- Email: [email protected]
Activation foils unfolding for neutron spectrometry: Comparison of different deconvolution methods
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425 www.elsevier.com/locate/nima
Activation foils unfolding for neutron spectrometry: Comparison of different deconvolution methods S.P. Tripathya,, C. Sunila, M. Nandyb, P.K. Sarkara,c, D.N. Sharmaa, B. Mukherjeed a
Radiation Safety Systems Division, BARC, Mumbai 400085, India Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India c Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India d Deutsches Elektronen-Synchrotron, LLRF Group, D-22607 Hamburg, Germany b
Received 15 July 2007; received in revised form 8 September 2007; accepted 17 September 2007 Available online 29 September 2007
Abstract The results obtained from the activation foils measurement are unfolded using two different deconvolution methods such as BUNKI and genetic algorithm (GA). The spectra produced by these codes agree fairly with each other and are comparable with that measured previously for the same system using NE213 liquid scintillator and by unfolding the neutron-induced proton pulse height distribution using two different methods, viz. FERDOR and BUNKI. The details of various unfolding procedures used in this work are reported in this paper. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Pb; Qc Keywords: Neutron spectrometry; Activation foil; Unfolding; BUNKI; Genetic algorithm
1. Introduction Precise knowledge on neutron spectrometry is highly essential for all dosimetry-related studies as well as many nuclear physics experiments. The current interest in neutron spectrometry has stimulated the development of several deconvolution procedures like BUNKI [1], FRUIT [2], MAXED [3], GRAVEL [4], ANDI-03 [5], etc. to attain improved energy resolution through spectrum unfolding. Several unfolding procedures combined with various types of experimental methods have been reported in the recent past [2,6–9]. All these competing methods have their own merits and demerits over each other in terms of energy resolution, useful energy range, neutron detector efficiency, and response functions. However, neutron detection in the presence of other radiations such as gamma, X-rays, etc. Corresponding author. Tel.: +91 22 25592012.
E-mail addresses: [email protected], [email protected] (S.P. Tripathy). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.09.028
demands the use of detectors which are insensitive to radiations other than neutrons. Therefore, the radioactivation methods are used extensively for measuring neutron fluences [10–12]. Being a passive method, this method also addresses the problem of measuring neutrons in the presence of pulsed radiation fields, where the active detectors lose their reliability. This method is based on the fact that, after the neutron-induced nuclear reactions such as (n,p), (n,g), (n,a), (n,f), etc., the reaction products are radioactive, many of which are usually gamma emitters. Cross-section of each of these reactions has a characteristic energy dependence. Hence, the total activity of a particular type gives a measure of the neutron fluence in a given energy range. Since the neutron energy spreads over a wide range, no single detector can cover the entire domain. The spectrum can be measured with a set of several such activation foils (a multi-detector system) [13] with distinct responses to different energy windows. The response matrix is then based on the evaluated excitation functions of the reactions employed [14]. The irradiated foils or wires are counted separately after the irradiation,
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
422
usually with gamma spectrometric methods [15]. A highresolution HPGe detector could be used for the purpose, and the yield of several nuclides from even the same activation foil [14] is measured. This method is often used for neutron flux distributions in reactors, accelerators, and in space (at high altitudes) due to the reaction specificity, simplicity of measurement, insensitivity to other radiation components, and the relative easiness in constructing the response matrix for the unfolding purposes [16–20]. A lot of experience is necessary to unfold neutron spectra using these codes. A large number of issues can arise such as multiple stable solutions, a unique solution with negative parts, and oscillating behaviour or spurious peaks appearing after a number of iterations. It is thus recommended to use multiple codes to unfold the same spectrum. In the present work, an attempt has been made to obtain the spectral information of fast neutrons using a set of multi-reactive activation foils with different threshold energies and then by unfolding the neutron-induced activities with different methods, viz. BUNKI, and genetic algorithm (GA). The unfolded spectra are compared with that measured previously for the same system using NE213 liquid scintillator and by unfolding the neutron-induced proton pulse height distribution using two different methods, viz. FERDOR and BUNKI. 2. Materials and methods Fast neutrons were generated from the interaction of 20 MeV protons with Cu target at the 14 UD Pelletron facility of BARC-TIFR, India. A total of 13 reactions were explored from 9 activation foils (Table 1). With an average neutron flux of 3.7 106 cm2 s1, the irradiation time (42 h) was sufficient to induce measurable activities in the foils (100 diameter, 1 mm thickness) which were placed at 901 angle with respect to the incident proton beam. The
