Fast detection of alpha particles in DAM–ADC nuclear track detectors

Fast detection of alpha particles in DAM–ADC nuclear track detectors

Radiation Physics and Chemistry 107 (2015) 183–188 Contents lists available at ScienceDirect Radiation Physics and Chemistry journal homepage: www.e...

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Radiation Physics and Chemistry 107 (2015) 183–188

Contents lists available at ScienceDirect

Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem

Fast detection of alpha particles in DAM–ADC nuclear track detectors Y.S. Rammah a,b,c,n, O. Ashraf d, A.M. Abdalla d,e,f, M. Eisa d, A.H. Ashry d, T. Tsuruta g a

Physics Department, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt Centre for Astronomy and Astrophysics, TU-Berlin, Hardenbergstr.36, ER 3-2, Berlin, Germany Centre for Theoretical Physics, The British University in Egypt, Sherouk City 11837, P.O. Box 43, Egypt d Physics Department, Faculty of Eduction, Ain Shams University, Cairo, Egypt e Physics Department, Faculty of Sciences and Arts, Najran University, Najran, P. O. Box. 11001, KSA f Promising Center for Sensors and Electronic Devices, Faculty of Arts and Sciences, Najran University, KSA g Atomic Energy Research Institute, Kinki University, Kowakae, Higashi-Osaka 577-8502, Japan b c

H I G H L I G H T S

   

Suitable analyzing software has been used. Samples of DAM–ADC detectors have been irradiated with fission fragments. Fast detection method of alpha particles in DAM–ADC detectors. The dependence of etching efficiency upon etchant concentrations.

art ic l e i nf o

a b s t r a c t

Article history: Received 6 June 2014 Received in revised form 3 October 2014 Accepted 29 October 2014 Available online 6 November 2014

Fast detection of alpha particles in DAM–ADC nuclear track detectors using a new chemical etchant was investigated. 252Cf and 241Am sources were used for irradiating samples of DAM–ADC SSNTDs with fission fragments and alpha particles in air at normal temperature and pressure. A series of experimental chemical etching are carried out using new etching solution (8 ml of 10 N NaOHþ 1 ml CH3OH) at 60 °C to detect alpha particle in short time in DAM–ADC detectors. Suitable analyzing software has been used to analyze experimental data. From fission and alpha track diameters, the value of bulk etching rate is equal to 8.52 μm/h. Both of the sensitivity and etching efficiency were found to vary with the amount of methanol in the etching solution and etching time. The DAM–ADC detectors represent the best efficiency applicable in detectors in the entire range of alpha energies (from 1 to 5 MeV). The activation energies of this etchant have been calculated; track activation energy, ET, has been found to be lower than the bulk activation energy, EB, for the DAM–ADC nuclear track detectors. These results are in more agreement with the previous work. & Elsevier Ltd. All rights reserved.

Keywords: Fission fragments Alpha particles DAM-ADC Etching efficiency

1. Introduction Solid state nuclear track detectors (SSNTDs) have been successfully employed in a large variety of applications in science and technology has been gained much interest (Price, 2005, 2008, Ashry et al., 2012; El-Hawary et al., 1999). Especially, qualitative and quantitative analysis of alpha particles in radioactive environmental and biological samples (Gaillard et al., 2005; Nikezic and Yu, 2004). The sensitivity of the plastic detector is known to n Corresponding author at: Physics Department, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt. E-mail addresses: [email protected], [email protected] (Y.S. Rammah).

http://dx.doi.org/10.1016/j.radphyschem.2014.10.013 0969-806X/& Elsevier Ltd. All rights reserved.

be affected by the purity of monomer and molecular structure (Portwood et al., 1986). Diallyl maleate (DAM) is a highly active monomer with a powerful affinity for many materials. Therefore, DAM is used as a raw material for many chemical products, such as adhesives, ion exchange resin, etc. It had been found that DAP (diallyl phthalate) and ADC have two allyl radicals, which are the components inherent in DAM. The molecule of DAM has four hands to link with another similarly to ADC and DAP. The DAM must have highly cross-linked three dimensional network structures in the plates. In the case of DAM, there is a possibility that the central carbon–carbon double bond contribute the crosslinking (Tsuruta, 1999, 2000). DAM, ADC, and mixtures of DAM and ADC (DAM–ADC) were cast into polymer plates under three kinds of polymerizing

