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Feasibility of a method to identify targets that are likely to contain conventional explosives
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 263 (2007) 179–182 www.elsevier.com/locate/nimb
Feasibility of a method to identify targets that are likely to contain conventional explosives W.L. Dunn *, K. Banerjee, A. Allen, J. van Meter Department of Mechanical and Nuclear Engineering, Kansas State University, 3002 Rathbone Hall, Manhattan, KS 66506, United States Available online 14 April 2007
Abstract A method to remotely identify vehicles or other targets that might be harboring conventional explosives is described. The method utilizes multiple responses from a target that is interrogated by gamma-ray and neutron pulses and employs a template-matching procedure that reduces the collected information into a figure-of-merit. The template-matching procedure seeks to identify suspect targets based on deviations between a response vector obtained from a target under scrutiny and templates from a library; the templates are characteristic of targets with known cargoes. The methodology is illustrated with simulated data and the results of preliminary experiments on simplified targets are presented. Ó 2007 Elsevier B.V. All rights reserved. PACS: 06.30.Dr; 07.85.Nc; 42.30.Sy; 78.70.Nx; 81.70.Jb Keywords: Explosives; Remote detection; Car bomb; Neutron scattering; Prompt gamma rays
1. Introduction Recent terrorism tactics involve the use of vehicles and other targets that contain explosives, which are detonated either remotely or by a participant acting as a suicide bomber. An ability to identify whether or not a given target contains conventional explosives without personnel having to inspect the target, and thus be put at-risk, would be invaluable in areas where car bombs and other explosive packages are used or suspected. The capability to quickly and accurately detect small amounts of explosive at large stand-off distances inside any type of target is beyond current technology, but it may be possible to detect a mass of explosive of several kg within a target using system components that are more than a meter from the target. In essence, the problem we address can be stated as follows. Assume that from a large population, N, of targets a small number, n, of them contain conventional explosive *
Corresponding author. Tel.: +1 785 532 5628; fax: +1 785 532 7057. E-mail address: [email protected] (W.L. Dunn).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.04.080
packages; the percentage of such ‘‘bad’’ targets is thus p ¼ 100 Nn . We seek to identify a number, m, of suspect targets that has the properties that all or most of the n bad targets are among the m suspect targets and the percentage q ¼ 100 Nm of suspect targets is relatively close to p. Thus, we are willing to tolerate some false positives in order to minimize false negatives. 2. Physical basis It is well known, e.g. [1], that most conventional explosives (such as RDX, TNT, Comp B, Comp A5, Comp C4 and PETN) contain similar proportions of hydrogen (H), carbon (C), nitrogen (N) and oxygen (O), and that these proportions differ from those for inert HCNO materials. Also, the mass densities of conventional explosives are typically higher than those of the common inert HCNO substances [2]. Most other materials, such as metals, contain elements of higher atomic number (Z) and have higher densities than either explosives or the light inert HCNO materials.
180
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182
Numerous authors have discussed the use of neutron techniques for explosive and contraband detection, e.g. see [3–8]. Neutron thermalization is a measure of hydrogen content, because neutrons lose more energy in interactions with hydrogen than with any other element. Once thermalized, neutrons also produce prompt neutron capture gamma rays in hydrogen, at 2.223 MeV, and nitrogen, at 10.38 MeV. Fast neutrons also scatter inelastically from carbon (4.43 MeV), nitrogen (1.64, 2.31, 5.11 MeV) and oxygen (6.128 MeV), giving rise to additional potential signatures (if the neutron energy is sufficiently high to excite these). The elastic scattering of fast neutrons is subject to strong resonances in carbon, nitrogen and oxygen [2]. In fact, the cross-sections for elastic scatter are generally higher than the capture or inelastic scatter cross-sections. Thus, fast neutron scatter responses also should depend on stoichiometry of the contents of a target. Recently, other techniques, such as nuclear quadrupole resonance [9], have also been investigated for the purpose of detecting hidden explosives. Gamma-ray transmission and back-scattering have long been used to measure mass density and liquid level. If the target contains a fuel tank, a pulse of gamma rays incident on the fuel tank can be used to estimate the amount of fuel on board. Two different responses from backscattered gamma rays can be used to estimate average density and, crudely, composition. We are investigating a technique to quickly identify suspect targets by employing a variety of neutron and gammaray signatures in order to generate a collection of responses that are dependent on the stoichiometry and density of the contents of a target. A collection of material that is characterized by smaller fractions of H, C and heavy elements, higher fractions of N and O, and mid-density values is a strong candidate to be an explosive.