induced activities of the product radionuclides were measured with a low-background HPGe spectrometer coupled with a data station. Measured count rates were corrected for the usual experimental errors, dead time, gamma-ray branching ratio, detector efficiency, and isotopic abundance to obtain the actual activities at the end of the irradiation (see Table 1). The excitation functions obtained from the cross-section values of the latest report of ENDF/B-VII.0 library were used to construct the response matrix, which summarises the detector response as a function of incident neutron energy and provides basis for the unfolding process. The final spectra obtained by different methods were compared with that measured previously for the same system using NE213 liquid scintillator, and by unfolding the neutroninduced proton pulse height distribution. This comparison of neutron spectra obtained from various methods provides a more correct estimate of the solution spectrum. This work also emphasises the importance of using more than one unfolding method to obtain an acceptable and well-resolved neutron spectrum. 3. Unfolding procedure The measured yield of a radionuclide is the convolution of the neutron energy distribution with the response function of the spectrometer summed over the interaction energy range. The spectral information needs to be unfolded from these detector responses by using any suitable computational codes such as BUNKI, MAXED, GA, etc., based on several methods like least square, iterative, Monte-Carlo, neural network, etc. At any given angle, the measured activity of a particular type is related to the neutron spectrum by Z Aj ¼ N j sj ðEÞFj ðEÞ dE (1)
Table 1 Details of activation foils, and the induced reactions, along with other important parameters needed for activity measurement at the TIFR pelletron accelerator Foil
Wt (g)
Reaction
Mg Al Ti
1.4131 4.4994 7.1755
24
Fe
7.6523
Co Ni Cu Zn
0.5263 7.5087 8.9727 4.7574
In
1.8955
24
Mg(n,p) Na Al(n,a)24Na 46 Ti(n,p)46Sc 47 Ti(n,p)47Sc 48 Ti(n,p)48Sc 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 59 Co(n,p)59Fe 58 Ni(n,p)58Co 65 Cu(n,p)65Ni 64 Zn(n,p)64Cu 66 Zn(n,2n)65Zn 115 In(n,n’)115Inm 27
T1/2 (h)
Eth (Eff) MeV
Eg MeV
BI (%)
Z (%)
A0 (Bq)
1.496E+1 1.496E+1 2.011E+3 8.028E+1 4.367E+1 7.491E+3 2.580E+0 1.068E+3 1.702E+3 2.520E+0 1.270E+1 5.861E+3 4.490E+0
6.1 5.6 3.2 0.9 5.0 1.7 5.0 3.1 1.3 3.3 1.7 11.4 0.34
1.37 1.37 1.12 0.16 0.98 0.83 0.85 1.29 0.81 1.48 0.51 1.12 0.34
100.0 100.0 99.99 67.91 100.0 99.98 98.9 43.21 99.45 23.59 35.7 50.6 45.82
2.4 2.4 2.81 10.4 3.11 3.52 3.48 2.51 3.59 2.25 5.0 2.82 6.62
5.635E+2 9.991E+2 1.010E+1 3.273E+2 1.323E+2 7.300E+0 9.397E+2 1.050E+1 3.616E+2 1.042E+2 4.791E+3 1.560E+1 5.358E+4
Wt ¼ weight of the samples, T1/2 ¼ product half-life, Eth (Eff) ¼ effective threshold energy, Eg ¼ g-energy, BI ¼ branching intensity, Z ¼ efficiency, A0 ¼ activity at the end of irradiation.
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
where Aj is the activity of the jth detector, sj(E) is the reaction cross-section of the jth detector (in cm2/atom) as a function of E, Fj (E) is the energy-dependent neutron flux density (cm2 s1). Furthermore, Nj is the total number of atoms in the sample is given by N j ¼ ðN A ki wÞ=aj
(2)
where, NA ¼ Avogadro’s number, ki ¼ isotopic abundance of jth species in the foil, w ¼ weight of the foil (g), and aj ¼ atomic weight of the jth species. Eq. (1) represents a Fredholm’s integral equation of the first kind without any unique solution, because a finite number of discrete measurements cannot define a continuous function. In real calculations, the discrete form of Eq (1) is used: Aj ¼
n X
sj ðE i ÞFj ðE i Þ
(3)
i¼1
where i ¼ 1,y,n: the energy bins; j ¼ 1,y,m: the detectors (reactions). The response matrix was formed by multiplying the total number of atoms (in the sample) with cross-section data (taken from the cross-section library of the ENDFB/VII.0) and then arranging them into 51 energy groups over the entire energy range on an evenly spaced logarithmic scale. The number of detectors that could reasonably be used in this type of measurements is generally much lower than the number of the energy points, thereby creating an underdetermined system of equations. The number of energy intervals was chosen so as to produce response up to a maximum expected energy, since in this type of underdetermined problem a larger energy interval may give spurious results as it tries to conserve the total number of neutrons over the entire range of available energy. In the case of underdetermined problems, the unfolding programs generally make use of ‘a-priori’ information that constitutes the best approximation to the output to be determined. The accuracy of the unfolding results may strongly be dependent on how close the input solution is to the true distribution on one hand, and the efficiency of the adjustment procedure on the other hand. In the present work, ‘a-priori’ information was supplied (wherever needed) in the form of a Maxwellian and 1/E initial trial spectrum from which the solution spectrum is determined. A GA was also used to search for the ‘best’ spectrum within the band of neutron fluence ranging upto 107 cm2 s1 with and without using a guess spectrum. 3.1. Unfolding with BUNKI The activity values along with the associated errors and the response matrix were processed through an iterative unfolding method (BUNKI) based on BON algorithm to determine neutron energy distribution. The algorithm is described below.
