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Determining Pu isotopic composition and Pu content of PuBe sources by neutron coincidence technique
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 262 (2007) 75–80 www.elsevier.com/locate/nimb
Determining Pu isotopic composition and Pu content of PuBe sources by neutron coincidence technique Cong Tam Nguyen *, Janos Bagi, Laszlo Lakosi Institute of Isotopes, P.O. Box 77, H-1525 Budapest, Hungary Received 17 August 2006; received in revised form 4 April 2007 Available online 16 May 2007
Abstract The paper describes a pure neutron method for determining both Pu content and Pu isotopic composition of PuBe neutron sources by neutron coincidence technique, without using gamma-spectrometry. The new procedure based on the R/T–T relationship is a developed version of the R/T-method based on R/T–MPu calibration curve described in [C.T. Nguyen, J. Bagi, L. Lakosi, A novel method of quantitative assay of PuBe neutron sources by neutron coincidence technique, Nucl. Instr. and Meth. B 246 (2006) 409], utilizing Pu isotopic correlations; here R, T, MPu are double count rate, single count rate and total Pu content, respectively. Accuracy of the method was found to be about 2–3% and 15% for 239Pu component and Pu content, respectively. Measurement time as a function of detector efficiency is treated in detail. It is shown that in a system of frame, a transuranium neutron source can be characterized by a pair of coordinates [R/T, T]. 2007 Elsevier B.V. All rights reserved. PACS: 28.20.v; 29.25.Dz; 29.40.n Keywords: NDA; Pu content; Pu isotopic composition; Transuranium neutron sources; Neutron coincidence technique
1. Introduction Upon developing non-destructive methods for characterizing PuBe neutron sources, estimate of the Pu content is of utmost importance from nuclear safety, safeguards and illicit trafficking viewpoints. Because Pu material in this type of sources contains five Pu isotopes (and 241Am) of different specific neutron yields, it seems that estimate of the Pu content, in principle, requires measurement of the Pu isotopic composition by gamma-spectrometry. Various procedures were considered for this purpose: (i) combining the Pu isotopic composition determined by gamma-spectrometry with the total neutron output (combination method [2,3]); (ii) use of pure gamma-spectro-
*
Corresponding author. Tel.: +36 1 392 2222/3342; fax: +36 1 392 2529. E-mail address: [email protected] (C.T. Nguyen).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.05.005
metry, e.g. of the so-called infinite energy method [4], or measuring the 375 and 413 keV gamma lines of 239Pu in cylindrical far-field geometry and apply absorption correction [5], (iii) combining the heat of PuBe neutron sources measured by calorimeter with the isotopic composition determined by gamma-spectrometry [6]. Thank to the accuracy of heat measurement, the sources assayed by this method can be considered as a set of secondary standard neutron sources. They were used for verifying the accuracy of other methods. Comparisons are in progress and powerfully help to reduce the systematic errors of the two other methods. Among NDA methods developed for quantitative assay of PuBe neutron sources, a pure neutron method (called R/T-method, based on the correlation between R/T ratio and total Pu content, MPu) was reported in [1]. Here R is the neutron double count rate and T is the single count rate measured by neutron coincidence collar. The advantage of
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C.T. Nguyen et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 75–80
the R/T-method is that there is no need of using gamma spectrometry for determining the isotopic composition. Random neutrons from Be(a,n) reaction induce fission in Pu itself, as target, and secondary fission neutrons measured by coincidence neutron technique are used for estimating the Pu content. In the usual neutron activation analysis, the neutron flux must be kept constant for the observed effect to be proportional to the quantity of concern in the target. In our case, the value of R/T represents the effect due to a single interrogating neutron, which is analogous to a constant flux. Therefore, the R/T–MPu function as a calibration curve can be used for determining the content of Pu in the sources. Thank to the fact that PuBe neutron sources contain mainly 239Pu (75–95%) and the fission cross section of 240Pu, forming about 5–20% of Pu in this type of sources, is not much different from that of 239Pu in the energy region concerned, the values of R/T are not very sensitive to the isotopic composition. Since isotope abundances in reactor-produced Pu (consequently also in PuBe neutron sources) exhibit a correlation among themselves [5], the Pu isotopic composition can be characterised by a linear function