N values estimation based on photon flux simulation with Geant4 toolkit

Applied Radiation and Isotopes 136 (2018) 127–132

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Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso

N values estimation based on photon flux simulation with Geant4 toolkit a,⁎

a

Z.J. Sun , M. Danjaji , Y. Kim a b

T

b

Nuclear Engineering Program, South Carolina State University, 300 College Street NE, Orangeburg, SC 29117, USA Department of Mathematics and Computer Sciences, South Carolina State University, Orangeburg, SC 29117, USA

H I G H L I G H T S equation of N values for computer simulation was derived and Bremsstrahlung photon flux was simulated with Geant4. • The confirmed the feasibility of estimating N values before the irradiation starts with MC simulations of photon flux. • We are highly correlated with the beam parameters and the setup of the electron-photon converter. • NThisvalues • practice is valuable for radiation safety concerns before the irradiation starts.

A R T I C L E I N F O

A B S T R A C T

Keywords: Photon activation Radiation safety Geant4 N values LINAC

N values are routinely introduced in photon activation analysis (PAA) as the ratio of special activities of product nuclides to compare the relative intensities of different reaction channels. They determine the individual activities of each radioisotope and the total activity of the sample, which are the primary concerns of radiation safety. Traditionally, N values are calculated from the gamma spectroscopy in real measurements by normalizing the activities of individual nuclides to the reference reaction [58Ni(γ, n)57Ni] of the nickel monitor simultaneously irradiated in photon activation. Is it possible to use photon flux simulated by Monte Carlo software to calculate N values even before the actual irradiation starts? This study has applied Geant4 toolkit, a popular platform of simulating the passage of particles through matter, to generate photon flux in the samples. Assisted with photonuclear cross section from IAEA database, it is feasible to predict N values in different experimental setups for simulated target material. We have validated of this method and its consistency with Geant4. Results also show that N values are highly correlated with the beam parameters of incoming electrons and the setup of the electron-photon converter.

1. Introduction Photon activation analysis (PAA) is a well-established and versatile tool in nuclear and radioanalytical chemistry (Segebade et al., 1988; Segebade and Berger, 2008; Starovoitova and Segebade, 2016). After irradiating samples with high energy photons, the qualitative and quantitative information of the target nuclides can be obtained from the decay spectra of product nuclides recorded by gamma spectrometers. In recent years, this traditional technique has found new applications in agriculture, medical isotope production, archeology, cosmochemistry, environmental sciences, and nuclear physics (Sun et al., 2013, 2014; Rotsch et al., 2016; Mamtimin et al., 2013; Agar et al., 2017; Boztosun et al., 2016; Aygun et al., 2016; Tickner, 2015). In all these cases, the high-energy photon beam for activation was unanimously created by an electron LINAC via an electron-photon converter made of high Z material, such as Tungsten or Tantalum (Starovoitova and Segebade,

⁎

2016). Using Bremsstrahlung radiation as the photon source allows the irradiation achieving photon fluxes many orders of magnitude higher than traditional isotopic sources. However, since the Bremsstrahlung beam has an energy range from zero to the maximum energy of the incoming electrons, generally it creates a series of nuclear reactions in irradiation. Typically, (γ, n), (γ, 2n), (γ, 3n), (γ, p), (γ, pn) reactions all can be produced in samples. Besides these photon-induced reactions, neutron capture reactions will exist as well, since an electron-photon converter itself is also a strong neutron source (Starovoitova and Segebade, 2016). The multichannel reactions in the sample are inevitable. This situation makes the calculation of activity of end products very difficult. In some cases, the respective activity contribution from each reaction channel is hard to estimate. To compare the relative activities of the product nuclides of these multichannel reactions, N values are routinely introduced in nuclear

Corresponding author. E-mail address: [email protected] (Z.J. Sun).

https://doi.org/10.1016/j.apradiso.2018.02.017 Received 17 September 2017; Received in revised form 12 February 2018; Accepted 14 February 2018 Available online 16 February 2018 0969-8043/ © 2018 Elsevier Ltd. All rights reserved.