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conditions. Pure ADC plate was sensitive to both of fission fragments and alpha particles. On the other hand, pure DAM plate was found to be sensitive to fission fragments, but to be insensitive to alpha particles. The mixtures of DAM and ADC form co-polymers containing various ratios and show various intermediate characteristics between DAM and ADC polymer (Ashry et al., 2012). The observed characteristics in DAM–ADC co-polymers are similar to those observed in the case of DAP–ADC (Tsuruta et al., 2011). These characteristics are suitable for control of the sensitivity as the nuclear track detector. The fabrication of the copolymers makes it possible to adjust the discrimination level for the detection of heavy charged particles (Tsuruta et al., 2011). Chemical etching is an essential method being used in various studies of surfaces and technical applications (Fleischer et al., 1975). If a piece of material containing the latent track is exposed to some chemically aggressive solution, such as NaOH or KOH solution, the chemical reaction would be more intensive in the latent track (Nikezic and Yu, 2004). It is found that, The fierce bulk etch rates for NaOH/ethanol etchants compared to that for the 6.25 N NaOH/H2O etchant are due to the miscibility of ethanol with the organic etched products from etching the ADC detector (Tse et al., 2007). The optimum etching condition, 10 N NaOH with etching temperature 343 K and etching time is 2.5 h has been used successively to register alpha particles in the DAM–ADC detector with energy in the range from 1 to 5 MeV (El-Samman et al., 2014). In the present study, we introduce a new etchant solution for DAM–ADC detector to investigate several important parameters that control the track formation such as the bulk etch rate (VB), track etching rate (VT), sensitivity, etching efficiency, and registration efficiency for alpha particles in short etching time, in order to approve the benefit of these plates as the nuclear track detectors.

2. Materials and methodology The molecular formula of the DAM–ADC detector used in the present study is expressed as (C22H30O11), its thickness is 1 mm and density is 1.2 g/cm3. The main constituents of the detector plate are the DAM (15%) and ADC (85%). A small amount of diisopropyl peroxy dicarbonate (IPP) was used as a polymerizing initiator. The co-polymer of DAM–ADC detector was obtained from Yamamoto Kogaku Co., Ltd., Japan. The relationship between the concentration of DAM and the etch pit diameter of alpha particle and fission fragment have been studied by Tsuruta et al. (2011); up to 10% or 25% of the concentration of DAM, the diameter has a tendency to increase. When the concentrations exceed those percentages, on the other hand, the diameter decreases gradually.

25 Min

35 Min

Samples of DAM–ADC detector with an area of 1.0  1.0 cm2 were carefully cut with laser beam. A group of DAM–ADC detectors were exposed to a thin open 252 Cf disk source as an alpha, fission fragment and fast neutrons source of activity 9.65  10  3 mCi and surface area of 19.64 mm2. 252 Cf disk source was contact with detectors and all samples were exposed for 20 min to the source. Another group was exposed to thin 241Am disk source that emit alpha with energy of 5.5 MeV and activity 0.924 mCi. Using a variable length of air column, energies from 1 to 5 MeV were used. Mixture of 10 N sodium hydroxide and pure methanol (CH3OH) with different ratios were used as the etching solutions at 55, 60 and 65 °C. It is found that the fierce bulk etch rates for NaOH/alcoholic etchants compared to that for the 6.25 N NaOH/H2O etchant are due to the miscibility of alcoholic with the organic etched products from etching the solid state detector (Tse et al., 2007). The etching was done in a bottle with a tight lid to prevent change in the concentration of the etching solution due to vaporization of water and absorption of moisture. For etching process, a water path of stabilizing temperature with accuracy 70.5 °C was used. All etched samples were held at the same depth in the etchant solution. After etching the samples were immersed in running water for suitable time interval to remove all etchant products from the surfaces. Finally, the samples were carefully dried and then used for analysis. For estimation of track diameter an optical microscope fitted with a magnification of 400  was used. The microscope was connected with a web digital camera to capture the sample image from microscope and save it in P.C unit, software program (INFINITY ANALYZE software) was used to analyze the tracks after calibration. The bulk etch rate VB is the rate of removing of the undamaged surface of the detector due to the chemical reaction between the etching solution and the detector material, and it can be determined using the following equation.