423
In the matrix form, Eq. (3) can be written as A¼RU
(4)
where A is the vector of activities in all the detectors, U is the unknown neutron spectrum, and R is the response matrix. For iterative solution, Eq. (4) is multiplied by the transposed matrix RT to yield RT A ¼ RT R U, or Y ¼ X U, with Y ¼ RT A, X ¼ RT R. A physically relevant solution can be reached with the ðkÞ n iteration, Uðkþ1Þ ¼ ðY j UðkÞ j j Þ=Sj¼1 ; ðX j Uj Þ, where k is the iteration step. The solution is not very sensitive to the initial guess U(0), which favours the situations where ‘a-priori’ information is not enough [13]. In this work, a total of 2000 iterative steps were to be followed to obtain the final neutron distribution. 3.2. Unfolding with genetic algorithm The GA [4,21] emulates the ‘survival of the fittest’ strategy to find out the best possible solution vector (neutron spectrum) from a large number of prospective solutions when the following conditions are reached: P ((AMeas–AGA)2)All foil species=4Minimum F(Ei)40, where i=1,y,n is the number of energy bins. These activities of the daughter products were inverse calculated using a GA, with the ‘‘Goal’’ set as the ‘‘minimum residue’’ of the measured and inverse calculated activity vectors. 4. Results and discussion It can be seen from Table 1 that a total of 13 reactions were explored from 9 activation foils. The multiple reactions induced in some detectors were useful in supplying additional data points, which enhanced the quality of the final spectrum. The product nuclides monitored were 24Na, 46,47,48Sc, 54,56Mn, 59Fe, 58Co, 65Ni, 64 Cu, 65Zn, 115In. Fig. 1 shows the energy distribution of fast neutrons generated from 20 MeV protons hitting a natCu target at BARC-TIFR pelletron. The spectrum obtained by the activation foil method and unfolded with BUNKI is compared with that obtained previously by NE213 liquid scintillator and unfolded with two codes FERDOR and BUNKI. Even the same unfolding method (BUNKI) used for two different types of measurements (i.e., NE213 and activation foil) produces slight difference towards the higher side of the spectrum, which could possibly be due to the absence of more activation foils with threshold values lying in this region of energy. However, the distribution matches fairly in other parts of the spectrum. It can also be seen from Fig. 1 that the spectra obtained by two different unfolding codes (i.e., BUNKI and FERDOR) for the same system of measurement (NE213) differ slightly. Moreover, the spectrum unfolded with FERDOR remains softer at both the lower and higher ends. Nevertheless,
ARTICLE IN PRESS 424
S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
Fig. 1. Energy distribution of fast neutrons generated from 20 MeV protons hitting the natCu target at BARC-TIFR pelletron. The spectrum obtained by the activation foil method (unfolded with BUNKI) is compared with that obtained previously by NE213 liquid scintillators (unfolded with FERDOR and BUNKI). The error bars indicate a 68% confidence interval.
the shapes of all spectra generated by each method match very well with each other, though the NE213 measurements unfolded with BUNKI remains harder by more than 20% towards the higher side of the spectrum than that obtained by FERDOR. The unfolding code BUNKI exploits a Maxwell spectrum with suitable neutron temperature as start-up (guess) kernel. It is well known that neutrons produced by the interaction of low-energy protons with copper target (this case) are ‘‘evaporation neutrons’’ possessing a Maxwellian energy distribution, whereas the position of the energy peak depends on the primary proton energy and the atomic weight of the target material [22]. The GA method does not depend much on the initial guess (Fig. 2), so it is highly useful in situations where the a-priori informations are not enough. However, the inclusion of a suitable (1/E) guess spectrum in the present GA could make the unfolding procedure faster, requiring much less computation time. In this case the characteristics of the unfolded spectrum would solely depend on the correctness of the guess spectrum. The implementation of a guess spectrum is mandatory for common unfolding codes like BUNKI or MAXED. The neutron cross-section data (same as response matrix) is a vital parameter in the GA-based spectra unfolding method. Consequently, the goodness of unfolded spectra primarily depends on the accuracies in cross-section data. The results vindicate the GA as a reliable spectra-unfolding tool. Both the figures reveal the fact that all spectra fairly agree with each other though they differ in details. The slight discrepancies at some energy points could be due to the inherent errors associated in the experiments as well as the uncertainties involved in the unfolding procedures. The most significant source of uncertainty in spectra unfolding lies evidently in the accuracy of the cross-section data, on the estimated activation products, selection of a
Fig. 2. Neutron spectrum generated by GA (with and without guess spectrum) from the activation foils data. The spectra are compared with that obtained with BUNKI. The error bars indicate a 68% confidence interval.