of 239Pu abundance (see Fig. 1). Then, the total specific neutron yield of a PuBe source can be described versus the 239Pu fraction by a linear equation as well. The isotopic correlation can be explained by the fact that Pu isotopes are produced by subsequent neutron capture reactions on uranium in a nuclear reactor. This feature is utilised to determine 239Pu fraction by the neutron coincidence technique. Assume that upon assaying two PuBe sources of the same total Pu content but different 239Pu fractions. On the basis of the R/T–MPu relationship described in [1], the same R/T obtained corresponds to the same the total Pu content, however, different R and T values are observed. If we represent these sources in a new dimension system R/T–T the single point on R/T–MPu curve will split into two points. If we represent a lot of PuBe neutron sources
on R/T–T, the sources with the sample value of 239Pu fraction will be grouped on one curve. By this way a system of R/T–T curves will be structured. In this paper we show, how to derive two parameters of 239Pu fraction and total Pu content due to the system of R/T–T curves. 2. Determining 239 Pu fraction and Pu content by neutron coincidence technique Random neutrons emitted from 9Be(a,n)12C reaction interact with the material in the source by Pu(n,f) and Be(n,2n) reactions [7,8]. By this way, these primary neutrons induce the time-correlated secondary neutrons, which can be measured by neutron coincidence technique. Using a simple model [1], we have shown that the R/T ratio normalized for parameters of detector, (R/T)norm, is a function of the total Pu content, MPu: ln M Pu ; ðR=T Þnorm ¼ 1:787M 0:44þ0:024 Pu
ð1Þ
where T norm ¼ Rnorm ¼
T ; e0
ð2Þ R ; eG=s Þ
e2f eP =s ð1
ðR=T Þnorm ¼
Rnorm : T norm
ð3Þ ð4Þ
Here e0 and ef is the absolute detector efficiency for primary and fission neutrons, respectively, P is predelay, G is the coincidence gate length and s is the detector die-away time. Assuming a linear dependence of the isotopic abundances mi of 238Pu, 240Pu, 241Pu, 242Pu and 241Am on the 239 Pu component, m239, i.e. mi = ai + bi * m239, the total neutron specific yield, y = Ryimi (now i runs over the Pu isotopes and Am, from 1 to 6) also can be represented in the same way: y ¼ yðm239 Þ ¼ a þ b m239 n=s-gPu:
ð5Þ
Using the isotopic composition determined by gammaspectrometry (see Fig. 1), the specific neutron yields [2,3] and a correction factor 1.26 [5] taking into account the systematic error in specific neutron yields, the values a and b are found to be (21.4 ± 2.1) · 105 and (0.214 ± 0.01) · 105 n/s-g Pu, respectively. In general, the total specific neutron yield y of a source is derived from the output rate of primary neutrons, N0, or of total neutron output, N and the total mass, MPu y¼
Fig. 1. 238Pu, 240Pu, 241Pu, 242Pu and 241Am isotopic abundances versus 239 Pu isotopic abundance in eight PuBe sources [5].
N0 ðN =M 1 Þ ¼ ; M Pu M Pu
ð6Þ
where M1 is the neutron self-multiplication factor. In case of small Pu content, the neutron self-multiplication can be assumed to be negligible, i.e. M1 = 1. For larger Pu contents the values of M1 can be derived, for example, by correcting M1 using the secondary neutron by coincidence technique [3] or by the calculation model presented in [1].
C.T. Nguyen et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 75–80
Eq. (6) can be re-written in the form M Pu ¼
N =M 1 : a þ b m239
ð7Þ
and
By inserting (7) to formula (1), a new correlation N =M 1 0:44þ0:024 ln aþbm 239 N =M 1 ðR=T Þnorm ¼ 1:787 a þ b m239
ð8Þ
is obtained. Mathematically, if we know the values of (R/T)norm and N by measurement, we can derive the values m239 from formula (8), y from (5) and MPu from (7). This procedure, in which the isotopic composition and Pu content can at the same time be determined only by neutron counting technique, can be called R/T–T method. This method can be used out graphically in the following steps: • Plot the (R/T)norm versus Tnorm = N according to Eq. (10) with various m239 values of 70–100% in the system of frame R/T and T. Fig. 2 shows the curves with steps of, for example, 5%. • For assaying a PuBe source, normalize the measured R and T to receive (R/T)norm and Tnorm = N, which creates a point with co-ordinates [(R/T)norm, N]. • Comparing this point with the above system of curves gives the value m239. Then y and MPu can be estimated by formulae (5) and (7), respectively. The accuracy of the method can be estimated by comparing m239 and MPu derived by the R/T–T method, mR/TT and MR/TT, with those measured by gammaspectrometry and calorimetry. The double (R) and single (T) count rates were measured by the commercial neutron coincidence collar type JCC-13, the thermal power by a heat flow calorimeter, ANTECH SSCal-1 [6]. The uncertainty of R/T–T method, r, can be calculated from the formula
.
.
.
.
.