3. Template-matching procedure We suggest a template-matching procedure that compares a vector of detector responses, R, from an unknown target with a ‘‘template,’’ S, which is a vector of detector responses typical of a similar target with known contents. By creating a database of templates – characteristic of, for instance, different vehicle types, different cargoes and different fuel levels – one can in principle detect the presence of an explosive package from the way R differs from all of the relevant templates for that target type. For generality we consider an arbitrary number K of individual responses. We assume that the total number of possible responses has been reduced to the K responses that are sensitive to the presence of explosives and further that we know the ‘‘direction’’ of the deviation from the template for each response, i.e. if an explosive package is on-board we presume we know whether a given response will be greater or less than the corresponding template response. Let S‘ be a vector of responses for a target that contains
a known cargo, where the subscript ‘ indicates a particular target configuration, i.e. S‘ ¼ ðS ‘1 S ‘2 . . . S ‘K Þ;
ð1Þ
and let R be a vector of responses for a test target, R ¼ ðR1 R2 . . . RK Þ:
ð2Þ
Further, suppose that the K responses are ordered such that for the first I of them, we expect R > S and for the remaining J of them the opposite is true; thus K = I + J. We suggest a template-matching procedure that utilizes the figure-of-merit defined by f¼
I X
ai
i¼1
Ri S ‘i ½r2 ðR
iÞ
þ
r2 ðS
‘i Þ
þ 1=2
J X j¼1
bj
S ‘j Rj ½r2 ðR
jÞ
þ r2 ðS ‘j Þ1=2
;
ð3Þ where r2 is variance and ai and bj and weight factors. This figure-of-merit will increase as deviations from the templates grow in the expected directions and will decrease, perhaps even becoming negative, as deviations from the templates grow in the unexpected directions. The specific signatures can be weighted as desired, allowing the strongest signatures to dominate. In principle, judicious use of this figure-of-merit should allow one to identify suspect vehicles. If we use templates typical of inert cargoes, we can say that any target for which jfj P f0, where f0 is a positive cut-off value, becomes a suspect target. For templates typical of targets containing explosives, jfj < f0 identifies a suspect target. The value chosen for the figure-of-merit cut-off is a measure of how certain one wishes to be that a target contains explosives. A low value of f0 reduces the false negative rate but increases the false positive rate whereas high values have the opposite effect. This process can possibly protect against counter-measures. For instance, a bomb hidden within a target and covered by lead, in order to reduce the prompt and inelastic gamma-ray signatures, would lead to a response vector that should be very different from all templates. The templatematching approach obviously allows inclusion of nonnuclear signatures, such as target weight, as well as nuclear signatures. 4. Results The MCNP code [10] was used to simulate a 2 m diameter by 2 m long cylindrical target whose long axis is along the direction of an incident beam and which is surrounded by 50 detector surfaces that cover a solid angle of 4p sr. The target contained a cylindrical package of one of sixteen generic materials – H, C, N, O, Al, Si, Cu, Fe, water, petroleum, wood/paper, glass, plastic, clothing, explosive and ammonium nitrate (as an explosive surrogate). Table 1 gives the assumed weight fractions for the HCNO compounds. We simulated monoenergetic neutron beams
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182 Table 1 Assumed weight fractions and densities of eight generic materials
181
Table 2 Gamma signatures and weight factors for simulation results
Material
H
C
N
O
q (g cm3)
Signature
Energy (MeV)
a
Water Petroleum Wood/paper Glass Plastic Clothing Generic explosive Ammonium nitrate
0.1190 0.1115 0.0475 0.0 0.0916 0.0599 0.0275 0.0500
0.0 0.6063 0.5378 0.0 0.6141 0.4511 0.2169 0.0
0.0 0.0 0.0 0.0 0.1516 0.1378 0.02940 0.3500
0.8881 0.2821 0.4147 0.5326a 0.1432 0.3511 0.4616 0.6000
1.0 0.9 1.2 2.2 0.9 0.9 1.5 1.7
H N N N N
2.223 2.317 5.11 6.128 10.83
4.219 1.0 1.0 1.0
a
Balance is silicon. 6
