Photon and neutron kerma coefficients for polymer gel dosimeters

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Photon and neutron kerma coefficients for polymer gel dosimeters A.M. El-Khayatt, Hector Rene Vega-Carrillo

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S0168-9002(15)00521-5 http://dx.doi.org/10.1016/j.nima.2015.04.033 NIMA57691

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Nuclear Instruments and Methods in Physics Research A

Received date: 6 February 2015 Revised date: 12 April 2015 Accepted date: 13 April 2015 Cite this article as: A.M. El-Khayatt, Hector Rene Vega-Carrillo, Photon and neutron kerma coefficients for polymer gel dosimeters, Nuclear Instruments and Methods in Physics Research A, http://dx.doi.org/10.1016/j.nima.2015.04.033 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Title page A.M. El-Khayatta,b∗, Hector Rene Vega-Carrilloc

Photon and neutron kerma coefficients for polymer gel dosimeters a

Physics Department, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia.

b

Reactor Physics Department, Nuclear Research Centre, Atomic Energy Authority, 13759, Cairo, Egypt. c Unidad Academica de Estudios Nucleares, Universidad Autonoma de Zacatecas, C. Cipres 10, Fracc. La Peñuela, 98068 Zacatecas, Zac., Mexico. Corresponding author (A.M. El-Khayatt): [email protected], [email protected]

Abstract Neutron and gamma ray kerma coefficients were calculated for seventeen 3D dosimeters, for the neutron and gamma ray energy ranges extend from 2.53 x 10-8 to 29 MeV and from 1.0 x 10-3 to 20 MeV, respectively. The calculated kermas given here for discrete energies and the kerma coefficients are referred to as “point-wise data”. Curves of gamma ray kermas showed slight dips at about 60 keV for most 3D dosimeters. Also, a noticeable departure between thermal and epithermal neutrons kerma sets for water and polymers has been observed. Finally, the obtained results could be useful for dose estimation in the studied 3D dosimeters.

Key words: Gamma ray; Neutrons; kerma coefficients; dose; 3D dosimeters. 1. Introduction The kerma, K, is the acronym for "kinetic energy released in material". Kerma and absorbed dose at a point in an irradiated target are equal when charged-particle ∗

Corresponding author. Tel.: +966504942745; fax: +966 12586922. E-mail addresses:[email protected], [email protected] (A.M. El-Khayatt).

1

equilibrium exists there and bremsstrahlung losses are negligible. As well as, the kerma replaces the traditional exposure as the shielding design parameter [1]. An essential step in the dosimetry evaluation is to relate the number of particles per unit area of a material of interest that cross a plane perpendicular to the beam (fluence, Φ, having the unit m–2), to the energy release (kerma, Gy) in the material, which determines the absorbed dose. The fluence-to-kerma conversion coefficient or kerma per fluence, K/Φ, is termed the kerma coefficient, having units J m2 kg-1 or Gy m2, for uncharged particles of energy E in a specified material. The term kerma coefficient is used in preference to the older term kerma factor, as the word coefficient implies a physical dimension whereas the word factor does not [2]. Many researchers reported calculated and measured values for kerma coefficients. Caswell et al., (1982) reported calculated neutron kerma coefficients for 19 elements, and 44 compounds, for the neutron energy range from 8 eV to 30 MeV [3]. The neutron kerma coefficients for human body organs have been reported in ICRU, 1989 [4]. Vega-Carrillo et al. (2007) reported a computer program for calculating the neutron kerma coefficients [5] based on Caswell et al. tabulation [3]. Also, Singh et al. (2014) calculate the neutron kerma coefficients of 24 tissue-substitutes [6]. Moreover, Paredes et al. (2010) showed that the neutron kerma coefficients for malignant tumors are smaller than soft tissue from 6% to 9% in the neutron energy range 11 eV- 29 MeV [7]. On the other hand, gel dosimeters offer the advantage of 3D dose detection and of tissue equivalence [8]. They fulfill the requirements of conformal radiotherapy [9] accurately and are therefore suitable dosimeters for the verification of complex 3D dose distributions [10]. In addition, Gel dosimeters can be prepared in any shape (eg. an anthropomorphic phantom) and they have shown to be a valuable device for displaying 3D dose distributions. While the effective atomic numbers, radiological properties and water equivalent studies have been widely carried out for different polymer dosimeter [11-13], there are almost no studies in literature for kerma coefficients determination. In fact, these coefficients are of interest for biomedical applications. As well as, they are used for determining the heat deposited by radiation in materials for energy applications such as 2