VB =

D ff 2t e

(1)

Where Dff is the track diameter of fission fragment projectile that bombarded the detector as shown in Fig. 1, and te is the etching duration. The traditional method for determining the track etching rate of solid state nuclear detector is based on the measurement of track diameter (D). The relation between VT and D takes into account the removal of a detector layer h¼VBt and bulk etching rate (Durrani and Bull, 1987). In this method DAM–ADC detectors were exposed to normal incident alpha particle of energy 2 MeV and then etched for etching time 60 min. with different etching concentrations at different etching temperatures. From the track

45 Min

55 Min

Fig. 1. Typical optical images of fission tracks in the DAM–ADC detector with etching condition (8 ml of 10 N NaOH þ 1 ml CH3OH) at 60 °C.

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diameter and removed layer the track etching rate VT was determined. The sensitivity (V) of an etched track detector to alpha particle is a strong function of detector material properties, particle charge, energy and direction of the incident ions. The sensitivity (V) of the detector has been determined from the following equation (Durrani and Bull, 1987):

V=

VT 4V B2 t 2 + D2 = VB 4V B2 t 2 − D2

(2)

where VT is the track etching rate and h is the removed layer and 2r is the track diameter. The critical angle (θc) is one of the geometrical limitations for the revelation of the etched tracks in SSNTDs; it can be determined by this equation (Yu and Nikezic, 2009):

θc =

VB sin−1 VT

Fig. 2. Variation of VB with etching time (min) at different temperatures for DAM– ADC detector with etching condition (8 ml of 10 N NaOH þ 1 ml CH3OH).

(3)

The etching efficiency of a detector is defined as the proportion of tracks etched out expressed as a fraction of particles actually incident on the detector surface. The etching efficiency of the detector (η) can be measured using the following equation (Yu et al., 2005).

η = 1 − sin θc

(4)

3. Result and discussion Fission fragments are easily obtained from a 252Cf radioactive source and registered in DAM–ADC detector sheets after exposure time. Since the ranges of fission products are relatively small, Eq. (1) can be used for measuring the bulk and track etches rates (El-Badry et al., 2007). In this study, our basic movement was in the direction of finding out an optimum new etching condition to detect alpha particles registration in DAM–ADC nuclear track detector in short time. In order to achieve this goal, a great deal of efforts was done. We test various stages of etching conditions until a best acceptable condition was reached. This new suggested condition was (8 ml of 10 N NaOHþX ml CH3OH) at 60 °C. It is found that the average value of VB for DAM–ADC detector using (8 ml of 10 N NaOHþ1 ml CH3OH) at 60 °C is 8.52 μm/h. In this work, we study the effect of adding CH3OH to the etching solution in the etching parameter (bulk etching rate, track etching rate, sensitivity, etching efficiency and critical angle) at different temperature of etching. Bulk etch rate VB of DAM–ADC nuclear track detector was determined in temperature range from 55 to 65 °C in step of 5 °C using the new etching condition with different amount of methanol with different etching time. Typical optical images for fission tracks in DAM–ADC detector is illustrated in Fig. 1, the track diameter of fission was used to determine the bulk etching rate VB. Figs. 2 and 3 depict the variation of the bulk etch rate VB with etching time at different temperature using etching conditions (8 ml of 10 N NaOH þ1 ml CH3OH) and (8 ml of 10 N NaOH þ2 ml CH3OH), respectively. Results from these figures show that the bulk etching rate increases with increasing the amount of CH3OH and increases with increasing the temperature. Fig. 4 shows the variation of VB with temperature at different amount of CH3OH. One can notice that values of VB at etching by using 2 ml CH3OH is higher than these of using 1 ml CH3OH and etching solution without using methanol. This may be attributed to; the mixture of NaOH with CH3OH producing CH3O  Na þ (sodium methoxide), it is very active compound relative to NaOH, which increasing corrosion due to the

Fig. 3. Variation of VB with etching time (min) at different temperatures for DAM– ADC detector with etching condition (8 ml of 10 N NaOH þ 2 ml CH3OH).