Fig. 2. Relationship R/T-T at different
239
rm ¼
rM ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i uP h mR=T T mc 2 u t mc k1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i uP h M R=T T M CAL 2 u t M CAL k1
77
ð9Þ
ð10Þ
for the abundance of 239Pu component mc by gamma spectrometry and for the total mass MCAL, determined by calorimetry, respectively. Here k is the number of PuBe sources measured. The values of r for 13 sources were calculated and found to be about 2% for mR/TT and 15% for MR/TT. 3. Application to other transuranium neutron sources In transuranium neutron sources as AmBe, 238PuBe and AmLi the secondary neutrons are also induced by fission reactions and can be determined by a neutron coincidence collar. Because the parameters of neutron energy spectra [9], the values of fission cross section of AmBe, 238PuBe [10,11] are close to those of 239PuBe sources, Eq. (1) for PuBe can be also used for AmBe and 238PuBe in the first approach. However, the specific neutron yields y are different among one another, therefore, the curves R/T–T were split into different curves corresponding each type of the sources. Since the energy spectrum of AmLi sources [9] is shifted below the fission threshold of Am [10], the measured R/T is smaller than that of AmBe sources by a factor of about an order of magnitude. In general, we can describe all transuranium neutron sources by the equation below: BþC ln N=My 1 N =M 1 ðR=T Þnorm ¼ A : ð11Þ y Here the set of {A, B, C and y} are experimental parameters of a type of sources.
.
Pu fractions.
Fig. 3. Ratio R/T as a function of total count rate T of some neutron sources measured by the detector of 2.8% efficiency.
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4. Measurement time as function of the detector efficiency The measurement time tm is a very important parameter from application viewpoints. The statistical uncertainty is determined first of all by the measured double count rate Rm. The uncertainty equation can be written as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rm þ 2GT 2m DRm pffiffiffiffiffi D¼ ¼ ; ð12Þ Rm t m Rm where Tm is the measured total count rate. The values R and T corrected for counting dead times dt and dc were calculated from Rm and Tm [9] by the equations R ¼ Rm e d t T m ; Fig. 4. [R/T, T] data plots of individual sources fitting the curves calculated for similar types of sources. The data were measured by the detector of 28% efficiency (JCC-13).
1
10
0
R/T
10
10
10
2Ge2edC N 0 ðDÞ
2
2 ðR=T Þnorm ½eeP =s ð1
eG=s Þ
2
:
ð14Þ
On the basis of this formula, we studied tm as a function of detector efficiency for PuBe sources, with relative errors D = 1, 2, 5 and 10%. Detector parameters were dc = 1 · 106 + 0.5 · 1012Tm (s1) and dc = 0.5 · 106 + 0.25 · 1012Tm (s1), P = 10, G = 80 and s = 70 ls, nearly the used ones. The results are shown in Figs. 6 and 7 for a weak and a strong source, respectively. A third set of parameters was also included in the calculation: dc = 0.12 · 106 + 0.06 · 1012 Tm (s1), P = 10, G = 64 and s = 50 ls and the results are also shown. Some remarks are appropriate to be made:
-1
-2
ð13Þ
The measurement time tm, as a function of detector efficiency, of the required relative error D and other characteristics of detector and the source, reads from this as tm ¼
10
T ¼ T m edc T m :
AmBe
-3
AmLi 10
-4
Fig. 5. Ratio R/T as a function of T – data from [13].
• For assaying a source of low neutron output, the detector efficiency should be as high as possible, for example, JCC-13 of 28% efficiency. • In case of high neutron output, the measurement time will get a minimum at a detector efficiency, which
The measured R/T and T by 2.8% detector efficiency for PuBe [2], AmBe, 238PuBe and AmLi sources [12] are plotted in Fig. 3 together with those of fission 244Cm and 252 Cf sources. We note that the ratios R/T of spontaneous fission 244Cm and 252Cf sources are constant. Fig. 4 plot the R/T as a function of T of transuranium neutron sources measured by 28% detectors efficiency (JCC-13). The R/T– T of AmBe and AmLi of [13] were also plotted in Fig. 5. All date show that the co-ordinate values [(R/T)norm, Tnorm] (while Tnorm = N) depend on the parameters of the type of sources. For example, in Fig. 4 each plotted point corresponds to a particular source. It means that the type of the source can be identified by the particular curve; the point fits and its parameters (m239 for PuBe, neutron output and MTru content) can be estimated by the procedure described above.
Fig. 6. Calculated measurement time as function of detector efficiency for a PuBe neutron source of 1 g Pu, 76% 239Pu and 6 · 105 n/s output.