fission power reactors and fusion [14-16]. This prompted us to carry out the present work. In this study, we aimed to calculate the neutron and gamma kerma coefficients of 17 polymer 3D dosimeters. 2. Material and Methods Photon and neutron kerma coefficients are energy dependent coefficients used to convert photon or neutron fluence spectra to kerma (absorbed dose). Consequently, determination of kerma coefficients is an essential for any dosimeter. The chemical compositions of the studied polymer dosimeter are taken from the references [11, 17] and listed in the Table 1. Beside the Fricke gel dosimeter, polymer gel dosimeters may be generally classified as either hypoxic, reduced toxic or normoxic gels. Different types of these polymers are listed in Table 1. In order to provide a set of kerma coefficients for polymer dosimeter, the mass energy absorption coefficients for photons by Hubbell and Seltzer [18], and the elemental kerma coefficients for neutrons from Caswell et al. [3] have been employed. Some calculation details are given in the following section. 2.1 Kerma calculation from nuclear constants Photon kerma coefficients for polymer dosimeter are obtained by summing the products of the mass fraction wi of the ith constituent element in polymer, the photon energy Eγ , and the mass energy-absorption coefficient ( µ en ( Eγ ) / ρ ) i of the element for photons of that energy.

k P ( Eγ ) = kD .Eγ ∑ wi .[µen ( Eγ ) / ρ ] i Gy. cm2 / photon.

(1)

i

or k P ( Eγ ) = ∑ wi .ki ( Eγ )

Gy. cm2 / photon.

( 2)

i

Where

ki ( Eγ ) = k D .Eγ × [ µen ( Eγ ) / ρ ] i k ( Eγ ) is

Gy. cm2 / photon.

(3)

the energy dependence of specific photon kerma (kerma coefficient),

k D ( k D = 1.602 × 10 −13 Gy.g / MeV

) is the energy conversion coefficient from MeV to Gy.g,

3

(obtained from the well known relation: 1 MeV = 1.602 × 10 −13 J ),

Eγ

is photon energy in

MeV, and µ en ( Eγ ) / ρ is the mass energy-absorption coefficient in cm2/g. These coefficients are tabulated by Hubbell and Seltzer [18] and online available on the site: http://physics.nist.gov/PhysRefData/XrayMassCoef/. To calculate neutron kerma coefficients a similar relation can be used k n ( En ) = k D

∑ w .k (E ) i

i

n

i

Gy. cm 2 / neutron.

(4)

i

Where k ( En ) are the elemental kerma coefficients for neutrons from Caswell et al. [3]. Their tabulation gave the kerma coefficients for a "thermal neutron point" at 0.0253 eV and for 116 contiguous energy “groups” or “bins” extending from 0.026 eV to 30 MeV. Each bin was characterized by a mean energy and an energy interval of a given width [3]. The kerma coefficients were calculated from cross sections averaged over the full energy width of each bin. Neutron kerma calculations have been carried out using the Kerma program (Vega-Carrillo et. al. 2007). It is important to emphasize that the sums of the Eqs. (2) and (4) are, respectively, calculated for discrete photon and neutron energies, and the kerma coefficients are referred to as “point-wise data”. 3. Results and discussion The kerma coefficients given here are the kerma in polymer dosimeter per unit particle fluence of either neutrons or photons at a specified energy. Figures 1 and 2 present these kerma factors for 17 polymer dosimeters as a function of neutron and gamma energies from 2.53 x 10-8 to 29 MeV and 1.0 x 10-3 to 20 MeV, respectively. The neutron kerma coefficients of the selected polymer dosimeters can be divided into three regions according to the neutron energy, as shown in Fig.1. These regions are the thermal (< 0.4 eV), the epithermal and the intermediate (energy range of 0.4 eV to 10 keV), and the fast neutrons (>10 keV). It is seen that thermal neutron kerma coefficients for water, Fricke, Formulation 2, and Formulation1 go down with neutron energy, reaching minima at neutron energies of 2, 11, 36 and 63 eV, respectively. The most majority of the other polymer dosimeters are reaching to their minima at 20 eV.

