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Determination of the emission rate of an Am–Be neutron source with a Bonner sphere spectrometer
Radiation Measurements 45 (2010) 1271e1275
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Determination of the emission rate of an AmeBe neutron source with a Bonner sphere spectrometer R. Méndez-Villafañe a, *, J.M. Los Arcos Merino a, E. Gallego Díaz b, A. Lorente Fillol b a b
Ionizing Radiation Standard Laboratory LMRI, CIEMAT, Av. Complutense 22, E02.P0.16, E-28040 Madrid, Spain Nuclear Engineering Laboratory, Universidad Politécnica de Madrid (UPM), ETS Ing. Industriales, José Gutiérrez Abascal 2, E-28006 Madrid, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 November 2009 Received in revised form 31 August 2010 Accepted 22 September 2010
The Neutron Measurements Laboratory of the Technical University of Madrid (LMN) has an automated panoramic irradiator with a 111 GBq 241AmeBe neutron source installed in a bunker-type large room. This facility is going to be used for calibration purposes. Recently, a spectrometry campaign involving four research groups working with different Bonner Sphere Spectrometers (BSS) and using different spectral unfolding codes was carried out. As part of these measurements the emission rate, B(t), was estimated. The application of the generalized fitting method to account for the scattering contribution is difficult due to specific characteristics of the neutron installation. A reduced fitting method, which includes room-return and in-scatter, has instead been used to overcome this problem. Detailed Monte Carlo simulations (with MCNPX code) were also performed to estimate the fluence rate using the measured source strength value. This was performed at different points. Results were then compared with measurements. Finally, the ambient dose equivalent rate measured with a neutron monitor (LB6411) was compared with results using the BSS. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Emission rate Neutron source AmeBe Bonner sphere spectrometer Monte Carlo simulation
1. Introduction The Neutron Measurements Laboratory (LMN) of the Technical Engineering University of Madrid (UPM) wants to become a secondary standard laboratory for neutron calibration. This laboratory will be traced to the Spanish primary standard laboratory at CIEMAT in Madrid, which is under construction at this moment. The LMN has an uncalibrated 111 GBq 241AmeBe neutron source installed in a bunker-type room with dimensions of 9 m 16 m 8 m and 50 cm thick concrete walls (Gallego et al., 2004). In the future, this source will be calibrated using the manganese bath technique at CIEMAT. In the meantime however, its emission rate is estimated with BSS. Recently an international comparison with four spectrometers from UPM, UAB (Universidad Autónoma de Barcelona), CIEMAT and INFN (Insituto Nazionale di Fisica Nucleare, Italy) was held at this installation (Gallego et al., 2009). The LMN has a set of 6 spheres and a 4 mm 4 mm Ludlum 6LiI:Eu neutron detector. This
* Corresponding author. Tel.: þ34 91 346 6097; fax: þ34 91 346 6442. E-mail address: [email protected] (R. Méndez-Villafañe). 1350-4487/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2010.09.004
laboratory also uses the BUNKI unfolding code (Lowry and Johnson, 1984) with the UTA4 matrix collapsed to 25 energy groups. The INFNeBSS has a set of 7 spheres (which allows 9 different configurations) and a 6LiI:Eu neutron detector. Besides this they use the FRUIT code (Bedogni et al., 2007) for unfolding with its own response matrix. The UABeBSS is composed of 8 spheres with a cylindrical 3He (type 05NH1 by Eurisys) detector which allows 11 different configurations. This group uses the FRUIT code and its own response matrix. Finally, the CIEMATeBSS has 12 spheres with a spherical 3He detector. The CIEMAT uses the UMG 3.3 unfolding package (Reginatto and Goldhagen, 1999) with its own response matrix calculated and validated by the PTB. As part of this comparison, the source strength was estimated. Usually this magnitude is measured making use of several shadow cones. This procedure allows one to isolate the direct contribution from the backscattered contribution. However, at the time, not enough shadow cones were available to use this measurement procedure. The other alternative was the generalized fit interpolation method used in the calibration processes of neutron monitors in some laboratories. This technique however, is not directly applicable to Bonner spheres and requires a very large irradiation bench. For these reasons a new fit model based on the generalized method has been applied. Monte Carlo simulations with the MCNPX code were used to check its consistency.