Applied Radiation and Isotopes 136 (2018) 127–132

Z.J. Sun et al.

activation. N value is the ratio of specific activity of the product nuclides normalized by the reference reaction [58Ni(γ, n)57Ni], which is simultaneously activated with the same experimental setup at the moment exactly one hour after irradiation. [58Ni(γ, n)57Ni] reaction is selected because Ni foil is widely used as the flux monitor in photon activation. N values can be obtained experimentally by the measurements of decay spectra of products nuclides and Ni-57. Experiments have shown that N values are highly related to the experimental setup of electron-gamma converter and the physical parameters of the incident electron beam (Sun et al., 2017). It is obvious that N values are very important in determining the individual activities of each radioisotope and the total activity of the sample, which are the primary concerns of radiation safety and work control documents. However, in reality, radiation safety and work control documents usually have to be drafted and approved before the actual experiment starts, instead of being as an after effect of irradiation. Health physicists need to know what kind of radioisotopes will be produced, what is the activity of each radioisotope is, and what the total radioactivity will be generated. Experimentally determined N values are accurate and reliable, but may be too late for radiation safety and work control documents. Based on physical setup of electron-gamma converter and parameters of the incident electron beam, could we have a good estimation of N values even before the actual irradiation starts? At present, the only feasible way is to conduct calculations with the assistance from photon flux and cross sections, which accordingly are originated from Monte Carlo simulations of photon shower with high performance computers and IAEA database of photonuclear cross sections. Monte Carlo method is a stochastic technique which uses random numbers and probability statistics to simulate physical phenomena and problems in the real world. Monte Carlo method was initially invented by the physicists at Los Alamos National Laboratory (LANL) when they investigated particle-matter interaction problems for the Manhattan project (Waters, 2002). The most popular ones in nuclear simulations are MCNPX from LNAL and Geant4 from the European Organization for Nuclear Research (CERN) (Waters, 2002; Geant4 Collaboration, 2017). As a common platform and toolkit for description of the particles passing through matter in a wide energy range, Geant4 has some irreplaceable advantage: unlike MCNPX programs completely finalized after compilation, Geant4 uses the advanced software-engineering techniques and the object-oriented programming language C++ to achieve its transparency. Users can modify the underlying codes to customize their own simulation. Beneath the Geant4 toolkit are a series of physics lists supported by repositories of nuclear data and models in contemporary nuclear and particle physics (Agostinelli et al., 2003; Allison et al., 2006; Boudreau et al., 2010). In this paper, we employed Geant4 toolkit to simulate the photon shower of the photon activation and obtained the photon flux in the sample with its energy distributions. With the assistance of historical cross sections from IAEA databases, we can calculate the reaction density of the reaction channels of interest. With the reaction density information and initial incoming electron beam parameters, we can computer the activities of the different radioisotopes of the sample can be computed, which leads directly to the prediction of N values. The aim of the paper is to estimate N values even before the actual irradiation starts. For this purpose, we firstly derive the modified equation of N value according to the particular situation of computer simulations, from either the original definition of N value or its equation of traditional measurements.

Ap (T ) = For

mp h p L

58

ANi (T ) =

Ar , p

Emax

∫

(1 − e−λp T )

φ (E )p σ (E )p dE (1)

Ethres 57

Ni(γ, n) Ni reaction, the activity of

mNi hNi L (1 − e−λNi T ) Ar , Ni

57

Ni is

Emax

∫

φ (E )Ni σ (E )Ni dE

Ethres

(2)

In the above Eqs. (1) and (2), A is the activity, T is the normalized irradiation time (exactly equals to one hour), λ is the decay constant of the product, m is the mass of irradiated material, h is natural abundance of the nuclide under study, L is Avogadro constant, Ar is the relative atomic mass of irradiated nuclides, φ (E ) is the energy differential Bremsstrahlung flux density, σ (E ) is the energy-differential activation cross section within the corresponding energy range, subscript p refers to the element under study, subscript Ni refers to the Nickel reference monitor, Ethres is the threshold energy, i.e. the minimum photon energy to induce a photonuclear reaction, and Emax is the maximum energy of the Bremsstrahlung continuum, which equals the energy of the electrons incident to the converter. The ratio of the specific activities (SA ) after an hour of irradiation leads to N value,

N=

SAp (T ) SANi (T )

=

Ap (T )/ mp ANi (T )/ mNi

(3)

Inserting Eqs. (1) and (2) into (3), we obtain Emax

∫ φ (E )p σ (E )p dE hp Ar , Ni 1−e−λp T Ethres N= ⋅ ⋅ ⋅ hNi Ar , p 1−e−λNi T Emax ∫ φ (E )Ni σ (E ) Ni dE Ethres

(4)

Eq. (4) usually cannot be directly applied to Monte Carlo simulations, because simulations are not able to generate φ (E ) directly, but the conversion rate Y (E ) of the incoming electrons and emitting photons instead. Their relationship is described as