incident at thirteen different energies from 10 to 14 MeV and found that 8 MeV and above were ideal for exciting the desired inelastic scatter gamma rays, as shown schematically in Fig. 1 for one detector surface. We compared the seven prompt gamma and inelastic scatter gamma responses and identified preferred detector positions to obtain the maximum ratios of these signatures between inert and explosive compositions. We used simulated responses from three different detector surfaces for the five gamma signatures and weight factors identified in Table 2 and used the responses of the generic explosive as the template to obtain the following figure-of-merit values:
Water
Petroleum
Wood/ paper
SiO2
Plastic
Clothing
Ammonium nitrate
153
182
142
76.6
129
102
0.0001
These results clearly indicate that, for the simplified situation of a single material in a simple enclosure, the tem-
prompt c inelastic c inelastic c inelastic c prompt c
b 1.0
Table 3 Gamma signatures and weight factors for simulation results Signature
Energy (MeV)
a
Annihilation c Al prompt c H prompt c N inelastic c N inelastic c
0.511 1.77 2.223 2.317 5.11
1.0
b 2.0 0.5
1.0 1.0
plate-matching procedure very clearly differentiates the explosive surrogate from the inert materials. We next constructed an aluminum box 1 m on a side as a ‘‘mock-up’’ of a target, within which we could place small drums containing approximately 30 L of material. We irradiated the target with drums containing three different contents (water, aluminum and fertilizer) with a thin beam from the tangential beam tube of the TRIGA Mark II reactor at Kansas State University. A 20% Ge detector was located more than a meter from the target. Using the signatures and weight factors shown in Table 3 and the responses from the ammonium nitrate sample as our template, we obtained figure-of-merit values of 285 for water and 246 for aluminum. Again, these results clearly indicate that the fertilizer explosive surrogate is easily distinguished from the inert materials. Additional simulations in the experimental test geometry closely match measured responses, giving us confidence to proceed with simulations as a means to guide future experimental studies. 5. Discussion
Fig. 1. Simulated gamma-ray flux densities for beams of different neutron energies.
The template-matching technique allows one to detect targets whose response vectors differ from one or more library templates. We suggest using templates that are characteristic of targets containing explosives (since there are fewer explosive types than there are inert materials). Simulation and experimental results indicate that one can, in principle, identify suspect targets. Future research will investigate refinement of the template-matching procedure, investigation of additional signatures, irradiation with high-energy neutron beams and construction of templates for a range of increasingly realistic target situations. The research seeks to develop a capability to detect explosives hidden within targets from stand-off distances of several meters within short interrogation times (less than 10 s). Practically, it is likely that machine photon and
182
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182
neutron sources will be employed, in order to produce particle beams that deliver fluences of order 1010 particles cm2 at the target. Calculations suggest that such systems pose minimal radiation risk to bystanders who are not within the source beam and are removed from the target by a few meters or more. Acknowledgement This work was partially funded through the award of a contract from the United States Marine Corps Systems Command to M2 Technologies, Inc. References [1] A. Buffler, Rad. Phys. Chem. 71 (3–4) (2004) 853. [2] E.A. Hussein, M. Desrosiers, E.J. Waller, Rad. Phys. Chem. 73 (1) (2005) 7.
[3] E.M.A. Hussein, P.M. Lords, D.L. Bot, Nucl. Instr. and Meth. A 299 (1990) 453. [4] G. Vourvopoulis, F.J. Schultz, Nucl. Instr. and Meth. B 79 (1993) 585. [5] B.J. Micklich, M.K. Harper, A.H. Novick, D.L. Smith, Nucl. Instr. and Meth. A 353 (1994) 646. [6] D.R. Brown, T. Gozani, Proc. Int. Soc. Opt. Eng. 2396 (1997) 85. [7] T. Gozani, Nucl. Instr. and Meth. B 213 (2003) 460. [8] S. Blagus, D. Sudac, V. Valkovic, Nucl. Instr. and Meth. B 213 (2003) 434. [9] J.B. Miller, G.A. Barrall, Am. Scient. 93 (2004) 50. [10] J.F. Briesmeister, MCNP – A General Monte Carlo N-particle Transport Code, Los Alamos National Laboratory, LA-12625-M, Version 4C, 2000.