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2. Material and methods
MC ðlÞ ¼
As neutron sources are not placed in empty space, they are affected by the walls, floor, roof, air and all the surrounding measurement structures. All the scattering contributions, room scatter, air out and in-scatter and scatter by structures, were accounted for in a correction factor. The determination of the source emission rate has to be based on measurements of the unperturbed term also known as the direct contribution. It is not possible to get it directly and several methods have been developed to separate the primary and the scattering contributions. This is the fundamental problem in all the calibration processes. Two methods are usually used to overcome this issue: the shadow cone technique and the generalized fit method. These methods, originally developed for calibration purposes, may be adapted to solve the problem of the source strength calculation. 2.1. Shadow cones method
BðtÞF1 ðqÞ FA ðlÞ 4pl2
(1)
This is possible if the shadow cones technique is used and the corrected measurement is obtained from the difference between the measurement without (MT(l)) and with the shadow cones (MS(l)) (Eq. (2)),
Mc ðlÞ ¼ ½MT ðlÞ MS ðlÞFA ðlÞ
(2)
The shadow cones have to be specifically designed to be used with the Bonner spheres following the ISO recommendations (ISO 8529-2, 1998a, 1998b). They are placed between the source and the detector, so that the entire detector is shadowed by the cone and only indirect contribution can reach it. In order to get this, the minimum detector-source distance has to be at least twice the shadow cone length. Besides, if the sizes of the largest spheres are also considered, the measurement points will start at approximately 115 cm from the source. The farthest point in the UPM installation is around 2 m from the neutron source. Hence, the number of distances measurable is very limited. It is also worth to mention that the shadow over the detector has to be less than twice the detector surface. This condition forces one to have three or four shadow cones to cover a set of ten or twelve Bonner spheres. These reasons decrease the versatility and flexibility of the application of the shadow cone technique and was therefore not the method of choice used for the measurements presented in this work. 2.2. Generalized fit method The generalized fit method proposes a semi-empirical function (Eq. (3)) that takes into account all the possible perturbations of the direct contribution. The reading of a device due to the total radiation field M(l) is then given as the product of the measured reading corrected for all perturbation effects MC(l) and these effects expressed as F3(l).
MðlÞ ¼ MC ðlÞF3 ðlÞ
(3)
Taking into account that MC(l) is the direct contribution from the neutron source, this may be written as:
(4)
where B is the neutron source emission rate and F(q) is the source anisotropy correction factor. The function F3(l) corrects for the inverse square law. This term can be rewritten as follows:
F3 ðlÞ ¼
F1 ðlÞ þ F20 ðlÞ 1 FA ðlÞ
(5)
where F1(l) is a geometry factor which accounts for the finite size of the neutron source; FA(l) is the air attenuation correction factor; and F0 2(l) is the correction function which considers the additional contribution coming form inscattered neutrons. The geometry correction refers a spherical source which irradiates a spherical detector. This may be determined as a mathematical function:
F1 ¼ 1 þ
The determination of the source emission rate, B(t), obtained from a set of measurements may be carried out easily taking into account the inverse square distance 1/l2 decay being l the distance (Eq. (1)). F1(q) is the anisotropy factor and FA(l) is the air attenuation factor. The corrected measurement MC is the neutron fluence rate.
MC ðlÞ ¼
BFðqÞ 4pl2
a4
(6)
ð1 þ a5 LÞ2
with:
L ¼
l rS rD rD
(7)
where l is the distance from the source centre to the detector centre and rD and rS are the detector and source radii respectively. Recommended values for a small 252Cf and for a 241AmeBe source are a4 ¼ 0.29 0.02 and a5 ¼ 1.79 0.02 for the usual survey meters dimensions (rD z 10 cm). The air attenuation correction factor may be expressed by the following equation:
FA ðlÞ ¼ expðlSðEÞÞ
(8)
Finally, the inscattered neutrons may be represented by the expression:
F20 ðlÞ ¼ 1 þ A0 l þ sl2
(9)
This leads to a complex equation (Eq. (10)) with five parameters. A detailed description of this equation is provided in the literature (ISO 8529-2, 1998a, 1998b and Kluge et al., 1990). As recommended by the ISO, the use of this method implies a huge amount of measurements at different distances (30 or more points) in order to get good statistics. With Bonner spheres, measurements very close to the source are not practical and therefore a large irradiator bench is necessary.
MðlÞ ¼
Bf ðqÞ 4pl2
1þ
a4 expðSðEÞlÞ þ A0 l þ sl2 ð1 þ a5 LÞ
(10)
In conclusion, the generalized fit method is not applicable in this case. The reduced-fitting method (Eq. (11)) may be an alternative procedure but involves a drastic simplification and therefore leads to significant inaccuracies. Furthermore, as this method does not take scattering effects into consideration, the variation of experimental values and theoretical values with distance from the source is very different.
