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Significant discrepancies in air kerma rates measured with free-air and cavity ionization chambers
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480 www.elsevier.com/locate/nima
Significant discrepancies in air kerma rates measured with free-air and cavity ionization chambers L. Bu¨ermann, G. Hilgers Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany Available online 18 May 2007
Abstract Air kerma rates were measured in the same narrow X-ray beams in the range 300–400 kV with a free-air ionization chamber and a graphite cavity ionization chamber. The graphite-to-air stopping-power ratios that are necessary to determine the air kerma rates according to the cavity theory were calculated by means of Monte Carlo methods based on measured energy distributions of the photon fluence and the ICRU 37 stopping-power values. As a result, it was found that the air kerma rates obtained with the cavity chamber were significantly higher, by up to about 2%. The discrepancies disappeared when different stopping-power values for graphite were used in the calculation of the graphite-to-air stopping-power ratios. The ICRU 37 values were calculated on the basis of a mean excitation energy in graphite of I ¼ 78 eV, in contrast to I ¼ 86 eV used for the calculation of those values solving the discrepancies obtained in the first approach. The results are of fundamental interest for primary standard dosimetry laboratories because all of them employ graphite cavity chambers to realize the unit of air kerma for 137Cs- and 60Co-g-radiation. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Dq; 06.20.Fn; 87.50.Gi Keywords: Primary air kerma standards; Free-air ionization chamber; Graphite cavity chamber; Cavity theory
1. Introduction Primary standard dosimetry laboratories maintain air kerma standards using free-air ionization chambers (FACs) for kilovoltage X-rays in the range 10–300 kV and graphite cavity ionization chambers for 137Cs- and 60 Co-g-radiation [1]. FACs become impractical for measurements in photon beams with energies higher than approximately 400 keV because the ranges of the secondary electrons in air become too large and, therefore, graphite cavity chambers are used in this energy range [1]. Recently, Borg et al. [2] have shown that the cavity theory holds for photons with energies down to approximately 150 keV. This implies that there is a small intermediate photon energy range where the two types of standards can be used for air kerma rate measurements. A comparison of both types of measurements is of fundamental interest in dosimetry because they rely on different physical princiCorresponding author. Tel.: +49 531 592 6620; fax: +49 531 592 6015.
E-mail address: [email protected] (L. Bu¨ermann). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.144
ples. In this work, the air kerma rates were measured in the same narrow X-ray beams in the range 300–400 kV with both free-air ionization chamber and graphite cavity ionization chamber. 2. Theory For a free-air chamber of measuring volume VFAC, the air kerma rate is determined by the relation Y K_ a ¼ ðI=mÞFAC ðW =eÞ ki (1) i
where m ¼ raVFAC is the mass of dry air contained in the measuring volume, ra the density of dry air at temperature 293.15 K and pressure 1013.25 hPa I the ionization current under these conditions, W the mean energy expended by an electron to produce an ion pair in dry air, and e the elementary charge. ki are correction factors to be applied to the standard (see Section 3.3 and Table 3). Usually, relative standard uncertainties of the air kerma rates of about 0.25% can be achieved [1].
ARTICLE IN PRESS L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
478
For a graphite cavity chamber of cavity volume Vcav, the air kerma rate is determined by the relation Y ki (2) K_ a ¼ ðI=mÞcav ðW =eÞðmen =rÞac s¯ca i
where m ¼ raVcav is the mass of dry air contained in the cavity volume, ðmen =rÞac the ratio of air to graphite of the mean mass–energy absorption coefficients, and s¯ca the ratio graphite to air of the mean restricted mass collision stopping powers with the cutoff energy D ¼ 10 keV. ki are correction factors to be applied to the standard (see Section 3.4 and Table 5). Usually, relative standard uncertainties of the air kerma rates of about 0.2% can be achieved [1].
used to measure the energy distributions of the photon fluence at a distance of 1 m from the focal spot. 3.2. Radiation qualities The Cu half value layers (HVL) and other main characteristics of the radiation qualities used in the measurements, called N300, N350 and N400, are shown in Table 1. The measurements were performed at a distance of 1 m from the focal spot at mean air kerma rates of approximately 8 mGy/s. The diameter of the circular field in the reference plane was 8 cm. 3.3. Free-air ionization chamber
3. Measurements Air kerma rates were measured at the X-ray facility described in Section 3.1 and with the radiation qualities described in Section 3.2. Measurements were carried out at a distance of 1 m from the focal spot with the free-air chamber and the cavity chamber described in Sections 3.3 and 3.4, respectively. A transmission–monitor chamber was used to link the air kerma rates measured with the freeair and the cavity chamber. It is important to note that the diaphragm diameter of the FAC and the outer diameter of the pancake-type cavity chamber are nearly identical so that corrections for possible beam non-uniformities need not to be applied in the comparison.