Nuclear Instruments and Methods in Physics Research B 263 (2007) 179–182 www.elsevier.com/locate/nimb
Feasibility of a method to identify targets that are likely to contain conventional explosives W.L. Dunn *, K. Banerjee, A. Allen, J. van Meter Department of Mechanical and Nuclear Engineering, Kansas State University, 3002 Rathbone Hall, Manhattan, KS 66506, United States Available online 14 April 2007
Abstract A method to remotely identify vehicles or other targets that might be harboring conventional explosives is described. The method utilizes multiple responses from a target that is interrogated by gamma-ray and neutron pulses and employs a template-matching procedure that reduces the collected information into a figure-of-merit. The template-matching procedure seeks to identify suspect targets based on deviations between a response vector obtained from a target under scrutiny and templates from a library; the templates are characteristic of targets with known cargoes. The methodology is illustrated with simulated data and the results of preliminary experiments on simplified targets are presented. Ó 2007 Elsevier B.V. All rights reserved. PACS: 06.30.Dr; 07.85.Nc; 42.30.Sy; 78.70.Nx; 81.70.Jb Keywords: Explosives; Remote detection; Car bomb; Neutron scattering; Prompt gamma rays
1. Introduction Recent terrorism tactics involve the use of vehicles and other targets that contain explosives, which are detonated either remotely or by a participant acting as a suicide bomber. An ability to identify whether or not a given target contains conventional explosives without personnel having to inspect the target, and thus be put at-risk, would be invaluable in areas where car bombs and other explosive packages are used or suspected. The capability to quickly and accurately detect small amounts of explosive at large stand-off distances inside any type of target is beyond current technology, but it may be possible to detect a mass of explosive of several kg within a target using system components that are more than a meter from the target. In essence, the problem we address can be stated as follows. Assume that from a large population, N, of targets a small number, n, of them contain conventional explosive *
Corresponding author. Tel.: +1 785 532 5628; fax: +1 785 532 7057. E-mail address: [email protected] (W.L. Dunn).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.04.080
packages; the percentage of such ‘‘bad’’ targets is thus p ¼ 100 Nn . We seek to identify a number, m, of suspect targets that has the properties that all or most of the n bad targets are among the m suspect targets and the percentage q ¼ 100 Nm of suspect targets is relatively close to p. Thus, we are willing to tolerate some false positives in order to minimize false negatives. 2. Physical basis It is well known, e.g. [1], that most conventional explosives (such as RDX, TNT, Comp B, Comp A5, Comp C4 and PETN) contain similar proportions of hydrogen (H), carbon (C), nitrogen (N) and oxygen (O), and that these proportions differ from those for inert HCNO materials. Also, the mass densities of conventional explosives are typically higher than those of the common inert HCNO substances [2]. Most other materials, such as metals, contain elements of higher atomic number (Z) and have higher densities than either explosives or the light inert HCNO materials.
180
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182
Numerous authors have discussed the use of neutron techniques for explosive and contraband detection, e.g. see [3–8]. Neutron thermalization is a measure of hydrogen content, because neutrons lose more energy in interactions with hydrogen than with any other element. Once thermalized, neutrons also produce prompt neutron capture gamma rays in hydrogen, at 2.223 MeV, and nitrogen, at 10.38 MeV. Fast neutrons also scatter inelastically from carbon (4.43 MeV), nitrogen (1.64, 2.31, 5.11 MeV) and oxygen (6.128 MeV), giving rise to additional potential signatures (if the neutron energy is sufficiently high to excite these). The elastic scattering of fast neutrons is subject to strong resonances in carbon, nitrogen and oxygen [2]. In fact, the cross-sections for elastic scatter are generally higher than the capture or inelastic scatter cross-sections. Thus, fast neutron scatter responses also should depend on stoichiometry of the contents of a target. Recently, other techniques, such as nuclear quadrupole resonance [9], have also been investigated for the purpose of detecting hidden explosives. Gamma-ray transmission and back-scattering have long been used to measure mass density and liquid level. If the target contains a fuel tank, a pulse of gamma rays incident on the fuel tank can be used to estimate the amount of fuel on board. Two different responses from backscattered gamma rays can be used to estimate average density and, crudely, composition. We are investigating a technique to quickly identify suspect targets by employing a variety of neutron and gammaray signatures in order to generate a collection of responses that are dependent on the stoichiometry and density of the contents of a target. A collection of material that is characterized by smaller fractions of H, C and heavy elements, higher fractions of N and O, and mid-density values is a strong candidate to be an explosive.