10
-5
10
1
10
2
10
3
10
4
10
5
T
C.T. Nguyen et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 75–80
79
instead of 30–35% by the R/T-method. In other words, the measurement may be performed in a short time. 6. Conclusion
Fig. 7. Calculated measurement time as function of detector efficiency for a PuBe neutron source of 17 g Pu, 76% 239Pu and 1.2 · 107 n/s output.
depends on detector parameters such as dead time, dieaway time. According to the calculation, JCC-13 is not suitable for assaying sources above 3 · 106 n/s neutron output. • Lower dc allows higher detector efficiency at minimum measuring time. • Reducing the error of Rm by only one percent leads to essential increase of the measurement time.
A development work for characterizing PuBe and transuranium neutron sources using neutron coincidence technique has been described. Due to the fact of a correlation among Pu isotopic abundances, the pair of parameters [(R/T)norm, Tnorm] (while Tnorm = N) can be used for estimating both Pu isotopic composition and Pu content by the R/T–T method. Up to now the assay of PuBe and other neutron sources has required gamma spectrometry for identifying the type of the sources, then quantitatively assaying them by different NDA methods [12,13]. Based on the R/T–T correlation, a neutron source can be fully characterized by one neutron measurement. This achievement extends the application of coincidence technique to fully safeguarding transuranium neutron sources. About 200 PuBe sources in Hungary and also a good deal of them in a series of countries may be the object of serial measurements for such a fully characterizing assay. Acknowledgements
The calculation described above is still a rough approach. However, it helps us to choose or build a neutron coincidence collar for assaying PuBe sources; moreover, to discuss advantages of the R/T–T method in the next section.
This work was supported by the Hungarian Atomic Energy Authority under contracts No. OAH-ANI-ABA-16/ 01, -04/02, -04/03 and -01/04. The authors gratefully thank the IAEA and EC JRC Ispra for making available a shift register for complementing the equipment built at the Institute of Isotopes and the neutron coincidence collar type JCC-13 for test purposes, respectively.
5. Advantages of the R/T–T method
References
In case of R/T-method, the uncertainty reported in [1] for estimating Pu content was about 15%. However, the error of Rm requires less than 3–5%. When the DR increases, for example, using the data of the detector of 2.8% efficiency, with an error in Rm of about 7–10%, the error of R/T method may reach 30–35%. Using the R/T– MPu calibration curve, one can see that it requires a long measurement time to suppress DRm below 2–5%. By the graphical method it can be shown that the uncertainty of m239 was 2–3% even if DRm reaches 5–10%. Then, the Pu content was estimated by Eq. (12) with an error of about 15–20%. This error depends on Pu isotopic correlation, i.e. on the precision of Eq. (5) mainly. Reducing the error of Rm to below 2–3%, which requires a very long measuring time, the error of m239 can be reduced to below 1–2%. However, the uncertainty of the Pu content is not improved very much and is still about 15%. It means that the R/T–T method does not need long measurement time. For example, using the R/T–T method to assay by the detector of 2.8% efficiency with DRm of about 5–10%, even 15%, the error of Pu content now is reduced to below 20%
[1] C.T. Nguyen, J. Bagi, L. Lakosi, A novel method of quantitative assay of PuBe neutron sources by neutron coincidence technique, Nucl. Instr. and Meth. B 246 (2006) 409. [2] J. Bagi, C. Tam Nguyen, L. Lakosi, Assessment of the Pu content of PuBe sources, Nucl. Instr. and Meth. B 222 (2004) 242. [3] L. Lakosi, J. Bagi, C. Tam Nguyen, Quantitative non-destructive assay of PuBe neutron sources, Nucl. Instr. and Meth. B 243 (2006) 385. [4] J. Morel, M. Vallee, M. Etcheverry, Programme de mesure des quantites de plutonium par spectrometrie gamma Logiciel PuMa, Rapport CEA R-5484, Avril 1989. [5] C. Tam Nguyen, Verification of 239Pu content, isotopic composition and age of plutonium in PuBe neutron sources by gamma-spectrometry, Nucl. Instr. and Meth. B 251 (2006) 227. [6] J. Bagi, L. Lakosi, C. Tam Nguyen, H. Tagziria, B. Pedersen, R. Jaime, P. Schillebeeckx, Characterisation of PuBe sources by nondestructive assay, in: Proc. 26th Annual Meeting of ESARDA. Symp. on safeguards and nuclear materials management, London, 8–14 May 2005, CD-ROM. [7] M.E. Anderson, W.H. Bond Jr., Neutron spectrum of a plutonium– beryllium source, Nucl. Phys. 43 (1963) 330. [8] M.E. Anderson, R.A. Neff, Neutron energy spectra of different size 239 PuBe (a,n) sources, Nucl. Instr. and Meth. 99 (1972) 231. [9] D. Reilly, N. Ensslin, H. Smith Jr. (Eds.), Passive Non-destructive Assay of Nuclear Materials, US Nuclear Regulatory Commission, Nureg/CR-5550, LA-UR-90-732 Washington DC, USA, 1991.