4

At energies beyond about 100 eV (upper end epithermal, intermediate and fast neutron regions), the sets of neutron kermas of polymer dosimeters and water are in close agreement (Fig. 1). However, there is a noticeable departure between the polymers and water sets at lower energies, with the polymer kerma coefficients being larger than the water kerma coefficients by approximately 2 orders of magnitude for some polymers. We can decided that, these differences at lower neutron energies are mainly due to the significant kerma contribution from protons produced by neutron capture in nitrogen of those polymers. This conclusion can be discussed, in some details, in the following paragraph. While the deposition of energy by intermediate and fast neutrons in tissue (or low Zmaterials, similar to our samples) is mainly due to hydrogen recoil nuclei, thermal and epithermal neutrons release energy mostly from hydrogen and nitrogen, through the nuclear reactions, see the following reactions [19]: 1

H ( n , γ ) 2H

(σ = 0.33 b) and

14

N ( n, p )14C

(σ = 1.83 b)

(5)

Consequently, the abundances of nitrogen and hydrogen have a prime effect on the kerma coefficients in our samples. Since in our 3D dosimeters the mass percentage of hydrogen is very near to that of water (see Table 1) a good water equivalence is obtained for intermediate and fast neutron energies. Moreover, because of the proper amount of nitrogen in the dosimeter’s composition, the dosimeter becomes not equivalent to water for thermal neutron energies, as shown in Fig.1. This explanation can be supported by the fact that the maximum and minimum differences between water and polymer were, respectively, recorded for Formulation1, which have the highest nitrogen content (~5%) and Frick which have the lowest one (~0.7%), as shown in Table 1. Fig. 2 gives the gamma kerma coefficients for 17 polymer dosimeters and water as a function of gamma energy from 1 keV to 20 MeV. The ordinate gives the values of k P in units of Gy. cm2 / photon. . The figure includes many graphs for variation of kerma coefficient of individual dosimeters with photon energy. As well as, Fig. 2 plots water kerma coefficients for comparison task. In fact, the energy behavior of the gamma kerma coefficients mirrors the relative importance of the major contributing reactions for kerma coefficients in our energy 5

range. Namely are the photoelectric, Compton or incoherent scattering and pair production reactions. Photoelectric absorption is the main interaction process at low energies, whereas Compton scattering dominates at intermediate energies, and pair production at high energies. It is seen that the kerma curves of the studied dosimeters have a dip slightly above 60 keV. This minimum value refers to the dramatically decrease in the photoelectric absorption probability and to relatively low Compton absorption cross section at that energy. Thereafter, the Compton absorption cross section rise steeply. At the higher energies (≥1.02 MeV), pair production occurs increasingly with photon energy increase, and as a result the Compton and pair production become the major contributing reactions for gamma kerma coefficients. Graphs of simultaneous variation of neutron and gamma ray kerma coefficients with energy, for all the studied 3D dosimeters, have been constructed. Fig. 3 shows such graph for water. We can notice that, for lower energies the gamma kerma coefficient is always above the neutron kerma coefficient. However, at about 20 keV, neutron and gamma ray kerma coefficients are comparable. Thereafter, neutron kerma coefficient becomes considerably higher than gamma ray coefficient. 4. Conclusion The neutron and gamma ray kerma coefficients for seventeen 3D dosimeters have been calculated and graphed. Comparisons of calculated coefficients with that of water showed that: i.

For thermal and epithermal neutron kerma coefficients, there are a disagreement between the dosimeters and water attributed to nitrogen content.

ii.

For gamma ray kerma coefficients, good agreement was obtained for the full energy range, which extended from 1 keV to 20 MeV.

iii.

All gamma ray kerma curves of the studied dosimeters showed slightly dips above 60 keV, which attributed to the relative importance of the major contributing reactions for kerma coefficients at this energy.

iv.

While at lower energies (< 20 keV, for water) the gamma ray kerma coefficient is always above the neutron kerma coefficient, at higher energies intermediate and 6

fast neutron kerma coefficient become considerably higher than that of gamma ray. Finally, the results of this study could be useful for dose estimation in the studied 3D dosimeters. References [1] JE Turner, Atoms, Radiation, and Radiation Protection. Third edition. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2007. [2] ICRU, International Commission on Radiation Units and Measurements, Fundamental Quantities and Units for Ionizing Radiation (Revised). ICRU. J. of the ICRU

11

(1)

(2011)

Report

85,

page

22,

Oxford

University

Press:

doi:10.1093/jicru/ndr009 [3] RS Caswell, JJ Coyne, ML Randolph, Int. J. of App. Radiat. Isot. 33 (1982) 1227. [4] ICRU. International Commission on Radiation Units and Measurements. Tissue substitutes in radiation dosimetry and measurement, ICRU Report No. 44, Bethesda, MD (1989). [5] HR Vega-Carrillo, E Manzanres, R Barquero, JL Gutierrez-Villanueva, A Martin, ALASBIMN Journal 9 (37) (2007), Article N_ AJ37-5. [6] VP Singh, NM Badiger, HR Vega-Carrillo, Ann. Nucl. Energy 75 (2014) 189. [7] L Paredes, J Azorín, M Balcázar, JL Francois, Radiation Measurements 45(2010). 1445. [8] McAuley, AT Nasr, Journal of Physics: J. Phys.: Conf. Ser. (2013)012001. doi:10.1088/1742-6596/444/1/012001. [9] A Brahme, Acta Radiol Oncol. 23(5) (1984) 379. doi: 10.3109/02841868409136037. [10] AJ Venning, KN Nitschke, PJ Keall, C Baldock, Med. Phys. 32 (2005) 1047.