MðlÞ ¼
A 4pl2
(11)
Another intermediate fitting method has been proposed to solve the problem. This can be expressed as a simplification of the generalized fit method.
R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275
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Table 1 Comparison between fluence rate measurements with CIEMATeBSS and fluence rate simulations with MCNPX using the source strength obtained with the simplified generalized method. Position [cm]
CIEMATeBSS $
F½cm2 s1 80 100 115 130 150
87.6 60.8 48.1 39.4 31.1
MðlÞ ¼
Fig. 1. Total measured fluence rate, and fast, intermediate, and thermal neutron contributions.
2.3. Simplified generalized fit method From the generalized-fit method (Eq. (10)) a simplified version has been used (Eq. (17)). This approximation takes into account the 1/l2 drop off as well as the “room-return” and “in-scatter” corrections. First of all, the geometry correction may be approximated to the unity. For l/rD > 2 this term can be simplified as:
F1 ðlÞ ¼ 1 þ d
r 2 D
2l
(13)
where the quantity d z 0.5 0.1. Then, the second term of the equation is very small for the different points chosen and may be neglected. If the air-attenuation correction is considered negligible for the measurement points, these simplifications give an intermediate equation:
MðlÞ ¼
i Bf ðqÞh 1 þ A0 l þ sl2 2 4pl
(14)
Then can be written as:
Fig. 2. Total contribution with the simplified generalized fit and the fast neutron contribution with a 1/l2 fit.
0.9 0.6 0.5 0.4 0.4
MCNPX $
F½cm2 s1 87.2 60.7 47.9 39.9 31.5
Bf ðqÞ A0 þ þs l 4pl2
2.6 1.9 1.5 1.2 0.9
(15)
in this equation one is left with three components namely a 1/4pl2 term affecting the source emission rate which describes the variation of the uncollided or direct neutron fluence; a 1/l term due to air-scattering; and finally a component independent of l due to room-return neutrons. In order to obtain the source strength, B, one possibility may be to fit the uncollided neutron component with the first term. However, there is no method to obtain this direct contribution from the measured spectrum. Another option is to assume that A0 is negligible. This hypothesis is based on the Reduced-Fitting Method, (Eq. (11)) or (16). However it introduces significant statistical uncertainties. Therefore, a simplified version of the generalized fitting method has been proposed.
MðlÞ ¼
Bf ðqÞ þs 4pl2
(16)
Knowing the spectrum, it can be assumed that the room-return component is the sum of the thermal and epithermal neutron contributions (Fthþep ¼ 4.76 0.12 cm2s1). This consideration allows us to rewrite a new equation:
M0 ðlÞ ¼
Að1 þ BlÞ 4pl2
(17)
where M0 (l) is now the measured magnitude of the fluence rate, but limited to the fast neutron contribution. The A parameter is the product of the source emission rate, B(t), and the source anisotropy correction factor, f(q), while the parameter B includes the air in-scatter corrections. Thus, the
Fig. 3. MCNP simulation and fit of the simplified generalized method.
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R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275
uncorrected measurements, M(l), allows us to determine the source strength B(t). The anisotropy correction factor is considered usually in the 90 direction (ISO 8529-2, 1998a, 1998b). Data measured at the NPL for a 111 GBq 241AmeBe neutron source (Bardell et al., 1998) provided a value of F90 ¼ 1.04 0.01 which was used in this work. The use of only two parameters reduces the number of measurement points required to fit the experimental results. In fact, the emission rate is calculated from a set of five measurements with the appropriate statistics. This simplified form of the generalized method may then be an alternative when shadow cones are not available.
simulation is an update based on previous published results of simulations of the laboratory (Gallego et al., 2004). With this model, the fluence rate at several points along the irradiator bench was calculated. The point closest to the source was 3 cm and the furthest was 200 cm. A total number of 28 points were simulated. The MCNP results are always by default normalized by source particle. Therefore, it was necessary to multiply them by the previously estimated emission rate in order to get the fluence rate. The uncertainties are the quadratic sum of the uncertainty associated to the estimated emission rate and the statistical uncertainties obtained from simulation. In Table 1 the results obtained with simulation are compared with measurements using the BSS. A good agreement is observed. A new fit was made to the total number of simulated measurement points (Fig. 3). This provided an emission rate for the MCNP simulation of B(t) ¼ (5.60 0.33) 106 s1, Which was used to check the consistency of measurements and simulations. Moreover, comparisons of the ambient dose equivalent rate at these points between CIEMATeBSS measurements and neutron monitor based on a 3He active proportional counter, LB6411, have been carried out and are shown in Table 2 which also shows good agreement.