proper unfolding method (either multi- or few-channel depending on the over- or underdetermined nature of the problem), and a-priori information. So, the unfolding codes are not to be used as a ‘black box’ and the user needs some working experience to select the proper method of unfolding. It is therefore useful to unfold the same set of results by more than one method. Neutron spectrometry by passive methods using activation foils was employed successfully to study the neutron spectrum around the TIFR pelletron accelerator. The fact that the high-resolution HPGe detector could be used successfully to measure more than one nuclide from even the same activation foil has made it possible to explore several reactions simultaneously. Thus, by exposing a few foils, a well-resolved spectrum can be obtained. The proper combination of the multi-foil activation method and a suitable unfolding code can characterise the neutron flux density per unit energy from the measurements. From these distributions, it is observed that the high-energy contribution is small, and above 10 MeV it falls off by a factor of more than 60. From the shape of the spectrum it appears that the evaporation process dominates, and there is some non-equilibrium contribution. Work is in progress to develop a simple ‘response matrix generator’ for the activation foil unfolding, and to unfold the results using different unfolding methods and algorithms, as well as to develop a more user-friendly unfolding code. Acknowledgements The authors are thankful to the staff of BARC-TIFR pelletron for their help during irradiation, and to Dr. Anil Kumar for his valuable help in measurements with HPGe. The support of Anil Shanbag throughout the work is highly appreciated. The encouragement from Dr. H.S. Kushwaha, Director, Health, Safety and Environment group, is gratefully acknowledged.
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
References [1] K.A. Lowry, T.L. Johnson, NRL Memorandum Report 5340, Naval Research Laboratory, Washington, DC, 1984. [2] R. Bedogni, A. Esposito, C. Domingo, F. Ferna´ndez, M. J. Garcia, M. Angelone, Radiat. Prot. Dosim. Advance access 10.1093/rpd/ ncm071 (2007). [3] M. Reginatto, P. Goldhagen, EML-595, Environmental Measurements Laboratory, New York, 1998. [4] M. Matzke, Report PTB-N-19, Physikalisch-Technische Bundesanstalt, Braunschweig, 1994. [5] B. Mukherjee, Radiat. Prot. Dosim. 110 (2004) 249. [6] H.R. Vega-Carrillo, V.M. Herna´ndez-Da´vila, E. Manzanares-Acun˜a, G.A. Mercado, E. Gallego, A. Lorente, W.A. Perales-Mun˜oz, J.A. Robles-Rodrı´ guez, Radiat. Prot. Dosim. 118 (2006) 251. [7] A. Seghour, F.Z. Seghour, Nucl. Instr. and Meth. A 555 (2005) 347. [8] N.J. Roberts, Radiat. Prot. Dosim. Advance access (2007) 1–6. [9] T. Niedermayr, I.D. Hau, A. Burger, U.N. Roy, Z.W. Bell, S. Friedrich, Nucl. Instr. and Meth. A (2007). [10] P.R. Byerly, in: J.B. Marion, J.F. Fowler (Eds.), Fast Neutron Physics, Part 1, Interscience, New York, 1960, p. 657.
425
[11] L. Kuijpers, R. Herzing, P. Cloth, D. Filges, R. Hecker, Nucl. Instr. and Meth. 144 (1977) 215. [12] J.H. Baard, W.L. Zijp, H.J. Nolthenius, Nuclear Data Guide for Reactor Neutron Dosimetry, Kluwer Academic, Dordrecht, The Netherlands, 1989. [13] J.T. Roulti, J.V. Sandberg, Radiat. Prot. Dosim. 20 (1985) 103–110. [14] F.D. Brooks, H. Klein, Nucl. Instr. and Meth. A 476 (2002) 1. [15] G.F. Knoll, Radiation detection and measurement, 3rd ed, Wiley, 2000, 744. [16] G.S. Hurst, J.A. Harter, P.N. Hensley, W.A. Mills, M. Slater, P.W. Reinhardt. Rev. Sci. Instr 27 (1956) 153. [17] P.D. Holt, Radiat. Prot. Dosim. 10 (1964) 251. [18] B.J. Mijnheert, H. Haringat, H.J. Nolthenius, W.L. Zijp, Phys. Med. Biol. 26 (1981) 641. [19] G. Gualdrini, R. Bedogni, E. Fantuzzi, F. Mariotti, Radiat. Prot. Dosim. 110 (2004) 465. [20] A. Zanini, M. Storini, L. Visca, E.A.M. Durisi, F. Fasolo, M. Perosino, O. Borla, O. Saavedra, J. Atmos. Sol. Terrestr. Phys. 67 (2005) 755. [21] B. Mukherjee, Nucl. Instr. and Meth. A 432 (1999) 305. [22] J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, Wiley, New York, 1952, 365.
Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425 www.elsevier.com/locate/nima
Activation foils unfolding for neutron spectrometry: Comparison of different deconvolution methods S.P. Tripathya,, C. Sunila, M. Nandyb, P.K. Sarkara,c, D.N. Sharmaa, B. Mukherjeed a
Radiation Safety Systems Division, BARC, Mumbai 400085, India Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India c Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India d Deutsches Elektronen-Synchrotron, LLRF Group, D-22607 Hamburg, Germany b
Received 15 July 2007; received in revised form 8 September 2007; accepted 17 September 2007 Available online 29 September 2007
Abstract The results obtained from the activation foils measurement are unfolded using two different deconvolution methods such as BUNKI and genetic algorithm (GA). The spectra produced by these codes agree fairly with each other and are comparable with that measured previously for the same system using NE213 liquid scintillator and by unfolding the neutron-induced proton pulse height distribution using two different methods, viz. FERDOR and BUNKI. The details of various unfolding procedures used in this work are reported in this paper. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Pb; Qc Keywords: Neutron spectrometry; Activation foil; Unfolding; BUNKI; Genetic algorithm
1. Introduction Precise knowledge on neutron spectrometry is highly essential for all dosimetry-related studies as well as many nuclear physics experiments. The current interest in neutron spectrometry has stimulated the development of several deconvolution procedures like BUNKI [1], FRUIT [2], MAXED [3], GRAVEL [4], ANDI-03 [5], etc. to attain improved energy resolution through spectrum unfolding. Several unfolding procedures combined with various types of experimental methods have been reported in the recent past [2,6–9]. All these competing methods have their own merits and demerits over each other in terms of energy resolution, useful energy range, neutron detector efficiency, and response functions. However, neutron detection in the presence of other radiations such as gamma, X-rays, etc. Corresponding author. Tel.: +91 22 25592012.
E-mail addresses: [email protected], [email protected] (S.P. Tripathy). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.09.028
demands the use of detectors which are insensitive to radiations other than neutrons. Therefore, the radioactivation methods are used extensively for measuring neutron fluences [10–12]. Being a passive method, this method also addresses the problem of measuring neutrons in the presence of pulsed radiation fields, where the active detectors lose their reliability. This method is based on the fact that, after the neutron-induced nuclear reactions such as (n,p), (n,g), (n,a), (n,f), etc., the reaction products are radioactive, many of which are usually gamma emitters. Cross-section of each of these reactions has a characteristic energy dependence. Hence, the total activity of a particular type gives a measure of the neutron fluence in a given energy range. Since the neutron energy spreads over a wide range, no single detector can cover the entire domain. The spectrum can be measured with a set of several such activation foils (a multi-detector system) [13] with distinct responses to different energy windows. The response matrix is then based on the evaluated excitation functions of the reactions employed [14]. The irradiated foils or wires are counted separately after the irradiation,
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
422
usually with gamma spectrometric methods [15]. A highresolution HPGe detector could be used for the purpose, and the yield of several nuclides from even the same activation foil [14] is measured. This method is often used for neutron flux distributions in reactors, accelerators, and in space (at high altitudes) due to the reaction specificity, simplicity of measurement, insensitivity to other radiation components, and the relative easiness in constructing the response matrix for the unfolding purposes [16–20]. A lot of experience is necessary to unfold neutron spectra using these codes. A large number of issues can arise such as multiple stable solutions, a unique solution with negative parts, and oscillating behaviour or spurious peaks appearing after a number of iterations. It is thus recommended to use multiple codes to unfold the same spectrum. In the present work, an attempt has been made to obtain the spectral information of fast neutrons using a set of multi-reactive activation foils with different threshold energies and then by unfolding the neutron-induced activities with different methods, viz. BUNKI, and genetic algorithm (GA). The unfolded spectra are compared with that measured previously for the same system using NE213 liquid scintillator and by unfolding the neutron-induced proton pulse height distribution using two different methods, viz. FERDOR and BUNKI. 2. Materials and methods Fast neutrons were generated from the interaction of 20 MeV protons with Cu target at the 14 UD Pelletron facility of BARC-TIFR, India. A total of 13 reactions were explored from 9 activation foils (Table 1). With an average neutron flux of 3.7 106 cm2 s1, the irradiation time (42 h) was sufficient to induce measurable activities in the foils (100 diameter, 1 mm thickness) which were placed at 901 angle with respect to the incident proton beam. The