3. Template-matching procedure We suggest a template-matching procedure that compares a vector of detector responses, R, from an unknown target with a ‘‘template,’’ S, which is a vector of detector responses typical of a similar target with known contents. By creating a database of templates – characteristic of, for instance, different vehicle types, different cargoes and different fuel levels – one can in principle detect the presence of an explosive package from the way R differs from all of the relevant templates for that target type. For generality we consider an arbitrary number K of individual responses. We assume that the total number of possible responses has been reduced to the K responses that are sensitive to the presence of explosives and further that we know the ‘‘direction’’ of the deviation from the template for each response, i.e. if an explosive package is on-board we presume we know whether a given response will be greater or less than the corresponding template response. Let S‘ be a vector of responses for a target that contains
a known cargo, where the subscript ‘ indicates a particular target configuration, i.e. S‘ ¼ ðS ‘1 S ‘2 . . . S ‘K Þ;
ð1Þ
and let R be a vector of responses for a test target, R ¼ ðR1 R2 . . . RK Þ:
ð2Þ
Further, suppose that the K responses are ordered such that for the first I of them, we expect R > S and for the remaining J of them the opposite is true; thus K = I + J. We suggest a template-matching procedure that utilizes the figure-of-merit defined by f¼
I X
ai
i¼1
Ri S ‘i ½r2 ðR
iÞ
þ
r2 ðS
‘i Þ
þ 1=2
J X j¼1
bj
S ‘j Rj ½r2 ðR
jÞ
þ r2 ðS ‘j Þ1=2
;
ð3Þ where r2 is variance and ai and bj and weight factors. This figure-of-merit will increase as deviations from the templates grow in the expected directions and will decrease, perhaps even becoming negative, as deviations from the templates grow in the unexpected directions. The specific signatures can be weighted as desired, allowing the strongest signatures to dominate. In principle, judicious use of this figure-of-merit should allow one to identify suspect vehicles. If we use templates typical of inert cargoes, we can say that any target for which jfj P f0, where f0 is a positive cut-off value, becomes a suspect target. For templates typical of targets containing explosives, jfj < f0 identifies a suspect target. The value chosen for the figure-of-merit cut-off is a measure of how certain one wishes to be that a target contains explosives. A low value of f0 reduces the false negative rate but increases the false positive rate whereas high values have the opposite effect. This process can possibly protect against counter-measures. For instance, a bomb hidden within a target and covered by lead, in order to reduce the prompt and inelastic gamma-ray signatures, would lead to a response vector that should be very different from all templates. The templatematching approach obviously allows inclusion of nonnuclear signatures, such as target weight, as well as nuclear signatures. 4. Results The MCNP code [10] was used to simulate a 2 m diameter by 2 m long cylindrical target whose long axis is along the direction of an incident beam and which is surrounded by 50 detector surfaces that cover a solid angle of 4p sr. The target contained a cylindrical package of one of sixteen generic materials – H, C, N, O, Al, Si, Cu, Fe, water, petroleum, wood/paper, glass, plastic, clothing, explosive and ammonium nitrate (as an explosive surrogate). Table 1 gives the assumed weight fractions for the HCNO compounds. We simulated monoenergetic neutron beams
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182 Table 1 Assumed weight fractions and densities of eight generic materials
181
Table 2 Gamma signatures and weight factors for simulation results
Material
H
C
N
O
q (g cm3)
Signature
Energy (MeV)
a
Water Petroleum Wood/paper Glass Plastic Clothing Generic explosive Ammonium nitrate
0.1190 0.1115 0.0475 0.0 0.0916 0.0599 0.0275 0.0500
0.0 0.6063 0.5378 0.0 0.6141 0.4511 0.2169 0.0
0.0 0.0 0.0 0.0 0.1516 0.1378 0.02940 0.3500
0.8881 0.2821 0.4147 0.5326a 0.1432 0.3511 0.4616 0.6000
1.0 0.9 1.2 2.2 0.9 0.9 1.5 1.7
H N N N N
2.223 2.317 5.11 6.128 10.83
4.219 1.0 1.0 1.0
a
Balance is silicon. 6