3. Results
4. Conclusions
The fluence rate is obtained at five distances with the CIEMATeBSS. From the neutron spectra the total, thermal, intermediate and fast contributions are shown at Fig. 1. Fig. 2 shows the fast contribution of the neutron fluence rate. Several fitting methods have been applied. From this figure, it is obvious that this component does not decay with the inverse square of the distance (factor 1/l2) but is perturbed by scattering effects. The reduced fitting method gives an acceptable result but the proposed method fits even better. Hence, the fast fluence rate is fitted using the simplified generalized fit method (Eq. (17)) and from this method the emission rate is determined with its associated uncertainty, and compared to the nominal value. The nominal source strength corrected for decay is 6.23 106. No uncertainty associated to this value is estimated since the source is more than 40 years old and is no longer calibrated. From the above described approximation, the result obtained from the fit is B(t) ¼ (5.48 0.18) 106 s1 with a reduced c2 ¼ 1.98. The fitting procedure was carried out using the weighted leastsquare method, where the weighting factor chosen was the reciprocal of the neutron fluence variance. The uncertainty is obtained with k ¼ 1. These results have been compared with Monte Carlo simulations (using MCNPX) and measurements with a neutron monitor (model LB6411).
The determination of the emission rate from measurements with Bonner spheres is not trivial. Nowadays, the method recommended most is based on the use of a set of shadow cones that allows for the subtraction of the backscatter contribution. However, it is necessary to have three or four cones to cover all the spheres. When the specific number of shadow cones is not available, a different method has to be investigated. The use of the generalized fit method requires a large amount of measurements over the distance (not less than thirty). This is clearly time consuming. An alternative method which overcomes these problems has been proposed in this work. This method is based on a simplification of the generalized fit method and makes use of the known spectrum. The simplified generalized fit method accounts for the scattering effects and allows the direct determination of the source strength when other methods, such as shadow cone techniques or the generalized fit method are not available. The results agreed with those from the detailed Monte Carlo MCNP simulation of the installation model and with measurements performed with a neutron monitor.
Table 2 $ Comparison between H* ð10Þ rate measurements with CIEMATeBSS and LB6411. Position [cm]
CIEMATeBSS $
H* ð10Þ½mSvh1 80 100 115 130 150
120.16 81.58 63.55 50.56 38.48
2.20 1.09 0.74 0.59 0.52
LB6411 $
H* ð10Þ½mSvh1 120.13 79.50 61.31 49.25 38.37
0.55 0.77 0.82 1.63 2.15
3.1. Comparison with MCNP simulation and measurements A detailed MCNPX (Briesmeister, 2000 and Laurie, 2005) simulation of the installation has been carried out in order to compare with this method. The origin of co-ordinates used in the model is the source centre. Details of the facility included were: the source and capsule geometry, the positioning pneumatic system and all the bench structures. The surrounding walls, floor and ceiling have been modeled using a typical concrete composition. The number of histories executed was large enough to obtain an uncertainty of less than 5% in each energy bin of the spectra. This
References Bardell, A.G., Burke, M., Hunt, J.B., Tagziria, H., Thomas, D.J., 1998. Anisotropy of Emission from Radionuclide Neutron Sources. Report CIRM 24. NPL. Bedogni, R., Domingo, C., Esposito, A., Fernández, F., 2007. FRUIT: an operational tool for multisphere neutron spectrometry in workplaces. Nucl. Instrum. Methods A 580, 1301e1309. Briesmeister, J.F. (Ed.), 2000. MCNP e A General Monte Carlo N-Particle Transport Code, Version 4B. National Laboratory Report LA-13709-M, Los Alamos. Gallego, E., Lorente, A., Vega-Carrillo, H.R., 2004. Characteristics of the neutron field of the facility at DINeUPM. Radiat. Prot. Dosim. 110 (1e4), 73e79. Gallego, E., Amgarou, K., Bedogni, R., Domingo, C., Esposito, A., Lorente, A., Méndez, R., Vega-Carrillo, H.R., 2009. Characterization of an 241AmeBe neutron field by different spectrometric techniques. NEUDOS-11. International Organization for Standardization, Draft International Standard, Reference Neutron Radiations: Calibration Fundamentals Related to the Basic Quantities Characterizing the Radiation Field. ISO 8529-2.DIS, 24 February 1998a. International Organization for Standardization, Draft International Standard, Reference Neutron Radiations: Characteristics and Methods of Production. ISO 8529-1.DIS, 24 February 1998b.