induced activities of the product radionuclides were measured with a low-background HPGe spectrometer coupled with a data station. Measured count rates were corrected for the usual experimental errors, dead time, gamma-ray branching ratio, detector efficiency, and isotopic abundance to obtain the actual activities at the end of the irradiation (see Table 1). The excitation functions obtained from the cross-section values of the latest report of ENDF/B-VII.0 library were used to construct the response matrix, which summarises the detector response as a function of incident neutron energy and provides basis for the unfolding process. The final spectra obtained by different methods were compared with that measured previously for the same system using NE213 liquid scintillator, and by unfolding the neutroninduced proton pulse height distribution. This comparison of neutron spectra obtained from various methods provides a more correct estimate of the solution spectrum. This work also emphasises the importance of using more than one unfolding method to obtain an acceptable and well-resolved neutron spectrum. 3. Unfolding procedure The measured yield of a radionuclide is the convolution of the neutron energy distribution with the response function of the spectrometer summed over the interaction energy range. The spectral information needs to be unfolded from these detector responses by using any suitable computational codes such as BUNKI, MAXED, GA, etc., based on several methods like least square, iterative, Monte-Carlo, neural network, etc. At any given angle, the measured activity of a particular type is related to the neutron spectrum by Z Aj ¼ N j sj ðEÞFj ðEÞ dE (1)
Table 1 Details of activation foils, and the induced reactions, along with other important parameters needed for activity measurement at the TIFR pelletron accelerator Foil
Wt (g)
Reaction
Mg Al Ti
1.4131 4.4994 7.1755
24
Fe
7.6523
Co Ni Cu Zn
0.5263 7.5087 8.9727 4.7574
In
1.8955
24
Mg(n,p) Na Al(n,a)24Na 46 Ti(n,p)46Sc 47 Ti(n,p)47Sc 48 Ti(n,p)48Sc 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 59 Co(n,p)59Fe 58 Ni(n,p)58Co 65 Cu(n,p)65Ni 64 Zn(n,p)64Cu 66 Zn(n,2n)65Zn 115 In(n,n’)115Inm 27
T1/2 (h)
Eth (Eff) MeV
Eg MeV
BI (%)
Z (%)
A0 (Bq)
1.496E+1 1.496E+1 2.011E+3 8.028E+1 4.367E+1 7.491E+3 2.580E+0 1.068E+3 1.702E+3 2.520E+0 1.270E+1 5.861E+3 4.490E+0
6.1 5.6 3.2 0.9 5.0 1.7 5.0 3.1 1.3 3.3 1.7 11.4 0.34
1.37 1.37 1.12 0.16 0.98 0.83 0.85 1.29 0.81 1.48 0.51 1.12 0.34
100.0 100.0 99.99 67.91 100.0 99.98 98.9 43.21 99.45 23.59 35.7 50.6 45.82
2.4 2.4 2.81 10.4 3.11 3.52 3.48 2.51 3.59 2.25 5.0 2.82 6.62
5.635E+2 9.991E+2 1.010E+1 3.273E+2 1.323E+2 7.300E+0 9.397E+2 1.050E+1 3.616E+2 1.042E+2 4.791E+3 1.560E+1 5.358E+4
Wt ¼ weight of the samples, T1/2 ¼ product half-life, Eth (Eff) ¼ effective threshold energy, Eg ¼ g-energy, BI ¼ branching intensity, Z ¼ efficiency, A0 ¼ activity at the end of irradiation.
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
where Aj is the activity of the jth detector, sj(E) is the reaction cross-section of the jth detector (in cm2/atom) as a function of E, Fj (E) is the energy-dependent neutron flux density (cm2 s1). Furthermore, Nj is the total number of atoms in the sample is given by N j ¼ ðN A ki wÞ=aj
(2)
where, NA ¼ Avogadro’s number, ki ¼ isotopic abundance of jth species in the foil, w ¼ weight of the foil (g), and aj ¼ atomic weight of the jth species. Eq. (1) represents a Fredholm’s integral equation of the first kind without any unique solution, because a finite number of discrete measurements cannot define a continuous function. In real calculations, the discrete form of Eq (1) is used: Aj ¼
n X
sj ðE i ÞFj ðE i Þ
(3)
i¼1
where i ¼ 1,y,n: the energy bins; j ¼ 1,y,m: the detectors (reactions). The response matrix was formed by multiplying the total number of atoms (in the sample) with cross-section data (taken from the cross-section library of the ENDFB/VII.0) and then arranging them into 51 energy groups over the entire energy range on an evenly spaced logarithmic scale. The number of detectors that could reasonably be used in this type of measurements is generally much lower than the number of the energy points, thereby creating an underdetermined system of equations. The number of energy intervals was chosen so as to produce response up to a maximum expected energy, since in this type of underdetermined problem a larger energy interval may give spurious results as it tries to conserve the total number of neutrons over the entire range of available energy. In the case of underdetermined problems, the unfolding programs generally make use of ‘a-priori’ information that constitutes the best approximation to the output to be determined. The accuracy of the unfolding results may strongly be dependent on how close the input solution is to the true distribution on one hand, and the efficiency of the adjustment procedure on the other hand. In the present work, ‘a-priori’ information was supplied (wherever needed) in the form of a Maxwellian and 1/E initial trial spectrum from which the solution spectrum is determined. A GA was also used to search for the ‘best’ spectrum within the band of neutron fluence ranging upto 107 cm2 s1 with and without using a guess spectrum. 3.1. Unfolding with BUNKI The activity values along with the associated errors and the response matrix were processed through an iterative unfolding method (BUNKI) based on BON algorithm to determine neutron energy distribution. The algorithm is described below.