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[10] V. McLane, C.L. Dunford, P.F. Rose, Neutron Cross Sections, Neutron Cross Section Curves, Vol. 2, NNDC, Brookhaven National Laboratory, Academic Press, Upton, NY, Boston, MA, 1988. [11] D.M. Cifarelli, W. Hage, Models for a three-parameter analysis of neutron signal correlation measurements for fissile material assay, Nucl. Instr. and Meth. A 251 (1986) 550. [12] L. Lakosi, C.T. Nguyen, J. Bagi, Quantitative NDA of isotopic neutron sources, Appl. Radiat. Isot. 63 (2005) 681.
[13] A. Ravazzani, R, Jaime, M. Looman. B. Pedersen, P. Peerani, P. Schillebeeckx, M. Thornton, A. Foglio Para, V. Maiorov, Characterisation of neutron sources by NDA, in: C. Foggi (Ed.), Proc. 23th Ann. Symp. on Safeguards and Nuclear Material Management, Bruges, Belgium. ESARDA, Rep. EUR 1944 EN, JRC Ispra, Italy, 2001, p. 181.
Nuclear Instruments and Methods in Physics Research B 262 (2007) 75–80 www.elsevier.com/locate/nimb
Determining Pu isotopic composition and Pu content of PuBe sources by neutron coincidence technique Cong Tam Nguyen *, Janos Bagi, Laszlo Lakosi Institute of Isotopes, P.O. Box 77, H-1525 Budapest, Hungary Received 17 August 2006; received in revised form 4 April 2007 Available online 16 May 2007
Abstract The paper describes a pure neutron method for determining both Pu content and Pu isotopic composition of PuBe neutron sources by neutron coincidence technique, without using gamma-spectrometry. The new procedure based on the R/T–T relationship is a developed version of the R/T-method based on R/T–MPu calibration curve described in [C.T. Nguyen, J. Bagi, L. Lakosi, A novel method of quantitative assay of PuBe neutron sources by neutron coincidence technique, Nucl. Instr. and Meth. B 246 (2006) 409], utilizing Pu isotopic correlations; here R, T, MPu are double count rate, single count rate and total Pu content, respectively. Accuracy of the method was found to be about 2–3% and 15% for 239Pu component and Pu content, respectively. Measurement time as a function of detector efficiency is treated in detail. It is shown that in a system of frame, a transuranium neutron source can be characterized by a pair of coordinates [R/T, T]. 2007 Elsevier B.V. All rights reserved. PACS: 28.20.v; 29.25.Dz; 29.40.n Keywords: NDA; Pu content; Pu isotopic composition; Transuranium neutron sources; Neutron coincidence technique
1. Introduction Upon developing non-destructive methods for characterizing PuBe neutron sources, estimate of the Pu content is of utmost importance from nuclear safety, safeguards and illicit trafficking viewpoints. Because Pu material in this type of sources contains five Pu isotopes (and 241Am) of different specific neutron yields, it seems that estimate of the Pu content, in principle, requires measurement of the Pu isotopic composition by gamma-spectrometry. Various procedures were considered for this purpose: (i) combining the Pu isotopic composition determined by gamma-spectrometry with the total neutron output (combination method [2,3]); (ii) use of pure gamma-spectro-
*
Corresponding author. Tel.: +36 1 392 2222/3342; fax: +36 1 392 2529. E-mail address: [email protected] (C.T. Nguyen).