R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275 Kluge, H., Weise, K., Hunt, J.B., 1990. Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes. Radiat. Prot. Dosim. 32, 233e244. Laurie, S.Waters (Ed.), 2005. MCNPX User’s Manual, Version 2.5.0. National Laboratory Report LA- CP-05e0369, Los Alamos.
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Lowry, K.A., Johnson, T.L., 1984. Modifications to Iterative Recursion Unfolding Algorithms and Computer Codes to Find More Appropriate Neutron Spectra. Memorandum report 5340. US Naval Research Laboratory NRL, Washington, DC. Reginatto, M., Goldhagen, P., 1999. MAXED, a computer code for maximum entropy deconvolution of multisphere neutron spectrometer data. Health Phys. 77, 579.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Determination of the emission rate of an AmeBe neutron source with a Bonner sphere spectrometer R. Méndez-Villafañe a, *, J.M. Los Arcos Merino a, E. Gallego Díaz b, A. Lorente Fillol b a b
Ionizing Radiation Standard Laboratory LMRI, CIEMAT, Av. Complutense 22, E02.P0.16, E-28040 Madrid, Spain Nuclear Engineering Laboratory, Universidad Politécnica de Madrid (UPM), ETS Ing. Industriales, José Gutiérrez Abascal 2, E-28006 Madrid, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 November 2009 Received in revised form 31 August 2010 Accepted 22 September 2010
The Neutron Measurements Laboratory of the Technical University of Madrid (LMN) has an automated panoramic irradiator with a 111 GBq 241AmeBe neutron source installed in a bunker-type large room. This facility is going to be used for calibration purposes. Recently, a spectrometry campaign involving four research groups working with different Bonner Sphere Spectrometers (BSS) and using different spectral unfolding codes was carried out. As part of these measurements the emission rate, B(t), was estimated. The application of the generalized fitting method to account for the scattering contribution is difficult due to specific characteristics of the neutron installation. A reduced fitting method, which includes room-return and in-scatter, has instead been used to overcome this problem. Detailed Monte Carlo simulations (with MCNPX code) were also performed to estimate the fluence rate using the measured source strength value. This was performed at different points. Results were then compared with measurements. Finally, the ambient dose equivalent rate measured with a neutron monitor (LB6411) was compared with results using the BSS. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Emission rate Neutron source AmeBe Bonner sphere spectrometer Monte Carlo simulation
1. Introduction The Neutron Measurements Laboratory (LMN) of the Technical Engineering University of Madrid (UPM) wants to become a secondary standard laboratory for neutron calibration. This laboratory will be traced to the Spanish primary standard laboratory at CIEMAT in Madrid, which is under construction at this moment. The LMN has an uncalibrated 111 GBq 241AmeBe neutron source installed in a bunker-type room with dimensions of 9 m 16 m 8 m and 50 cm thick concrete walls (Gallego et al., 2004). In the future, this source will be calibrated using the manganese bath technique at CIEMAT. In the meantime however, its emission rate is estimated with BSS. Recently an international comparison with four spectrometers from UPM, UAB (Universidad Autónoma de Barcelona), CIEMAT and INFN (Insituto Nazionale di Fisica Nucleare, Italy) was held at this installation (Gallego et al., 2009). The LMN has a set of 6 spheres and a 4 mm 4 mm Ludlum 6LiI:Eu neutron detector. This
* Corresponding author. Tel.: þ34 91 346 6097; fax: þ34 91 346 6442. E-mail address: [email protected] (R. Méndez-Villafañe). 1350-4487/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2010.09.004
laboratory also uses the BUNKI unfolding code (Lowry and Johnson, 1984) with the UTA4 matrix collapsed to 25 energy groups. The INFNeBSS has a set of 7 spheres (which allows 9 different configurations) and a 6LiI:Eu neutron detector. Besides this they use the FRUIT code (Bedogni et al., 2007) for unfolding with its own response matrix. The UABeBSS is composed of 8 spheres with a cylindrical 3He (type 05NH1 by Eurisys) detector which allows 11 different configurations. This group uses the FRUIT code and its own response matrix. Finally, the CIEMATeBSS has 12 spheres with a spherical 3He detector. The CIEMAT uses the UMG 3.3 unfolding package (Reginatto and Goldhagen, 1999) with its own response matrix calculated and validated by the PTB. As part of this comparison, the source strength was estimated. Usually this magnitude is measured making use of several shadow cones. This procedure allows one to isolate the direct contribution from the backscattered contribution. However, at the time, not enough shadow cones were available to use this measurement procedure. The other alternative was the generalized fit interpolation method used in the calibration processes of neutron monitors in some laboratories. This technique however, is not directly applicable to Bonner spheres and requires a very large irradiation bench. For these reasons a new fit model based on the generalized method has been applied. Monte Carlo simulations with the MCNPX code were used to check its consistency.