φ (E ) = Y (E ) Ibeam/ qe

(5)

where Ibeam is the current of incoming electron beam and qe is the charge of an electron. By inserting Eq. (5) back to Eq. (4), we get Emax

N=

∫ Y (E ) p σ (E )p dE hp Ar , Ni Ethres ⋅ ⋅ ⋅ hNi Ar , p 1−e−λNi T Emax ∫ Y (E )Ni σ (E ) Ni dE 1−e−λp T

Ethres

(6)

Eq. (6) is the modified N value equation for the particularity of computer simulations. We will follow this equation in the section of data analysis and result discussions. Traditionally, N value is calculated after measurements of gamma spectra (Segebade et al., 1988; Sun et al., 2017). It follows

N=

SAp (T ) SANi (T ) ⋅

e−λNi td, Ni e−λp td, p

=

Pp mNi ξ γ , Ni ηγ , Ni λp 1−e−λp T 1−e−λNi ti 1−e−λNi tc, Ni ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ PNi mp ξ γ ,p ηγ , p λNi 1−e−λNi T 1−e−λp ti 1−e−λp tc, p (7)

where P is net peak area (viz. count number), ξ is absolute gamma-ray emission probability, η is detector counting efficiency at respective gamma-ray energy, subscript p refers to the gamma-ray under study, ti is the exposure time, td is the decay time, and tc is the counting period. At first sight, Eqs. (4) and (6) look quite different with (7). However, given the below formulas (8) and (9) of the net peak areas of product nuclides and Ni-57, one will immediately find that Eqs. (4) and (6) can be derived from Eq. (7) by inserting (8), (9) into (7). Therefore, the modified N value Eq. (6) for simulations is consistent with the

2. Theory According to reference (Segebade et al., 1988; Segebade and Berger, 2008), the activity of product nuclides of interest immidiately after an hour of irradiation is

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Z.J. Sun et al.

traditional N value Eq. (7) derived from experimental measurements.

Pp = ηγ , p ξ γ ,p

∫t A (t ) dE =

ηγ , p ξ γ ,pmp hp L Ar , p λp

c

− e−λp tc, p) e−λp td, p

∫E

Emax

φ (E ) p σ (E ) p dE

thres

PNi = ηγ , Ni ξ γ , Ni

∫t A (t ) dE = ∫E

(8)

ηγ , Ni ξ γ ,NimNi hNi L

c

− e−λNi tc, Ni) e−λNi td, Ni

(1 − e−λp ti )(1

Emax

thres

Ar , Ni λNi

(1 − e−λNi ti)(1

φ (E )Ni σ (E ) Ni dE

(9)

Eqs. (4) and (6) apparently indicate that N values are directly related to natural abundance (h ), relative atomic mass of parent isotope Emax

( Ar ), half-life of product isotope (λ ), and the integral (

∫ φ (E ) σ (E ) dE Ethres

Emax

or

∫ Y (E ) p σ (E )p dE ), which are named as reaction rate density and

Fig. 2. Energy distribution of the electron beam of the 44 MeV short pulsed LINAC (peak energy 30 MeV).

Ethres

reduced reaction rate density respectively. We will discuss how to deal with this tedious integral in the section of data analysis.

that the beam out of the converter is predominantly made of high energy photons. After a careful mass measurement, the sample is wrapped with Aluminum foil into a 1 cm × 1 cm× 1 mm square shape and positioned downstream behind the hardener along the beam axis. Usually, a wellknown certified reference material, such as the standard reference material 1648a (National Institute of Standards and Technology, 2008) (urban particulate matter) from NIST can be employed as a sample for N value measurements. Monte Carlo simulations were exactly based on the geometry and materials of the experimental setups shown in Fig. 2. As mentioned in the introduction section, Geant4 is used as the primarily simulation software because of its inherited advantages. The version of Geant4 toolkit we applied in simulation is the version 4.10.3 (Geant4 Collaboration, 2017). The Geant4 toolkit was installed on an HP ProDesk 600 G1SFF workstation running with 64 bits Ubuntu 16.04.1 LTS operating system. Our simulations are based on the modification of the basic exampleB4 in the Geant4 toolkit. Some variables of exampleB4 are kept intact, while others are defined differently in our simulations. The B4DetectionContruction.cc file in the include directory was modified to include the materials such as Aluminum, Tantalum (or Tungsten), water, air, and vacuum (in room temperature). G4Tubs class was added because pipes and disks are widely used in the experimental setup. A rotation matrix is employed to change the direction of tubes. For better visualization, some visualizing attributes in the detector construction file were added. In B4Physicslist.cc file, all the electromagnetic processes are added,