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[11] ML Taylor, RD Franich, JV Trapp, PN Johnston, Australas. Phys. Eng. Sci. Med. 31(2) (2008) 131. [12] S Brown, A Venning, Y De Deene, P Vial, L Oliver, J Adamovics, C Baldock, Int. J. of App. Radiat. Isot. 66 (2008) 1970. [13] P Sellakumar, E James Jebaseelan Samuel, SS Supe, J. Phys. Chem. 76(2007) 1108. [14] L Zhang, MA Abdou, Fusion Engineering and Design 36 (1997) 479. [15] MA Abdou, CW Maynard, Nucl. Sci. Eng. 56 (1975) 360. [16] HC Claiborne, M Solomito, JJ Ritts, Nuclear Engineering and Design 15 (1971) 232. [17] T Gorjiara, Z Kuncic, J Adamovics, C Baldock, J. Phys.: Conf. Ser. 444(2013) 012090 doi:10.1088/1742-6596/444/1/012090 [18] JH Hubbell, SM Seltzer, NISTIR-5632, National Institute of Standards and Technology, Gaithersburg (1995). [19] IAEA, Current status of neutron capture therapy, IAEA-TECDOC-1223, International Atomic Energy Agency, Vienna (2001).

8

Table 1. Elemental composition (% weight fraction) of water and different 3D polymer dosimeters taken from the Ref. [11]. Material

H

C

11.1898 a)Water 10.736 b)FRICKE c)Hypoxic BANG-1 10.7685 BANG-2 10.6369 PAG 10.7367 d)Reduced toxic VIPAR 10.7321 PABIG 10.6454 e) Normoxic MAGIC 10.5473 MAGAS 10.5087 MAGAT 10.522 PAGAT 10.7257 nPAG 10.7107 nMAG 10.6775 ABAGIC 10.5263 NIPAM 10.8055 HEAG 10.7641 f)PRESAGE* Formulation 1 8.8500 Formulation 2 8.9200

∗

N

O

Na

2

0.67

88.8102 85.736

0.0021

5.6936 5.6728 6.2009

2.0063 1.4152 2.1804

81.5316 81.7004 80.882

7.1825 6.8373

2.0638 1.5649

80.0217 80.9524

9.2231 9.3591 9.5417 6.2174 6.5251 7.5066 8.963 6.5998 5.7243

1.3916 1.3799 1.366 1.9688 2.1814 1.3868 3.105 1.7531 1.4152

78.8373 78.7523 77.6988 80.2166 80.1385 80.2527 77.4054 79.9702 82.0964

61.7800 60.7400

4.9600 4.4600

20.6900 21.7200

Mg P

S

Cl

0.85

0.0033

K ca Fe

Cu

Zn Br

0.0026

0.5748

0.0003 0.4064 0.4064 0.5748 0.0822

0.0005 0.4651 0.4651 0.2371 0.0941

0.0003 0.4064

0.0005 0.4651

0.3800

3.1100 3.3400

Calculated from the chemical formulae given in Ref. [17].

9

0.2300 0.8400

Research Highlights ∗

Neutron and gamma ray kerma coefficients were calculated in seventeen 3D dosimeters for extended energy ranges.

∗

Curves of gamma ray kermas showed slight dips at about 60keV for most 3Ddosimeters.

∗

A noticeable departure between thermal and epithermal neutrons kerma sets for water and polymers has been observed.

∗

The obtained results could be useful for dose estimation in the studied 3D dosimeters.