1272
R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275
2. Material and methods
MC ðlÞ ¼
As neutron sources are not placed in empty space, they are affected by the walls, floor, roof, air and all the surrounding measurement structures. All the scattering contributions, room scatter, air out and in-scatter and scatter by structures, were accounted for in a correction factor. The determination of the source emission rate has to be based on measurements of the unperturbed term also known as the direct contribution. It is not possible to get it directly and several methods have been developed to separate the primary and the scattering contributions. This is the fundamental problem in all the calibration processes. Two methods are usually used to overcome this issue: the shadow cone technique and the generalized fit method. These methods, originally developed for calibration purposes, may be adapted to solve the problem of the source strength calculation. 2.1. Shadow cones method
BðtÞF1 ðqÞ FA ðlÞ 4pl2
(1)
This is possible if the shadow cones technique is used and the corrected measurement is obtained from the difference between the measurement without (MT(l)) and with the shadow cones (MS(l)) (Eq. (2)),
Mc ðlÞ ¼ ½MT ðlÞ MS ðlÞFA ðlÞ
(2)
The shadow cones have to be specifically designed to be used with the Bonner spheres following the ISO recommendations (ISO 8529-2, 1998a, 1998b). They are placed between the source and the detector, so that the entire detector is shadowed by the cone and only indirect contribution can reach it. In order to get this, the minimum detector-source distance has to be at least twice the shadow cone length. Besides, if the sizes of the largest spheres are also considered, the measurement points will start at approximately 115 cm from the source. The farthest point in the UPM installation is around 2 m from the neutron source. Hence, the number of distances measurable is very limited. It is also worth to mention that the shadow over the detector has to be less than twice the detector surface. This condition forces one to have three or four shadow cones to cover a set of ten or twelve Bonner spheres. These reasons decrease the versatility and flexibility of the application of the shadow cone technique and was therefore not the method of choice used for the measurements presented in this work. 2.2. Generalized fit method The generalized fit method proposes a semi-empirical function (Eq. (3)) that takes into account all the possible perturbations of the direct contribution. The reading of a device due to the total radiation field M(l) is then given as the product of the measured reading corrected for all perturbation effects MC(l) and these effects expressed as F3(l).
MðlÞ ¼ MC ðlÞF3 ðlÞ
(3)
Taking into account that MC(l) is the direct contribution from the neutron source, this may be written as:
(4)
where B is the neutron source emission rate and F(q) is the source anisotropy correction factor. The function F3(l) corrects for the inverse square law. This term can be rewritten as follows:
F3 ðlÞ ¼
F1 ðlÞ þ F20 ðlÞ 1 FA ðlÞ
(5)
where F1(l) is a geometry factor which accounts for the finite size of the neutron source; FA(l) is the air attenuation correction factor; and F0 2(l) is the correction function which considers the additional contribution coming form inscattered neutrons. The geometry correction refers a spherical source which irradiates a spherical detector. This may be determined as a mathematical function:
F1 ¼ 1 þ
The determination of the source emission rate, B(t), obtained from a set of measurements may be carried out easily taking into account the inverse square distance 1/l2 decay being l the distance (Eq. (1)). F1(q) is the anisotropy factor and FA(l) is the air attenuation factor. The corrected measurement MC is the neutron fluence rate.