3. Experimental setups and simulations Fig. 1 indicates the two different experimental setups for photon activation at the Idaho Accelerator Center with 44 MeV Santa Barbara LINAC. Both of them include three parts: electron gun, the electronphoton converter, and the sample. The electrons are initially produced by the hot cathode and then accelerated by a series of alternating RF electric fields in the acceleration cells. The electron accelerator is operated in pulsed mode and gives an electron beam of energy up to 44 MeV (for this study peak energies of 30–32 MeV are applied) and around 2 − 6 kW power. The electron beam is focused by magnetic fields to a radius of about 3 mm. The energy distribution of the electrons is shown in Fig. 3. It was measured with a Faraday cup, a magnetic spectrometer, and a beam-split to allow quasi-monochromatic electrons to pass after magnetic fields bending the track of electrons. The custom designed electron-photon converter or radiator is the crucial part in the photon activation setup. It is either made of a thin tungsten block of 3 mm thickness (left of Fig. 2) or 5 Tantalum disks with 0.5 mm thickness each (right of Fig. 2). Tungsten block is cooled with forced air and Tantalum disks are cooled with circulated water. The Bremsstrahlung photons are generated when the electrons are deaccelerated in these high Z materials. The photon flux produced directly after the converter by the accelerator at 30 MeV and 5 kW is approximately 1.3×1012 photons/sec/cm2/kW. The electron beam completely stops in the high Z material and the newly generated photon beam strikes an aluminum hardener of 3 in. thickness. The principal function of the hardener is to absorb the residual electrons and ensure

Fig. 1. Photon activation setups at the Idaho Accelerator Center (IAC).

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Fig. 3. Geant4 simulation of photon shower in photon activation analysis with a tungsten converter (view point θ = 45°, ϕ = 135° ).

including: ionization, multiple scattering, positron annihilation, photoelectric effects, Compton scattering, Bremsstrahlung radiation, and pair production (G4ComptonScattering.hh, G4GammaConversion.hh, G4PhotoElectricEffect.hh, G4eMultipleScattering.hh, G4eIonisation.hh, G4eBremsstrahlung.hh, G4eplusAnnihilation.hh, G4ionIonisation.hh). To create an electron beam with custom energy distribution, the default B4PrimaryGeneratorAction.hh file in include directory was modified. Instead of class G4ParitcleGun, we use another class—general particle source (GPS) (Ferguson, 2000). B4PrimaryGeneratorAction.cc in source directory is also modified accordingly. A file named beam.in stores all the user defined parameters in energy distribution of the beam. An ideally 1 cm × 1 cm× 1 mm “vacuum” sample is positioned downstream behind the hardener along the beam axis to register all the photons entering the sample area. In addition, B4SteppingVerbose.cc file in the source directory is modified to output the simulated data into a file named photon.txt, which records all the photons the sample can “see” with the information of their position ( x , y, z ), energy (E ), and momentum ( px , py , pz ). Fig. 3 illustrates the photon shower generated by Monto Carlo simulation with Geant4. The illustration is viewed from the side of the beam line. The yellow dots are the tracking points in Geant4. The relationship of the track colors and theirr corresponding particle are: photon: green, electron: red, positron: blue, and neutron: yellow. Magenta color illustrates the high Z materials, either Tungsten or Tantalum. The yellow flat cuboid right against the hardener simulates the sample.

Fig. 5. The distribution of the generations of the photons in the activated sample.

the energy distribution of the photons entering the sample behaves like a typical Bremsstrahlung curve: it starts from zero and ends up with the cut-off energy of the incoming photons. Fig. 5 shows that the photons entering the sample are dominantly second-generation particles (parentID = 1). Since the first-generation particles are incident electrons (parentID = 0), those photons (parentID = 1) must be created directly by Bremsstrahlung radiation. There are also some other generations of photons, but the number of them is quite limited compared with the Bremsstrahlung photons. These photons might be created by other physics processes, such as pair production, photonuclear reactions, etc.

