expression after can draw the relative detection efficiency value at different-energy energy peak, then its corresponding nucleic is solved by (4) formula
The ratio between atom number.
But the single nucleic of a comparison " ideal " is typically difficult to find that in real work, multiple kinds of energy can be launched
Gamma-rays, and can meets the energy wide coverage of its power spectrum, interfere it is small, can the high requirement of peak counting rate.Therefore need
With multiple nucleic, the relative detection efficiency curve of its covering energy section is each made, is then connected as total relative spy
Efficiency curve is surveyed, this just needs to carry out these relative detection efficiency curves normalization (because their efficiency a reference value is not
Together).
According to aforementioned principles, when being fitted the relative detection efficiency curve of uranium sample, it is necessary to choose multiple nucleic features
Peak net count.As shown in Fig. 1 in the slightly enriched uranium sample obtained by the principle235U and238U data points.Obviously,235U and238Although the respective relative detection efficiency curve that U data points are formed, not on same curve, what it is due to its reaction is detection
Efficiency is identical on these curve shapes, simply amplitude is different, is reflected on curve with the relation of energy variation
It is then the difference of upper-lower position.
Due to containing in slightly enriched uranium sample235U and238U isotopes, thus originally it is operated in the relative detection efficiency of slightly enriched uranium
Used in the fitting of curve235U and238U data point is calculated, and describes relative detection efficiency song from following empirical equation
Line：
Ln (Area/BR)=C1+C2E-2+C3 ln E+C4(ln E)2+C5(ln E)3+C6 (8)
It is right238For U each feature γ energy peak, it is assumed that it meets following formula：
ln(A238ε)=ln (Area238/BR238)=f (E) (9)
Wherein：
F (E)=C1+C2/E2+C3 ln E+C4(ln E)2+C5(ln E)3 (10)
In formula：A238For238U activity, ε are full energy peak detection efficient, and Area is net peak area, and BR is the branch at energy peak
Than.
F (E) curve be by238The relative detection efficiency curve of U each feature γ energy peak composition, and by235U each spy
Sign γ energy peak can equally obtain other one and correspond to235U relative detection efficiency curve.Due to235U and238U is respective relative
Consistent difference be present between detection efficient curvilinear function, the difference is corresponding with the activity ratio k of the two, therefore can obtain：
ln(A235ε)=ln (Area235/BR235)=f (E)+ln k (11)
Note235U enrichments are enr, then235U and238The activity ratio of U isotopes is：
In formula：T1/2,235(T1/2,238) represent235U(238U) the half-life period of isotope.
Thus, you can obtain all data points for matched curve f (E)：(1) independent variable (x-axis) is the energy at energy peak
E, unit MeV；(2) dependent variable (y-axis) is y=ln (Area238/BR238)-ln k。
Wherein, if the energy peak belongs to238U, corresponding k=0；If the energy peak belongs to235U, it is corresponding
Data point (E, y) is fitted by curve form f (E), you can obtain relative detection efficiency curve.
It is actual when calculating, because enrichment is unknown quantity, it is necessary to which being found out using the method enumerated makes regression criterion minimum
It is enriched with angle value, as final enrichment angle value.The initial value available energy enumerated is two γ of 205.3keV and 258.3keV
Feature energy peak calculates.Assume that the detection efficient at the two γ feature energy peaks is equal, can approximate calculation go out enrichment：
In formula：A235/238Represent235U and238The activity ratio of U isotopes.
In formula：N235/238Represent235U and238The atomicity ratio of U isotopes.
In formula：enr0Enrichment during the detection efficient approximation of two characteristic peaks of expression, that is, the starting enrichment enumerated.
By starting enrichment, optimal enrichment angle value is found out by way of enumerating and comparing.
Although 6 unknown quantity (i.e. c are shared in relative detection efficiency curve model (formula 8)1, c2, c3, c4, c5, c6), but
Unknown quantity c6Enumerate235U enrichments, so the unknown quantity for being fitted solution only has 5.Using non-linear least square
Method fitting relative detection efficiency curve is exactly to be enumerated each235Under U enrichments, one group of most suitable parameter is found so that intend
Close function and measurement data points are closest, i.e., the χ in (15) formula2Value is minimum, then passes through more each χ2The size of value, it is determined that most
Whole235U enrichments.
In formula：c1、c2、c3、c4、c5Five unknown quantitys respectively in relative detection efficiency curve model, y (xi) it is data
Point, fj(xi, c1, c2, c3, c4, c5) it is the curve being fitted, N is data point number.
Thus, you can draw up the relative detection efficiency curve of slightly enriched uranium sample, as shown in Figure 2.
With235U enrichments increase,238U content is reduced, and causes the net count of 258.3keV characteristic peaks to reduce, and is counted
Property is very bad, can not apply, therefore can not be utilized for high-enriched uranium235U and238U characteristic peak correctly fits
Relative detection efficiency curve.It is a small amount of in view of can generally contain in high-enriched uranium232U, its daughter228Th 238.6keV
Feature γ energy peak is exactly in Low Energy Region, and fitting of the energy peak to high-enriched uranium relative detection efficiency curve plays highly important work
With.