423
In the matrix form, Eq. (3) can be written as A¼RU
(4)
where A is the vector of activities in all the detectors, U is the unknown neutron spectrum, and R is the response matrix. For iterative solution, Eq. (4) is multiplied by the transposed matrix RT to yield RT A ¼ RT R U, or Y ¼ X U, with Y ¼ RT A, X ¼ RT R. A physically relevant solution can be reached with the ðkÞ n iteration, Uðkþ1Þ ¼ ðY j UðkÞ j j Þ=Sj¼1 ; ðX j Uj Þ, where k is the iteration step. The solution is not very sensitive to the initial guess U(0), which favours the situations where ‘a-priori’ information is not enough [13]. In this work, a total of 2000 iterative steps were to be followed to obtain the final neutron distribution. 3.2. Unfolding with genetic algorithm The GA [4,21] emulates the ‘survival of the fittest’ strategy to find out the best possible solution vector (neutron spectrum) from a large number of prospective solutions when the following conditions are reached: P ((AMeas–AGA)2)All foil species=4Minimum F(Ei)40, where i=1,y,n is the number of energy bins. These activities of the daughter products were inverse calculated using a GA, with the ‘‘Goal’’ set as the ‘‘minimum residue’’ of the measured and inverse calculated activity vectors. 4. Results and discussion It can be seen from Table 1 that a total of 13 reactions were explored from 9 activation foils. The multiple reactions induced in some detectors were useful in supplying additional data points, which enhanced the quality of the final spectrum. The product nuclides monitored were 24Na, 46,47,48Sc, 54,56Mn, 59Fe, 58Co, 65Ni, 64 Cu, 65Zn, 115In. Fig. 1 shows the energy distribution of fast neutrons generated from 20 MeV protons hitting a natCu target at BARC-TIFR pelletron. The spectrum obtained by the activation foil method and unfolded with BUNKI is compared with that obtained previously by NE213 liquid scintillator and unfolded with two codes FERDOR and BUNKI. Even the same unfolding method (BUNKI) used for two different types of measurements (i.e., NE213 and activation foil) produces slight difference towards the higher side of the spectrum, which could possibly be due to the absence of more activation foils with threshold values lying in this region of energy. However, the distribution matches fairly in other parts of the spectrum. It can also be seen from Fig. 1 that the spectra obtained by two different unfolding codes (i.e., BUNKI and FERDOR) for the same system of measurement (NE213) differ slightly. Moreover, the spectrum unfolded with FERDOR remains softer at both the lower and higher ends. Nevertheless,
ARTICLE IN PRESS 424
S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
Fig. 1. Energy distribution of fast neutrons generated from 20 MeV protons hitting the natCu target at BARC-TIFR pelletron. The spectrum obtained by the activation foil method (unfolded with BUNKI) is compared with that obtained previously by NE213 liquid scintillators (unfolded with FERDOR and BUNKI). The error bars indicate a 68% confidence interval.
the shapes of all spectra generated by each method match very well with each other, though the NE213 measurements unfolded with BUNKI remains harder by more than 20% towards the higher side of the spectrum than that obtained by FERDOR. The unfolding code BUNKI exploits a Maxwell spectrum with suitable neutron temperature as start-up (guess) kernel. It is well known that neutrons produced by the interaction of low-energy protons with copper target (this case) are ‘‘evaporation neutrons’’ possessing a Maxwellian energy distribution, whereas the position of the energy peak depends on the primary proton energy and the atomic weight of the target material [22]. The GA method does not depend much on the initial guess (Fig. 2), so it is highly useful in situations where the a-priori informations are not enough. However, the inclusion of a suitable (1/E) guess spectrum in the present GA could make the unfolding procedure faster, requiring much less computation time. In this case the characteristics of the unfolded spectrum would solely depend on the correctness of the guess spectrum. The implementation of a guess spectrum is mandatory for common unfolding codes like BUNKI or MAXED. The neutron cross-section data (same as response matrix) is a vital parameter in the GA-based spectra unfolding method. Consequently, the goodness of unfolded spectra primarily depends on the accuracies in cross-section data. The results vindicate the GA as a reliable spectra-unfolding tool. Both the figures reveal the fact that all spectra fairly agree with each other though they differ in details. The slight discrepancies at some energy points could be due to the inherent errors associated in the experiments as well as the uncertainties involved in the unfolding procedures. The most significant source of uncertainty in spectra unfolding lies evidently in the accuracy of the cross-section data, on the estimated activation products, selection of a
Fig. 2. Neutron spectrum generated by GA (with and without guess spectrum) from the activation foils data. The spectra are compared with that obtained with BUNKI. The error bars indicate a 68% confidence interval.