4. Result and discussion 4.2. Cross sections and reduced reaction density 4.1. Simulated Bremsstrahlung beam in the sample

Seven product radioisotopes (47Ca, 58Co, 57Ni, 65Zn, 84Rb, 122Sb, Ce) and their corresponding photonuclear reactions are selected for the discussion in this section. Their atomic number ranges from low to high in the period table. Most of them have (γ, n) reactions in the Bremstrahlung beam and their production nuclides usually have long half-lives. Original data of cross sections is in exchange format (EXFOR), which contains an extensive compilation of experimental nuclear reaction data (Pritychenko and Zerkin, 2014; IAEA, 2000). These records were retrieved and validated via a consortium of organizations, including the International Atomic Energy Agency (IAEA), the National Nuclear Data Center (NNDC), and the Center for Photonuclear Experiments (CDFE). Table 1 shows the EXFOR records of the selected photon nuclear reactions and their original references. Reliable tabulated cross section values obtained by experiments are scarce and those obtained by computer simulations frequently are still of poor reliability, especially those of higher order reactions, such as (γ , p) , (γ , np) , (γ , α ), etc. With proper cross section data, we can employ Eq. (6) in the theory section to calculate the predicted N values. Photon yield is obtained 139

Fig. 4 shows the energy distribution of the photons entering the sample with the Tungsten converter in one simulation. One can see that

Fig. 4. Energy distribution of the photons in the activated sample.

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Z.J. Sun et al.

during this energy rage almost has no noticeable change. This may be due to the fact that 29–31 MeV range is actually in the giant dipole resonance range of these reactions. Within the same energy rage, the dominant factor impacting on the N values is the experimental setup of the converter. In other words, if the energy fluctuation is very small (< 2 MeV), the N values will not change too much in the energy range fitting the giant dipole region. However, it is obvious that the energy of the incoming electrons is critical if energy fluctuation is comparably large, since it directly impacts the energy distribution of the outgoing Bremstralung photons. One interesting fact is that the absolute values of activity may be way different due to the simulation photon flux is usually higher than the reality, given by beam loading and electron energy distribution (Faddegon, 2008a, 2008b, 1990). But N values, the ratios of relative specific activity, are fluctuated less than we expected. However, what causes N values distinct is quite complicated since many factors can impact on the special activity of product radioisotopes. Although the electron-photon converter may be the dominant factors in our experiments, we cannot deny the factor from beam parameters, such as beam power, peak energy, peak current, pulse width, etc. In addition, N values are greatly affected by the self-absorption of the sample materials as well. Obviously, N values are very important for predicting the activity of the sample before irradiation starts, which is crucial for generating work control documents and getting to know the relativity activity of each isotope.

Table 1 Selected photon nuclear reactions and their EXFOR records. Reaction

Exfor Record

Cross section of Exfor

Reference

48

M0636007 L0028008 L0034003 L0164002 L0027002 L0035033 M0367005

σ (γ , n) σ (γ , n) + σ (γ , σ (γ , X ) σ (γ , n) σ (γ , X ) σ (γ , n) + σ (γ , σ (γ , n)

O′Keefe1987 Alvarez1979 Fultz1974 Coryachev1982 Lepretre1971 Lepretre1974 Beljaev1991

Ca(γ,n)47Ca Co(γ,n)58Co 58 Ni(γ,n)57Ni 66 Zn(γ,n)65Zn 85 Rb(γ,n)84Rb 123 Sb(γ,n)122Sb 140 Ce(γ,n)139Ce 59

n + p)

n + p)

from photon beam simulations by the ratio of the number of photons in a certain energy bin to total incident electrons (107 electrons). Photon.txt file is scanned into R workplace and the number of photons in different energy bins with varied sizes are counted by the function “hist” in statistical software R (R Core Team, 2013). Breakpoints are set according to the cross section of corresponding reactions. We tabulate the cross section data and photon yield, and sum the products of them to obtain the reduced reaction rate and its corresponding uncertainty. Table 2 gives an example of this process for Ce-140 to Ce-139 reaction. In Table 2, E is the energy in MeV, σ is cross section in mb, ∆σ is uncertainty of cross section in mb, “Energy Range” is the energy range centered on E , Np (E ) is the number of photons in the energy range, Y (E ) is photon yield in the energy range, Y (E ) σ (E ) is the reduced reaction rate in the energy range, ∆Y (E ) σ (E ) is the uncertainty of reEmax

duced reaction rate in the energy range, and

∫ Y (E )σ (E )dE is re-

5. Conclusions and future work

Ethres

duced reaction rate. After having obtained the reduced reaction rate and its uncertainty, we insert them into Eq. (6) to calculate the estimated N values of certain reaction channel.