Fig. 4. Variation of VB with temperature at different amount of CH3OH.

polymeric material such as DAM–ADC, also diffusion of NaOH/alcoholic is larger than that of NaOH due to the organophilicity of the former. It helps in dissolving the etched products facilitating its accessibility to the deeper regions of latent tracks. The dependence of ln VB on 1000/T (K  1) with different amount of methanol is illustrated in Fig. 5. The relation between ln VB and 1000/T (K  1) reflects and exponential behavior that can

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Fig. 7. Variation of alpha particle tracks diameter with energy at different removed layer for DAM–ADC detector with etching condition (8 ml of 10 N NaOH þ1 ml CH3OH) at 60 °C.

Fig. 5. Variation of ln VB and 1000/T at different amount of CH3OH.

be represented by the relation:

⎛ EB ⎞ ln (VB ) = ln (A) − ⎜ ⎟ ⎝ KT ⎠

(5)

where A is a constant, EB is the activation energy of etching, and k is the Boltzmann's constant. Activation energy is the energy required in activating the reaction between the detector material and the etching solution and it tells us about the kinetics of the reaction. Activation energy of etching is a measure of the thermal energy required to start bulk etching. Using a least square fit method the values of the bulk activation energy EB for DAM–ADC detector were calculated from the slopes of the straight lines given in Fig. 5. It shows that the average value of EB was found to be 0.644 eV. In addition, the activation energy for track etching, ET, which is that minimum energy which is required to etch a track along the latent path of an ion to make it visible under optical microscope (Neerja et al., 2007). The activation energy of track etching rate was calculated; its average value ET ¼ 0.573 eV was obtained. Thus track activation energy, ET is found to be lower than the bulk activation energy EB. This result is as similar as in case of CR-39 nuclear track detector (Matiullah et al., 2005a, Ashry et al., 2014). Three groups of irradiated DAM–ADC detectors with alpha particle from 1 to 5 MeV were etching using (8 ml NaOH þ1 ml CH3OH) at different temperatures for 60 min. Results of etching efficiency as a function of alpha particle energy show that the etching efficiency reaches its maximum values at 60 °C, so one can say that the optimum etching temperature is 60 °C, as shown in the Fig. 6.

Fig. 6. Etching efficiency (η) as a function of alpha particles energy at different temperature.

The variation of alpha particle etch pit diameter and energy (MeV) at different removed layer (mm) is depicted in Fig. 7. It shows that under the new etching condition which used in this work (8 ml of 10 N NaOHþ1 ml CH3OH) at 60 °C with different etching time, alpha particle tracks for some or all energies can be registered in DAM–ADC nuclear detector. Using the new etching condition for etching time 30 and 45 min, i.e. removed layer equal 4.26 and 6.39 μm, the tracks of alpha particles of energy in the range from 1 to 2.5 MeV and from 1 to 4 MeV, respectively are registered only in DAM–ADC detector. Using the etching condition for etching time 75 and 90 min i.e. removed layer equal 10.65 and 12.78 μm, the tracks of alpha particles of energy in the range from 2 to 5 MeV registered only. But when the etching condition for etching time 60 min, i.e., removed layer equal 8.52 μm, the tracks of alpha particles of energy in the range from 1 to 5 MeV are registered as shown in Fig. 7. This implies that the best etching time to register the track of alpha particles with energy from 1 to 5 MeV by (8 ml of 10 N NaOHþ1 ml CH3OH) etching solution at 60 °C is 60 min. In addition, Fig. 7 shows that under this etching conditions, when the removed layer increase up to 4.26 μm, the track diameter of 1 MeV alpha particles started to increase relative to 2 MeV alpha particles. This result may refer to increase in the path of 1 MeV alpha particles, after this point the value of damage inside the material started to decrease and the rate by which the track diameter was increasing started to decrease. Also, Fig. 7 depicts the specific maxima, which are shifted to higher alpha particle energies for the higher removed layer (Ashry et al., 2014). This means that tracks are etched out to the largest diameters only when the etching solution has unconstrained access to the end part of the particle trajectory, where the concentration of detector material defects is the highest. This takes place after removal of the detector external layer of a thickness equal to the projectile range (Szydlowski et al., 2013). This result supposes the availability of calibration curves of the track diameter versus particle energies for different removed layers (Sadowski et al., 1994). The sensitivity (V) of DAM–ADC nuclear track detector was determined using Eq. (2); it was obtained by measuring the track diameter and the removed layer. Fig. 8 illustrated the variation of the sensitivity of the detector with alpha particle energy when it etched with different amounts of CH3OH at 60 °C for etching time of 60 min. Results show that the sensitivity increasing with increasing amount of CH3OH for alpha energy from 2.5 to 5 MeV. According to Fig. 8, an increasing in sensitivity has been occurred by using our new etching conditions relative to previous etching condition (El-Samman et al., 2014). In addition, critical angle (θc) was determined using Eq. (3). The values of the critical angle