proper unfolding method (either multi- or few-channel depending on the over- or underdetermined nature of the problem), and a-priori information. So, the unfolding codes are not to be used as a ‘black box’ and the user needs some working experience to select the proper method of unfolding. It is therefore useful to unfold the same set of results by more than one method. Neutron spectrometry by passive methods using activation foils was employed successfully to study the neutron spectrum around the TIFR pelletron accelerator. The fact that the high-resolution HPGe detector could be used successfully to measure more than one nuclide from even the same activation foil has made it possible to explore several reactions simultaneously. Thus, by exposing a few foils, a well-resolved spectrum can be obtained. The proper combination of the multi-foil activation method and a suitable unfolding code can characterise the neutron flux density per unit energy from the measurements. From these distributions, it is observed that the high-energy contribution is small, and above 10 MeV it falls off by a factor of more than 60. From the shape of the spectrum it appears that the evaporation process dominates, and there is some non-equilibrium contribution. Work is in progress to develop a simple ‘response matrix generator’ for the activation foil unfolding, and to unfold the results using different unfolding methods and algorithms, as well as to develop a more user-friendly unfolding code. Acknowledgements The authors are thankful to the staff of BARC-TIFR pelletron for their help during irradiation, and to Dr. Anil Kumar for his valuable help in measurements with HPGe. The support of Anil Shanbag throughout the work is highly appreciated. The encouragement from Dr. H.S. Kushwaha, Director, Health, Safety and Environment group, is gratefully acknowledged.
ARTICLE IN PRESS S.P. Tripathy et al. / Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425
References [1] K.A. Lowry, T.L. Johnson, NRL Memorandum Report 5340, Naval Research Laboratory, Washington, DC, 1984. [2] R. Bedogni, A. Esposito, C. Domingo, F. Ferna´ndez, M. J. Garcia, M. Angelone, Radiat. Prot. Dosim. Advance access 10.1093/rpd/ ncm071 (2007). [3] M. Reginatto, P. Goldhagen, EML-595, Environmental Measurements Laboratory, New York, 1998. [4] M. Matzke, Report PTB-N-19, Physikalisch-Technische Bundesanstalt, Braunschweig, 1994. [5] B. Mukherjee, Radiat. Prot. Dosim. 110 (2004) 249. [6] H.R. Vega-Carrillo, V.M. Herna´ndez-Da´vila, E. Manzanares-Acun˜a, G.A. Mercado, E. Gallego, A. Lorente, W.A. Perales-Mun˜oz, J.A. Robles-Rodrı´ guez, Radiat. Prot. Dosim. 118 (2006) 251. [7] A. Seghour, F.Z. Seghour, Nucl. Instr. and Meth. A 555 (2005) 347. [8] N.J. Roberts, Radiat. Prot. Dosim. Advance access (2007) 1–6. [9] T. Niedermayr, I.D. Hau, A. Burger, U.N. Roy, Z.W. Bell, S. Friedrich, Nucl. Instr. and Meth. A (2007). [10] P.R. Byerly, in: J.B. Marion, J.F. Fowler (Eds.), Fast Neutron Physics, Part 1, Interscience, New York, 1960, p. 657.
425
[11] L. Kuijpers, R. Herzing, P. Cloth, D. Filges, R. Hecker, Nucl. Instr. and Meth. 144 (1977) 215. [12] J.H. Baard, W.L. Zijp, H.J. Nolthenius, Nuclear Data Guide for Reactor Neutron Dosimetry, Kluwer Academic, Dordrecht, The Netherlands, 1989. [13] J.T. Roulti, J.V. Sandberg, Radiat. Prot. Dosim. 20 (1985) 103–110. [14] F.D. Brooks, H. Klein, Nucl. Instr. and Meth. A 476 (2002) 1. [15] G.F. Knoll, Radiation detection and measurement, 3rd ed, Wiley, 2000, 744. [16] G.S. Hurst, J.A. Harter, P.N. Hensley, W.A. Mills, M. Slater, P.W. Reinhardt. Rev. Sci. Instr 27 (1956) 153. [17] P.D. Holt, Radiat. Prot. Dosim. 10 (1964) 251. [18] B.J. Mijnheert, H. Haringat, H.J. Nolthenius, W.L. Zijp, Phys. Med. Biol. 26 (1981) 641. [19] G. Gualdrini, R. Bedogni, E. Fantuzzi, F. Mariotti, Radiat. Prot. Dosim. 110 (2004) 465. [20] A. Zanini, M. Storini, L. Visca, E.A.M. Durisi, F. Fasolo, M. Perosino, O. Borla, O. Saavedra, J. Atmos. Sol. Terrestr. Phys. 67 (2005) 755. [21] B. Mukherjee, Nucl. Instr. and Meth. A 432 (1999) 305. [22] J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, Wiley, New York, 1952, 365.