0168-583X/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.05.005
metry, e.g. of the so-called infinite energy method [4], or measuring the 375 and 413 keV gamma lines of 239Pu in cylindrical far-field geometry and apply absorption correction [5], (iii) combining the heat of PuBe neutron sources measured by calorimeter with the isotopic composition determined by gamma-spectrometry [6]. Thank to the accuracy of heat measurement, the sources assayed by this method can be considered as a set of secondary standard neutron sources. They were used for verifying the accuracy of other methods. Comparisons are in progress and powerfully help to reduce the systematic errors of the two other methods. Among NDA methods developed for quantitative assay of PuBe neutron sources, a pure neutron method (called R/T-method, based on the correlation between R/T ratio and total Pu content, MPu) was reported in [1]. Here R is the neutron double count rate and T is the single count rate measured by neutron coincidence collar. The advantage of
76
C.T. Nguyen et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 75–80
the R/T-method is that there is no need of using gamma spectrometry for determining the isotopic composition. Random neutrons from Be(a,n) reaction induce fission in Pu itself, as target, and secondary fission neutrons measured by coincidence neutron technique are used for estimating the Pu content. In the usual neutron activation analysis, the neutron flux must be kept constant for the observed effect to be proportional to the quantity of concern in the target. In our case, the value of R/T represents the effect due to a single interrogating neutron, which is analogous to a constant flux. Therefore, the R/T–MPu function as a calibration curve can be used for determining the content of Pu in the sources. Thank to the fact that PuBe neutron sources contain mainly 239Pu (75–95%) and the fission cross section of 240Pu, forming about 5–20% of Pu in this type of sources, is not much different from that of 239Pu in the energy region concerned, the values of R/T are not very sensitive to the isotopic composition. Since isotope abundances in reactor-produced Pu (consequently also in PuBe neutron sources) exhibit a correlation among themselves [5], the Pu isotopic composition can be characterised by a linear function of 239Pu abundance (see Fig. 1). Then, the total specific neutron yield of a PuBe source can be described versus the 239Pu fraction by a linear equation as well. The isotopic correlation can be explained by the fact that Pu isotopes are produced by subsequent neutron capture reactions on uranium in a nuclear reactor. This feature is utilised to determine 239Pu fraction by the neutron coincidence technique. Assume that upon assaying two PuBe sources of the same total Pu content but different 239Pu fractions. On the basis of the R/T–MPu relationship described in [1], the same R/T obtained corresponds to the same the total Pu content, however, different R and T values are observed. If we represent these sources in a new dimension system R/T–T the single point on R/T–MPu curve will split into two points. If we represent a lot of PuBe neutron sources
on R/T–T, the sources with the sample value of 239Pu fraction will be grouped on one curve. By this way a system of R/T–T curves will be structured. In this paper we show, how to derive two parameters of 239Pu fraction and total Pu content due to the system of R/T–T curves. 2. Determining 239 Pu fraction and Pu content by neutron coincidence technique Random neutrons emitted from 9Be(a,n)12C reaction interact with the material in the source by Pu(n,f) and Be(n,2n) reactions [7,8]. By this way, these primary neutrons induce the time-correlated secondary neutrons, which can be measured by neutron coincidence technique. Using a simple model [1], we have shown that the R/T ratio normalized for parameters of detector, (R/T)norm, is a function of the total Pu content, MPu: ln M Pu ; ðR=T Þnorm ¼ 1:787M 0:44þ0:024 Pu
ð1Þ
where T norm ¼ Rnorm ¼
T ; e0
ð2Þ R ; eG=s Þ
e2f eP =s ð1
ðR=T Þnorm ¼
Rnorm : T norm
ð3Þ ð4Þ
Here e0 and ef is the absolute detector efficiency for primary and fission neutrons, respectively, P is predelay, G is the coincidence gate length and s is the detector die-away time. Assuming a linear dependence of the isotopic abundances mi of 238Pu, 240Pu, 241Pu, 242Pu and 241Am on the 239 Pu component, m239, i.e. mi = ai + bi * m239, the total neutron specific yield, y = Ryimi (now i runs over the Pu isotopes and Am, from 1 to 6) also can be represented in the same way: y ¼ yðm239 Þ ¼ a þ b m239 n=s-gPu:
ð5Þ
Using the isotopic composition determined by gammaspectrometry (see Fig. 1), the specific neutron yields [2,3] and a correction factor 1.26 [5] taking into account the systematic error in specific neutron yields, the values a and b are found to be (21.4 ± 2.1) · 105 and (0.214 ± 0.01) · 105 n/s-g Pu, respectively. In general, the total specific neutron yield y of a source is derived from the output rate of primary neutrons, N0, or of total neutron output, N and the total mass, MPu y¼
Fig. 1. 238Pu, 240Pu, 241Pu, 242Pu and 241Am isotopic abundances versus 239 Pu isotopic abundance in eight PuBe sources [5].
N0 ðN =M 1 Þ ¼ ; M Pu M Pu
ð6Þ
where M1 is the neutron self-multiplication factor. In case of small Pu content, the neutron self-multiplication can be assumed to be negligible, i.e. M1 = 1. For larger Pu contents the values of M1 can be derived, for example, by correcting M1 using the secondary neutron by coincidence technique [3] or by the calculation model presented in [1].