10

Figure Captions Fig. 1. Neutron kerma coefficients for 3D dosimeters Fig. 2. Gamma ray kerma coefficients for 3D dosimeters Fig. 3. Gamma ray and neutron kerma coefficients for water

(a)

-7

Hypoxic

KERMA [ cGy-cm / neutron ]

10

-8

10

-9

-8

10

-9

10

2

10

2

KERMA [ cGy-cm / neutron ]

(b)

-7

10

-10

10

-11

10

-12

10

Water FRICK

-13

10

-10

10

-11

10

-12

10

Water BANG-1 BANG-2 PAG

-13

10

-14

-14

10

10 -8

10

-7

10

-6

10

-5

10

-4

-3

10

10

-2

10

-1

10

0

10

1

-8

10

-7

10

-6

10

-5

10

10

Neutron Energy [ MeV ] (c)

-7

-8

-2

10

-1

10

0

10

1

10

-8

KERMA [ cGy-cm / neutron ]

10

-9

10

10

-9

10

2 -10

10

-11

10

-12

10

Water VIPAR PABIG

-13

10

-10

10

-11

10

-12

10

Water MAGIC MAGAS MAGAT

-13

10

-14

-14

10

10 -8

10

-7

10

-6

10

-5

10

-4

-3

10

10

-2

10

-1

10

0

10

1

-8

10

-7

10

-6

10

-5

10

10

Neutron Energy [ MeV ]

-4

10

-3

10

-2

10

-1

10

0

10

1

10

Neutron Energy [ MeV ]

(e)

-7

(f)

-7

10

Normoxic

10

Normoxic -8

-8

KERMA [ cGy-cm / neutron ]

10

-9

10

-9

10

2

10

2

KERMA [ cGy-cm / neutron ]

-3

10

Normoxic

10

2

KERMA [ cGy-cm /neutron ]

(d)

-7

Reduced toxic

10

-4

10

Neutron Energy [ MeV ]

-10

10

-11

10

-12

10

Water PAGAT nPAG nMAG

-13

10

-10

10

-11

10

-12

10

Water ABAGIC NIPAM HEAG

-13

10

-14

-14

10

10 -6

10

-5

10

-4

-3

10

10

-2

10

-1

10

0

10

1

-8

10

-7

10

-6

10

-5

10

10

Neutron Energy [ MeV ] (g)

-7

-4

10

-3

10

-2

10

Neutron Energy [ MeV ] PRESAGE

10

-8

10

-9

10

2

-7

10

KERMA [ cGy-cm / neutron ]

-8

10

-10

10

-11

10

-12

10

Water FORMULATION 1 FORMULATION 2

-13

10

-14

10 -8

10

-7

10

-6

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

1

10

Neutron Energy [ MeV ]

Fig. 1. Neutron kerma coefficients for 3D dosimeters

-1

10

0

10

1

10

-7

(a)

(b)

-7

10

KERMA [ cGy-cm / photon ]

Water FRICK

-8

Hypoxic

-9

10

-10

10

-11

-8

10

-9

10

-10

10

-11

10

10 -3

10

-2

-1

10

0

10

1

10

-3

10

-2

10

10

Photon Energy [ MeV ] -7

(c)

-1

10

0

10

1

10

Photon Energy [ MeV ] (d)

-7

10

Reduced toxic

Normoxic

KERMA [ cGy-cm / photon ]

Water VIPAR PABIG -8

10

Water MAGIC MAGAS MAGAT

-8

10

2

2

KERMA [ cGy-cm / photon ]

10

-9

10

-10

10

-11

-9

10

-10

10

-11

10

10 -3

10

-2

-1

10

0

10

1

10

-3

10

-2

10

10

Photon Energy [ MeV ] (e)

-1

10

0

10

1

10

Photon Energy [ MeV ] (f)

-7

Normoxic

10

Water PAGAT nPAG nMAG

KERMA [ cGy-cm / photon ]

-7

10

-8

Normoxic

Water ABAGIC HEAG NIPAM

-8

10

2

10

2

KERMA [ cGy-cm / photon ]

Water BANG-1 BANG-2 PAG

2

10

2

KERMA [ cGy-cm / photon ]

10

-9

10

-10

10

-11

-9

10

-10

10

-11

10

10 -3

-2

-1

10

0

10

1

10

-3

10

-2

10

10

Photon Energy [ MeV ] -7

10

(g)

-1

10

0

10

Photon Energy [ MeV ] PRESAGE

Water FORMULATION 1 FORMULATION 2

-8

10

2

KERMA [ cGy-cm / photon ]

10

-9

10

-10

10

-11

10 -3

10

-2

10

-1

10

0

10

1

10

Photon Energy [ MeV ]

Fig. 2. Gamma ray kerma coefficients for 3D dosimeters

1

10

Kn Water Kg Water

-7

-8

10

-9

10

2

KERMA [ cGy-cm / particle]

10

-10

10

-11

10

-12

10

-13

10

-14

10 -8

10

-7

10

-6

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

Photon or Neutron Energy [ MeV ]

Fig. 3. Gamma ray and neutron kerma coefficients for water

1

10