A new equation of N values has been derived and modified according to the situation in photon flux simulations. The equation clearly indicates that the N value is directly related to the reaction rate density (or reduced reaction rate density) of the corresponding nuclear reaction. With the equation, we have validated the method of predicting N values with the assistance from MC simulations of photon flux and historical data on photonuclear cross sections from IAEA. This method is novel since it can obtain N values before the real irradiation starts, which satisfies the concerns on radiation safety and the need of work control documents. In addition, computer simulations have confirmed that N values are highly correlated to the beam parameters of incoming electrons and the setup of the electron-photon converter, which keeps in line with the experimental results (Sun et al., 2017). For a certain electron beam with unnoticeably energy fluctuation, the N values are dominated by the setup of electron-photon converter. For the future work on this research, we would like to design a module in the executive program in Geant4 toolkits to generate the N values automatically. After that, a complete list of N values can be created according to photon flux simulations and the existing cross section data, which can serve as references for future photon

4.3. Simulated N values Table 3 shows the predicted N values via photon flux simulations for different elctron-photon converters with the same electron beam at the peak energy of 30 MeV. The calculation is following Eq. (6) in the theory section. Because of the difference in physical converter setup, the integrals are different even with the same incident electron beam. Apparently, the setup of electron-gamma converter plays a significant role in determining the distribution of Breamstrulung photon. N values in experiments are different from BAM values because they were from completely different electron-converter setups. However, the predicted N values are in the same order of magnitude with measured values in the same experimental setups. Fig. 6 below indicates the change of N values between different peaks with the same Tungsten converter. The peak energies are from 29 to 31 MeV with a step of 500 keV. One can notice that even though the absolute activity of isotopes may change significantly, the N values Table 2 Reduced reaction rate and its uncertainty for

140

Ce(γ,n)139Ce reaction.

E(MeV)

σ(mb)

Δσ(mb)

Energy Range

Np(E)

Y(E)

Y(E)σ(E)

ΔY(E)σ(E)

7.86 7.98 8.1 8.22 8.34 … 21.3 21.42 21.54 21.66

0.1 0.08 0.13 0.01 0 … 55.78 54.7 53.75 52.89

0.86 0.9 0.88 0.88 0.9 … 7.14 7.27 7.76 8.85

7.86–7.98 7.98–8.1 8.1–8.22 8.22–8.34 8.34–8.46 … 21.3–21.42 21.42–21.54 21.54–21.66 21.66–30

1279 1313 1175 1221 1199

0.0001279 0.0001313 0.0001175 0.0001221 0.0001199 … 0.0000165 0.000018 0.0000191 0.0000474

1.279E−32 1.050E−32 1.528E−32 1.221E−33 0 … 9.2037E−31 9.846E−31 1.02663E−30 2.50699E−30

1.1E−31 1.18E−31 1.03E−31 1.07E−31 1.08E−31 … 1.1781E−31 1.3086E−31 1.48216E−31 4.1949E−31

165 180 191 474

Emax

Sum

∫ Y (E) σ (E ) dE = 6.619E-28 ± 1.99E-29 Ethres

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Table 3 Simulated N values with different electron-photon converters (peak erngy: 30 MeV). Reaction

Ca(γ,n)47Ca Co(γ,n)58Co 58 Ni(γ,n)57Ni 66 Zn(γ,n)65Zn 85 Rb(γ,n)84Rb 123 Sb(γ,n)122Sb 140 Ce(γ,n)139Ce

48

59

h%

0.187 100 68.08 27.90 72.17 42.79 88.45

Ar(AMU)

48 59 58 66 85 123 140

λ (s−1)

Tungsten Converter

1.76868E−06 1.13222E−07 5.40676E−06 3.28506E−08 2.44842E−07 2.9458E−06 5.82967E−08

Tantalum Converter

IW(cm2)

NW

ITa(cm2)

NTa

1.16891E−28 1.82734E−28 3.8085E−29 1.5136E−28 2.98579E−28 6.76713E−28 6.61919E−28

3.575E−04 6.393E−04 1.000E+00 1.342E−05 1.497E−03 8.837E−02 6.318E−05

9.35E−29 1.10E−28 2.67E−29 1.21E−28 2.69E−28 7.44E−28 4.63E−28

1.28E−07 4.09E−07 1.00E+00 1.80E−10 2.24E−06 7.81E−03 3.99E−09

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Fig. 6. N values from 29 MeV to 31 MeV for the Tungsten converter.

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