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Fig. 8. Variation of sensitivity with alpha particle energy for new optimum etching conditions and previous etching condition (El-Samman et al., 2014).

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the new etching condition at etching time before and after 60 min (see Fig. 7). From Figs. 7 and 9, one can say that the optimum new etching condition is 8 ml of 10 N NaOH þ 1 ml CH3OH at 60 °C for 60 min etching time. The etching efficiency of DAM–ADC nuclear detector was determined using the critical angle measurements. The variation of the etching efficiency of the detector with alpha particle energy at different amounts of CH3OH at 60 °C for etching duration time of 60 min is studied using two etching conditions: 8 ml of 10 N NaOH þ1 ml CH3OH and 8 ml of 10 N NaOH þ2 ml CH3OH as shown in Fig. 10. The results show that the etching efficiency of the DAM–ADC detector is higher to detect the tracks of alpha particles in the energy of the range (1–2 MeV) using the etching condition 8 ml of 10 N NaOH þ1 ml CH3OH than that from the second condition, while the etching efficiency of the detector becomes higher to detect the tracks of alpha particles in the energy of the range (3–5 MeV) using the second etching condition compared to that from first condition. Results that the etching condition 8 ml of 10 N NaOHþ 1 ml CH3OH can be used to detect the tracks of alpha particles in the energy of the range (E ≤ 2 MeV ), while the condition 8 ml of 10 N NaOHþ2 ml CH3OH can be used to detect the tracks of alpha particles in the energy of the range (E ≥ 3 MeV ) at 60 °C for etching time of 60 min. One can be claimed that our new etching condition has high etching efficiency for the DAM–ADC detector at low alpha energy compared to the other conditions. Thus, we conclude that the new etching condition which introduced in this work becomes better than that used in previous works (i.e., El-Samman et al., 2014). This for the following reasons: Firstly, using mixture of NaOH and CH3OH reducing the etching time from 2.5 h to 1 h because of increasing in VB. Secondly, in order to control the etching process and keep detectors undamaged etching temperature decrease to 60 °C. Finally, variation of sensitivity with alpha particle energy for new optimum etching conditions and previous etching condition (ElSamman et al., 2014); represents a clear increase in sensitivity by using our new optimum etching conditions as shown in the Fig. 8.

Fig. 9. Etching efficiency (η) as a function of alpha particles energy at different etching time.

4. Conclusion

Fig. 10. Etching efficiency (η) as a function of alpha particles energy etched at different amount of CH3OH at 60 °C for 60 min.

decrease with increasing the amount of CH3OH at 60 °C for etching time of 60 min, for alpha energy from 2.5 to 5 MeV. This implies that; both sensitivity and critical angle are strongly depends on alpha particle energy and etching conditions. The relation between etching efficiency (η) as a function of alpha particle energy at different etching times, using etching condition (8 ml of 10 N NaOHþ 1 ml CH3OH) at 60 °C is depicted in Fig. 9. It is observed that approximately, the etching efficiency increases with increasing the etching time in the energy range of 1–4 MeV. As mentioned above all alpha particle tracks for energy in the range of 1–5 MeV cannot able to register in DAM–ADC detector by using