C.T. Nguyen et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 75–80
Eq. (6) can be re-written in the form M Pu ¼
N =M 1 : a þ b m239
ð7Þ
and
By inserting (7) to formula (1), a new correlation N =M 1 0:44þ0:024 ln aþbm 239 N =M 1 ðR=T Þnorm ¼ 1:787 a þ b m239
ð8Þ
is obtained. Mathematically, if we know the values of (R/T)norm and N by measurement, we can derive the values m239 from formula (8), y from (5) and MPu from (7). This procedure, in which the isotopic composition and Pu content can at the same time be determined only by neutron counting technique, can be called R/T–T method. This method can be used out graphically in the following steps: • Plot the (R/T)norm versus Tnorm = N according to Eq. (10) with various m239 values of 70–100% in the system of frame R/T and T. Fig. 2 shows the curves with steps of, for example, 5%. • For assaying a PuBe source, normalize the measured R and T to receive (R/T)norm and Tnorm = N, which creates a point with co-ordinates [(R/T)norm, N]. • Comparing this point with the above system of curves gives the value m239. Then y and MPu can be estimated by formulae (5) and (7), respectively. The accuracy of the method can be estimated by comparing m239 and MPu derived by the R/T–T method, mR/TT and MR/TT, with those measured by gammaspectrometry and calorimetry. The double (R) and single (T) count rates were measured by the commercial neutron coincidence collar type JCC-13, the thermal power by a heat flow calorimeter, ANTECH SSCal-1 [6]. The uncertainty of R/T–T method, r, can be calculated from the formula
.
.
.
.
.
Fig. 2. Relationship R/T-T at different
239
rm ¼
rM ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i uP h mR=T T mc 2 u t mc k1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i uP h M R=T T M CAL 2 u t M CAL k1
77
ð9Þ
ð10Þ
for the abundance of 239Pu component mc by gamma spectrometry and for the total mass MCAL, determined by calorimetry, respectively. Here k is the number of PuBe sources measured. The values of r for 13 sources were calculated and found to be about 2% for mR/TT and 15% for MR/TT. 3. Application to other transuranium neutron sources In transuranium neutron sources as AmBe, 238PuBe and AmLi the secondary neutrons are also induced by fission reactions and can be determined by a neutron coincidence collar. Because the parameters of neutron energy spectra [9], the values of fission cross section of AmBe, 238PuBe [10,11] are close to those of 239PuBe sources, Eq. (1) for PuBe can be also used for AmBe and 238PuBe in the first approach. However, the specific neutron yields y are different among one another, therefore, the curves R/T–T were split into different curves corresponding each type of the sources. Since the energy spectrum of AmLi sources [9] is shifted below the fission threshold of Am [10], the measured R/T is smaller than that of AmBe sources by a factor of about an order of magnitude. In general, we can describe all transuranium neutron sources by the equation below: BþC ln N=My 1 N =M 1 ðR=T Þnorm ¼ A : ð11Þ y Here the set of {A, B, C and y} are experimental parameters of a type of sources.
.
Pu fractions.
Fig. 3. Ratio R/T as a function of total count rate T of some neutron sources measured by the detector of 2.8% efficiency.
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4. Measurement time as function of the detector efficiency The measurement time tm is a very important parameter from application viewpoints. The statistical uncertainty is determined first of all by the measured double count rate Rm. The uncertainty equation can be written as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rm þ 2GT 2m DRm pffiffiffiffiffi D¼ ¼ ; ð12Þ Rm t m Rm where Tm is the measured total count rate. The values R and T corrected for counting dead times dt and dc were calculated from Rm and Tm [9] by the equations R ¼ Rm e d t T m ; Fig. 4. [R/T, T] data plots of individual sources fitting the curves calculated for similar types of sources. The data were measured by the detector of 28% efficiency (JCC-13).
1
10
0
R/T
10
10
10
2Ge2edC N 0 ðDÞ
2
2 ðR=T Þnorm ½eeP =s ð1
eG=s Þ
2
:
ð14Þ
On the basis of this formula, we studied tm as a function of detector efficiency for PuBe sources, with relative errors D = 1, 2, 5 and 10%. Detector parameters were dc = 1 · 106 + 0.5 · 1012Tm (s1) and dc = 0.5 · 106 + 0.25 · 1012Tm (s1), P = 10, G = 80 and s = 70 ls, nearly the used ones. The results are shown in Figs. 6 and 7 for a weak and a strong source, respectively. A third set of parameters was also included in the calculation: dc = 0.12 · 106 + 0.06 · 1012 Tm (s1), P = 10, G = 64 and s = 50 ls and the results are also shown. Some remarks are appropriate to be made:
-1
-2
ð13Þ
The measurement time tm, as a function of detector efficiency, of the required relative error D and other characteristics of detector and the source, reads from this as tm ¼
10
T ¼ T m edc T m :
AmBe
-3
AmLi 10
-4
Fig. 5. Ratio R/T as a function of T – data from [13].