incident at thirteen different energies from 10 to 14 MeV and found that 8 MeV and above were ideal for exciting the desired inelastic scatter gamma rays, as shown schematically in Fig. 1 for one detector surface. We compared the seven prompt gamma and inelastic scatter gamma responses and identified preferred detector positions to obtain the maximum ratios of these signatures between inert and explosive compositions. We used simulated responses from three different detector surfaces for the five gamma signatures and weight factors identified in Table 2 and used the responses of the generic explosive as the template to obtain the following figure-of-merit values:
Water
Petroleum
Wood/ paper
SiO2
Plastic
Clothing
Ammonium nitrate
153
182
142
76.6
129
102
0.0001
These results clearly indicate that, for the simplified situation of a single material in a simple enclosure, the tem-
prompt c inelastic c inelastic c inelastic c prompt c
b 1.0
Table 3 Gamma signatures and weight factors for simulation results Signature
Energy (MeV)
a
Annihilation c Al prompt c H prompt c N inelastic c N inelastic c
0.511 1.77 2.223 2.317 5.11
1.0
b 2.0 0.5
1.0 1.0
plate-matching procedure very clearly differentiates the explosive surrogate from the inert materials. We next constructed an aluminum box 1 m on a side as a ‘‘mock-up’’ of a target, within which we could place small drums containing approximately 30 L of material. We irradiated the target with drums containing three different contents (water, aluminum and fertilizer) with a thin beam from the tangential beam tube of the TRIGA Mark II reactor at Kansas State University. A 20% Ge detector was located more than a meter from the target. Using the signatures and weight factors shown in Table 3 and the responses from the ammonium nitrate sample as our template, we obtained figure-of-merit values of 285 for water and 246 for aluminum. Again, these results clearly indicate that the fertilizer explosive surrogate is easily distinguished from the inert materials. Additional simulations in the experimental test geometry closely match measured responses, giving us confidence to proceed with simulations as a means to guide future experimental studies. 5. Discussion
Fig. 1. Simulated gamma-ray flux densities for beams of different neutron energies.
The template-matching technique allows one to detect targets whose response vectors differ from one or more library templates. We suggest using templates that are characteristic of targets containing explosives (since there are fewer explosive types than there are inert materials). Simulation and experimental results indicate that one can, in principle, identify suspect targets. Future research will investigate refinement of the template-matching procedure, investigation of additional signatures, irradiation with high-energy neutron beams and construction of templates for a range of increasingly realistic target situations. The research seeks to develop a capability to detect explosives hidden within targets from stand-off distances of several meters within short interrogation times (less than 10 s). Practically, it is likely that machine photon and
182
W.L. Dunn et al. / Nucl. Instr. and Meth. in Phys. Res. B 263 (2007) 179–182
neutron sources will be employed, in order to produce particle beams that deliver fluences of order 1010 particles cm2 at the target. Calculations suggest that such systems pose minimal radiation risk to bystanders who are not within the source beam and are removed from the target by a few meters or more. Acknowledgement This work was partially funded through the award of a contract from the United States Marine Corps Systems Command to M2 Technologies, Inc. References [1] A. Buffler, Rad. Phys. Chem. 71 (3–4) (2004) 853. [2] E.A. Hussein, M. Desrosiers, E.J. Waller, Rad. Phys. Chem. 73 (1) (2005) 7.
[3] E.M.A. Hussein, P.M. Lords, D.L. Bot, Nucl. Instr. and Meth. A 299 (1990) 453. [4] G. Vourvopoulis, F.J. Schultz, Nucl. Instr. and Meth. B 79 (1993) 585. [5] B.J. Micklich, M.K. Harper, A.H. Novick, D.L. Smith, Nucl. Instr. and Meth. A 353 (1994) 646. [6] D.R. Brown, T. Gozani, Proc. Int. Soc. Opt. Eng. 2396 (1997) 85. [7] T. Gozani, Nucl. Instr. and Meth. B 213 (2003) 460. [8] S. Blagus, D. Sudac, V. Valkovic, Nucl. Instr. and Meth. B 213 (2003) 434. [9] J.B. Miller, G.A. Barrall, Am. Scient. 93 (2004) 50. [10] J.F. Briesmeister, MCNP – A General Monte Carlo N-particle Transport Code, Los Alamos National Laboratory, LA-12625-M, Version 4C, 2000.