A new chemical etching condition is introduced in order to detect and investigate the characteristics of the co-polymer DAM– ADC as a solid state nuclear track detector in short duration time. The best chemical etching conditions for fast detection of alpha particles in the energy of the range (E ≤ 2 MeV ) is 8 ml of 10 N NaOH þ1 ml CH3OH at 60 °C for etching time of 60 min, while the condition 8 ml of 10 N NaOHþ2 ml CH3OH can be used to detect the tracks of alpha particles in the energy of the range (E ≥ 3 MeV ) at 60 °C for etching time of 60 min with considerable efficiency. In addition, the effect of etching conditions upon the sensitivity, critical angle and etching efficiency has been studied. The activation energies of this etchant have been calculated. Moreover, track activation energy, ET, has been found to be lower than the bulk activation energy, EB, for the DAM–ADC nuclear track detectors. DAM–ADC can be used in the field of radon gas measurement and detection of fission fragment in short time.

References Ashry, A.A., El-Samman, H., Abou-leila, M., Arafa, W., Umar, Ahmed, Abdalla, A.M., Tsuruta, T., 2012. Nucl. Instrum. Methods Phys. Res. B 290, 39–42. Ashry, H.A., Abdalla, A.M., Rammah, Y.S., Eisa, M., Ashraf, O., 2014. Radiat. Phys. Chem. 101, 41–45. Durrani, S.A., Bull, R.K., 1987. Solid State Nuclear Track Detection. Principles, Methods and Applications. Pergamon Press, Oxford. El-Badry, B.A., ZAKI, M.F., Hgazy, T.M., Morsy, A.A., 2007. Indian Acad. Sci. 69 (4), 669–674.

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El-Hawary, M., Mansy, M., Hussein, A., Ammar, A., El-Sersy, A., 1999. Radiat. Phys. Chem. 54, 547–550. El-Samman, H., Ashry, A.H., Arafa, W., Abou-leila, M., Abdalla, A.M., Tsuruta, T., 2014. Radiat. Phys. Chem. 102, 79–83. Fleischer, R.L., Price, P.B., Walker, R.M., 1975. Nuclear Tracks in Solid. University of California Press, Berkeley. Gaillard, S., Armbruster, V., Hill, M.A., Gharbi, T., Fromm, M., 2005. Radiat. Res. 163, 343. Matiullah, Rehman S., Rehman, S., Mati, N., Ahmed, S., 2005a. Radiat. Meas. 39, 551–555. Neerja, Prasher, S., Singh, S., 2007. Radiat. Meas. 42, 135–137. Nikezic, D., Yu, K.N., 2004. Mater. Sci. Eng. R 46, 51. Portwood, T., Hensshaw, D.L., Stejny, J., 1986. Nucl. Tracks 12, 109–112. Price, P.B., 2005. Radiat. Meas. 40, 146–159. Price, P.B., 2008. Radiat. Meas. 43, 13–25. Sadowski, M., Al-Mashhadani., E.M., Szydlowski., A., Czyewski., T., Glowacka., L., Wielunski, M., 1994. Investigation on the response of CR-39 and PM-355 track

detectors to fast protons in the energy range 0.2–4.5 MeV. Nucl. Instrum. Methods B 86, 311–316. Szydlowski, A., Malinowska, Jaskola M., Korman, A., Malinowski, K., Kuk, M., 2013. Calibration studies and the application of nuclear track detectors to the detection of charged particles. Radiat. Meas. 50, 258–260. Tsuruta, T., 1999. Radiat. Meas. 31, 99. Tsuruta, T., 2000. Radiat. Meas. 32, 289. Tsuruta, T., Nakanishi, Y., Shimba, H., 2011. Radiat. Meas. 46, 59–63. Tse, K.C.C., Nikezic., D., Yu., K.N., 2007. Nucl. Instrum. Methods Phys. Res. B 263, 300–305. Yu, K.N., Nikezic, D., 2009. Alpha-particle radiobiological experiments involving solid state nuclear track detectors as substrates. In: Maksim, Sidorov, Oleg, Ivanov (Eds.), Nuclear Track Detectors: Design, Methods and Applications. Nova Science Publishers, NewYork, pp. 133–154. Yu, K.N., Ng, F.M.F., Nikezic, D., 2005. Radiat. Meas. 40, 380–383.