• For assaying a source of low neutron output, the detector efficiency should be as high as possible, for example, JCC-13 of 28% efficiency. • In case of high neutron output, the measurement time will get a minimum at a detector efficiency, which
The measured R/T and T by 2.8% detector efficiency for PuBe [2], AmBe, 238PuBe and AmLi sources [12] are plotted in Fig. 3 together with those of fission 244Cm and 252 Cf sources. We note that the ratios R/T of spontaneous fission 244Cm and 252Cf sources are constant. Fig. 4 plot the R/T as a function of T of transuranium neutron sources measured by 28% detectors efficiency (JCC-13). The R/T– T of AmBe and AmLi of [13] were also plotted in Fig. 5. All date show that the co-ordinate values [(R/T)norm, Tnorm] (while Tnorm = N) depend on the parameters of the type of sources. For example, in Fig. 4 each plotted point corresponds to a particular source. It means that the type of the source can be identified by the particular curve; the point fits and its parameters (m239 for PuBe, neutron output and MTru content) can be estimated by the procedure described above.
Fig. 6. Calculated measurement time as function of detector efficiency for a PuBe neutron source of 1 g Pu, 76% 239Pu and 6 · 105 n/s output.
10
-5
10
1
10
2
10
3
10
4
10
5
T
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79
instead of 30–35% by the R/T-method. In other words, the measurement may be performed in a short time. 6. Conclusion
Fig. 7. Calculated measurement time as function of detector efficiency for a PuBe neutron source of 17 g Pu, 76% 239Pu and 1.2 · 107 n/s output.
depends on detector parameters such as dead time, dieaway time. According to the calculation, JCC-13 is not suitable for assaying sources above 3 · 106 n/s neutron output. • Lower dc allows higher detector efficiency at minimum measuring time. • Reducing the error of Rm by only one percent leads to essential increase of the measurement time.
A development work for characterizing PuBe and transuranium neutron sources using neutron coincidence technique has been described. Due to the fact of a correlation among Pu isotopic abundances, the pair of parameters [(R/T)norm, Tnorm] (while Tnorm = N) can be used for estimating both Pu isotopic composition and Pu content by the R/T–T method. Up to now the assay of PuBe and other neutron sources has required gamma spectrometry for identifying the type of the sources, then quantitatively assaying them by different NDA methods [12,13]. Based on the R/T–T correlation, a neutron source can be fully characterized by one neutron measurement. This achievement extends the application of coincidence technique to fully safeguarding transuranium neutron sources. About 200 PuBe sources in Hungary and also a good deal of them in a series of countries may be the object of serial measurements for such a fully characterizing assay. Acknowledgements
The calculation described above is still a rough approach. However, it helps us to choose or build a neutron coincidence collar for assaying PuBe sources; moreover, to discuss advantages of the R/T–T method in the next section.
This work was supported by the Hungarian Atomic Energy Authority under contracts No. OAH-ANI-ABA-16/ 01, -04/02, -04/03 and -01/04. The authors gratefully thank the IAEA and EC JRC Ispra for making available a shift register for complementing the equipment built at the Institute of Isotopes and the neutron coincidence collar type JCC-13 for test purposes, respectively.
5. Advantages of the R/T–T method
References
In case of R/T-method, the uncertainty reported in [1] for estimating Pu content was about 15%. However, the error of Rm requires less than 3–5%. When the DR increases, for example, using the data of the detector of 2.8% efficiency, with an error in Rm of about 7–10%, the error of R/T method may reach 30–35%. Using the R/T– MPu calibration curve, one can see that it requires a long measurement time to suppress DRm below 2–5%. By the graphical method it can be shown that the uncertainty of m239 was 2–3% even if DRm reaches 5–10%. Then, the Pu content was estimated by Eq. (12) with an error of about 15–20%. This error depends on Pu isotopic correlation, i.e. on the precision of Eq. (5) mainly. Reducing the error of Rm to below 2–3%, which requires a very long measuring time, the error of m239 can be reduced to below 1–2%. However, the uncertainty of the Pu content is not improved very much and is still about 15%. It means that the R/T–T method does not need long measurement time. For example, using the R/T–T method to assay by the detector of 2.8% efficiency with DRm of about 5–10%, even 15%, the error of Pu content now is reduced to below 20%
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