MC ðlÞ ¼
BFðqÞ 4pl2
a4
(6)
ð1 þ a5 LÞ2
with:
L ¼
l rS rD rD
(7)
where l is the distance from the source centre to the detector centre and rD and rS are the detector and source radii respectively. Recommended values for a small 252Cf and for a 241AmeBe source are a4 ¼ 0.29 0.02 and a5 ¼ 1.79 0.02 for the usual survey meters dimensions (rD z 10 cm). The air attenuation correction factor may be expressed by the following equation:
FA ðlÞ ¼ expðlSðEÞÞ
(8)
Finally, the inscattered neutrons may be represented by the expression:
F20 ðlÞ ¼ 1 þ A0 l þ sl2
(9)
This leads to a complex equation (Eq. (10)) with five parameters. A detailed description of this equation is provided in the literature (ISO 8529-2, 1998a, 1998b and Kluge et al., 1990). As recommended by the ISO, the use of this method implies a huge amount of measurements at different distances (30 or more points) in order to get good statistics. With Bonner spheres, measurements very close to the source are not practical and therefore a large irradiator bench is necessary.
MðlÞ ¼
Bf ðqÞ 4pl2
1þ
a4 expðSðEÞlÞ þ A0 l þ sl2 ð1 þ a5 LÞ
(10)
In conclusion, the generalized fit method is not applicable in this case. The reduced-fitting method (Eq. (11)) may be an alternative procedure but involves a drastic simplification and therefore leads to significant inaccuracies. Furthermore, as this method does not take scattering effects into consideration, the variation of experimental values and theoretical values with distance from the source is very different.
MðlÞ ¼
A 4pl2
(11)
Another intermediate fitting method has been proposed to solve the problem. This can be expressed as a simplification of the generalized fit method.
R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275
1273
Table 1 Comparison between fluence rate measurements with CIEMATeBSS and fluence rate simulations with MCNPX using the source strength obtained with the simplified generalized method. Position [cm]
CIEMATeBSS $
F½cm2 s1 80 100 115 130 150
87.6 60.8 48.1 39.4 31.1
MðlÞ ¼
Fig. 1. Total measured fluence rate, and fast, intermediate, and thermal neutron contributions.
2.3. Simplified generalized fit method From the generalized-fit method (Eq. (10)) a simplified version has been used (Eq. (17)). This approximation takes into account the 1/l2 drop off as well as the “room-return” and “in-scatter” corrections. First of all, the geometry correction may be approximated to the unity. For l/rD > 2 this term can be simplified as:
F1 ðlÞ ¼ 1 þ d
r 2 D
2l
(13)
where the quantity d z 0.5 0.1. Then, the second term of the equation is very small for the different points chosen and may be neglected. If the air-attenuation correction is considered negligible for the measurement points, these simplifications give an intermediate equation:
MðlÞ ¼
i Bf ðqÞh 1 þ A0 l þ sl2 2 4pl
(14)
Then can be written as:
Fig. 2. Total contribution with the simplified generalized fit and the fast neutron contribution with a 1/l2 fit.
0.9 0.6 0.5 0.4 0.4
MCNPX $
F½cm2 s1 87.2 60.7 47.9 39.9 31.5
Bf ðqÞ A0 þ þs l 4pl2
2.6 1.9 1.5 1.2 0.9
(15)
in this equation one is left with three components namely a 1/4pl2 term affecting the source emission rate which describes the variation of the uncollided or direct neutron fluence; a 1/l term due to air-scattering; and finally a component independent of l due to room-return neutrons. In order to obtain the source strength, B, one possibility may be to fit the uncollided neutron component with the first term. However, there is no method to obtain this direct contribution from the measured spectrum. Another option is to assume that A0 is negligible. This hypothesis is based on the Reduced-Fitting Method, (Eq. (11)) or (16). However it introduces significant statistical uncertainties. Therefore, a simplified version of the generalized fitting method has been proposed.
MðlÞ ¼
Bf ðqÞ þs 4pl2
(16)
Knowing the spectrum, it can be assumed that the room-return component is the sum of the thermal and epithermal neutron contributions (Fthþep ¼ 4.76 0.12 cm2s1). This consideration allows us to rewrite a new equation:
M0 ðlÞ ¼
Að1 þ BlÞ 4pl2
(17)
where M0 (l) is now the measured magnitude of the fluence rate, but limited to the fast neutron contribution. The A parameter is the product of the source emission rate, B(t), and the source anisotropy correction factor, f(q), while the parameter B includes the air in-scatter corrections. Thus, the
Fig. 3. MCNP simulation and fit of the simplified generalized method.