For high-enriched uranium, using the above method, pass through235U and228Th feature γ energy peak can fit covering 143-
The relative detection efficiency curve in 1001keV energy area, then will238U each characteristic peak is according to the relative detection efficiency curve fitted
Shape is fitted, you can solves the enrichment of high-enriched uranium.Relative detection efficiency curve such as Fig. 3 of the highly concentrated uranium sample fitted
It is shown.
The iterative fitting flow of above-mentioned relative detection efficiency curve is as shown in Figure 4.
(3) applicating example
Using portable HPGe detector measurements to three kinds of different types (NDA standard samples, UO2Fuel ball, U3O8
Powder), uranium enrichment scope 1.58wt%~90.20wt% altogether 9 samples carried out repetition measurement.Meanwhile select
Develop the method that faster computational language Matlab establishes this work in recent years and enter line program realization, and power spectrum has been carried out point
Analysis, it is as a result as shown in table 1 below.From the result of table 1, in the analysis to slightly enriched uranium, repeatedly measurement analysis average value is relative
Deviation is no more than 2.5%；In the analysis to high-enriched uranium, repeatedly the relative deviation of measurement analysis average value is no more than 0.6%.
The energy spectrum analysis data of table 1
Obviously, those skilled in the art can carry out the essence of various changes and modification without departing from the present invention to the present invention
God and scope.So, if belonging to the model of the claims in the present invention and its equivalent technology to these modifications and variations of the present invention
Within enclosing, then the present invention is also intended to comprising including these changes and modification.Above-described embodiment or embodiment are simply to the present invention
For example, the present invention can also be implemented with other ad hoc fashions or other particular forms, without departing from the present invention's
Main idea or substantive characteristics.Therefore, it is regarded as from the point of view of the embodiment of description is in terms of any illustrative and non-limiting.This
The scope of invention should be illustrated that any change equivalent with the intention of claim and scope should also include by appended claims
Within the scope of the invention.
Claims (4)
- A kind of 1. method for determining uranium enrichment, it is characterised in that described method utilizes gamma spectrum, passes through relative detection efficiency Uranium enrichment measure is carried out from scale method, is comprised the following steps：(1) basis235U and238U intends in the relative detection efficiency RE and ENERGY E of the intermediate energy region of power spectrum and high energy region relation respectively Conjunction obtains relative detection efficiency curve function f (E)；(2) calculated according to f (E)235U uranium enrichments.
- 2. according to the method for claim 1, it is characterised in that in step (1), for238U is in the high energy region of power spectrum, ln (A238ε)=ln (Area238/BR238)=f (E),Wherein：Area238For238The peak area at U net feature γ energy peak；BR238For238The branching ratio at U net feature γ energy peak；A238For238U activity；ε is full energy peak detection efficient.
- 3. according to the method for claim 2, it is characterised in that in step (1), for235U is in the intermediate energy region of power spectrum, ln (A235ε)=ln (Area235/BR235)=f (E)+lnk,Wherein：Area235For235The peak area at U net feature γ energy peak；BR235For235The branching ratio at U net feature γ energy peak；ε is full energy peak detection efficient；K is235U and238U activity ratio,Wherein：A235For235U activity；A238For238U activity；T235For235U half-life period；T238For238U half-life period；enr For uranium enrichment.
- 4. according to the method for claim 1, it is characterised in that the calculation formula of the uranium enrichment described in step (2) is：<mrow> <mfrac> <msup> <mi>N</mi> <mi>i</mi> </msup> <msup> <mi>N</mi> <mi>k</mi> </msup> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>A</mi> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mrow> <mo>(</mo> <msubsup> <mi>E</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>A</mi> <mi>r</mi> <mi>e</mi> <mi>a</mi> <mrow> <mo>(</mo> <msubsup> <mi>E</mi> <mi>l</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <msup> <mi>&lambda;</mi> <mi>k</mi> </msup> <msup> <mi>&lambda;</mi> <mi>i</mi> </msup> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <msubsup> <mi>BR</mi> <mi>l</mi> <mi>k</mi> </msubsup> </mrow> <mrow> <msubsup> <mi>BR</mi> <mi>j</mi> <mi>i</mi> </msubsup> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <mrow> <mi>R</mi> <mi>E</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>R</mi> <mi>E</mi> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>Wherein：NiFor isotope i atom number；NkFor isotope k atom number；It is E by the isotope i energy sentjγ can peak j peak area；It is E by the isotope k energy sentlγ can peak l peak area；λiFor isotope i decay coefficient；λkFor isotope k decay coefficient；γ energy peak j branching ratio is sent by isotope i；γ energy peak l branching ratio is sent by isotope k；RE(El) it is ENERGY ElThe relative detection efficiency at place；RE(Ej) it is ENERGY EjThe relative detection efficiency at place.
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| CN112694129A (en) * | 2020-11-20 | 2021-04-23 | 中核北方核燃料元件有限公司 | Preparation method of uranium dioxide powder with different enrichments |
| CN113050148A (en) * | 2021-03-15 | 2021-06-29 | 中国原子能科学研究院 | Method for measuring abundance of uranium-235 |
| CN113250686A (en) * | 2021-05-26 | 2021-08-13 | 核工业北京地质研究院 | Method and system for directly measuring uranium by using underground gamma energy spectrum |
| CN113851237A (en) * | 2021-08-10 | 2021-12-28 | 中国核电工程有限公司 | Nuclear fuel rod PuO2Abundance online detection method and system |
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