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R. Méndez-Villafañe et al. / Radiation Measurements 45 (2010) 1271e1275
uncorrected measurements, M(l), allows us to determine the source strength B(t). The anisotropy correction factor is considered usually in the 90 direction (ISO 8529-2, 1998a, 1998b). Data measured at the NPL for a 111 GBq 241AmeBe neutron source (Bardell et al., 1998) provided a value of F90 ¼ 1.04 0.01 which was used in this work. The use of only two parameters reduces the number of measurement points required to fit the experimental results. In fact, the emission rate is calculated from a set of five measurements with the appropriate statistics. This simplified form of the generalized method may then be an alternative when shadow cones are not available.
simulation is an update based on previous published results of simulations of the laboratory (Gallego et al., 2004). With this model, the fluence rate at several points along the irradiator bench was calculated. The point closest to the source was 3 cm and the furthest was 200 cm. A total number of 28 points were simulated. The MCNP results are always by default normalized by source particle. Therefore, it was necessary to multiply them by the previously estimated emission rate in order to get the fluence rate. The uncertainties are the quadratic sum of the uncertainty associated to the estimated emission rate and the statistical uncertainties obtained from simulation. In Table 1 the results obtained with simulation are compared with measurements using the BSS. A good agreement is observed. A new fit was made to the total number of simulated measurement points (Fig. 3). This provided an emission rate for the MCNP simulation of B(t) ¼ (5.60 0.33) 106 s1, Which was used to check the consistency of measurements and simulations. Moreover, comparisons of the ambient dose equivalent rate at these points between CIEMATeBSS measurements and neutron monitor based on a 3He active proportional counter, LB6411, have been carried out and are shown in Table 2 which also shows good agreement.
3. Results
4. Conclusions
The fluence rate is obtained at five distances with the CIEMATeBSS. From the neutron spectra the total, thermal, intermediate and fast contributions are shown at Fig. 1. Fig. 2 shows the fast contribution of the neutron fluence rate. Several fitting methods have been applied. From this figure, it is obvious that this component does not decay with the inverse square of the distance (factor 1/l2) but is perturbed by scattering effects. The reduced fitting method gives an acceptable result but the proposed method fits even better. Hence, the fast fluence rate is fitted using the simplified generalized fit method (Eq. (17)) and from this method the emission rate is determined with its associated uncertainty, and compared to the nominal value. The nominal source strength corrected for decay is 6.23 106. No uncertainty associated to this value is estimated since the source is more than 40 years old and is no longer calibrated. From the above described approximation, the result obtained from the fit is B(t) ¼ (5.48 0.18) 106 s1 with a reduced c2 ¼ 1.98. The fitting procedure was carried out using the weighted leastsquare method, where the weighting factor chosen was the reciprocal of the neutron fluence variance. The uncertainty is obtained with k ¼ 1. These results have been compared with Monte Carlo simulations (using MCNPX) and measurements with a neutron monitor (model LB6411).
The determination of the emission rate from measurements with Bonner spheres is not trivial. Nowadays, the method recommended most is based on the use of a set of shadow cones that allows for the subtraction of the backscatter contribution. However, it is necessary to have three or four cones to cover all the spheres. When the specific number of shadow cones is not available, a different method has to be investigated. The use of the generalized fit method requires a large amount of measurements over the distance (not less than thirty). This is clearly time consuming. An alternative method which overcomes these problems has been proposed in this work. This method is based on a simplification of the generalized fit method and makes use of the known spectrum. The simplified generalized fit method accounts for the scattering effects and allows the direct determination of the source strength when other methods, such as shadow cone techniques or the generalized fit method are not available. The results agreed with those from the detailed Monte Carlo MCNP simulation of the installation model and with measurements performed with a neutron monitor.
Table 2 $ Comparison between H* ð10Þ rate measurements with CIEMATeBSS and LB6411. Position [cm]
CIEMATeBSS $
H* ð10Þ½mSvh1 80 100 115 130 150
120.16 81.58 63.55 50.56 38.48
2.20 1.09 0.74 0.59 0.52
LB6411 $
H* ð10Þ½mSvh1 120.13 79.50 61.31 49.25 38.37
0.55 0.77 0.82 1.63 2.15
3.1. Comparison with MCNP simulation and measurements A detailed MCNPX (Briesmeister, 2000 and Laurie, 2005) simulation of the installation has been carried out in order to compare with this method. The origin of co-ordinates used in the model is the source centre. Details of the facility included were: the source and capsule geometry, the positioning pneumatic system and all the bench structures. The surrounding walls, floor and ceiling have been modeled using a typical concrete composition. The number of histories executed was large enough to obtain an uncertainty of less than 5% in each energy bin of the spectra. This
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