A large primary standard parallel-plate free-air chamber, called PK400, which is suitable to measure air kerma rates for X-ray qualities generated with tube voltages of up to 400 kV (Table 2) was used. The correction factors to be applied for the PK400 are listed in Table 3. Corrections for ionization gain by scattered photons, electron loss and aperture edge transmission were calculated by means of Monte Carlo methods using the EGSnrc code system [3]. The air humidity correction factor was 0.9980(4) according to ICRU 31 [4]. The correction factors for wall transmission, field
Table 2 Main dimensions of the PK400 free-air chamber
3.1. X-ray facility The air kerma rate measurements were performed at PTB’s X-ray facility which is normally used for the routine calibration of secondary air kerma standards. The facility is under strong quality management system control and all measuring instruments, such as electrometers, thermometers, pressure gauges, are calibrated traceably to primary standards of PTB. The X-ray source used for the investigations was of the type MG452, manufactured by YXLON. The converter-type generator operates at a frequency of 40 kHz and yields a constant potential which can be varied between 20 and 450 kV in steps of 25 V. The bipolar X-ray tube MB 450/1 has a 7 mm beryllium window. The high voltage was measured invasively by means of a voltage divider traceable to the primary standard of PTB for DC high voltage, and non-invasively using a high-purity Ge-spectrometer. The latter was also
Aperture diameter (cm) Air path length (cm) Collecting length (cm) Electrode separation (cm) Electrode height (cm) Measuring volume (cm3) Applied voltage (V)
4.9999(10) 63.15(5) 5.0257(10) 58 60 98.675(44) 10,000
Table 3 Correction factors and uncertainties of the PK400 free-air chamber Quality
N300
N350
N400
u
Air attenuation Scattered radiation Electron loss Aperture transmission
1.0087 0.9953 1.0013 0.9988
1.0084 0.9955 1.0016 0.9984
1.0079 0.9962 1.0042 0.9976
0.0010 0.0005 0.0005 0.0005
Table 1 Main characteristics of the radiation qualities Quality
Tube voltage (kV)
Filtration mm Al
mm Sn
mm Pb
1st HVL mm Cu
Mean energy (keV)
N300 N350 N400
300 350 400
4.0 4.0 4.0
3.0 3.0 3.0
5.0 5.0 10.0
5.99 6.51 7.26
248.5 281.1 329.3
ARTICLE IN PRESS L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
distortion, ion recombination, polarity effect and bremsstrahlung loss were found to be equal to 1 within relative uncertainties of 0.05%. The relative standard uncertainty of the air kerma rate measurements with the PK400 was estimated at 0.26%. 3.4. Graphite cavity ionization chamber A pancake-type graphite cavity ionization chamber, called HRK3, normally in use as a primary air kerma standard for 60Co and 137Cs-gamma radiation [5], was used to measure the air kerma rate in the X-ray beams by applying the cavity theory (Table 4). The correction factors for ion recombination, stem scattering and polarity effect were 1.0011(5), 0.9990(5) and 1.0000(5), respectively. The air humidity correction factor was 0.9970(3) according to ICRU 31 [4]. The wall correction factors, kwall, the values of ðmen =rÞac and s¯ca were calculated by means of the CAVRZnrc, DOSRZnrc and SPRRZnrc user codes [6], respectively, using the measured energy distribution of the photon fluence as a photon source. Results are listed in Table 5. Values of s¯ ca were also calculated with different sets of graphite stopping-power values, generated with Berger’s ESTAR program [7] by using different mean excitation energies (I-values) of graphite. Values calculated with I ¼ 78 eV according to ICRU 37 [8] and those obtained with I ¼ 86 and 87 eV are shown in Table 5. If one ignores the uncertainty contribution from the values of s¯ca , the relative standard uncertainty of the air kerma rate determined with the HRK3 is 0.23%.
Table 4 Main nominal dimensions of the HRK3 graphite cavity chamber Outer height (mm) Outer diameter (mm) Inner height (mm) Inner diameter (mm) Wall thickness (mm) Density of wall material (g/cm3) Electrode diameter (mm) Cavity volume (cm3) Applied voltage (V)
8.5 48 4.5 44 2 1.775 20 6.138(5) 100
Table 5 Wall correction factor kwall, ratio of the mean mass–energy absorption coefficients of air and graphite, and ratio of the mean restricted mass stopping powers of graphite and air calculated for three different sets of stopping power values for graphite Quality
N300
N350
N400
u
kwall ðmen =rÞac s¯ca (IC ¼ 78 eV) s¯ca (IC ¼ 86 eV) s¯ca (IC ¼ 87 eV)
0.9866 1.0055 1.0159 0.9989 0.9969
0.9887 1.0024 1.0158 0.9988 0.9968
0.9912 1.0007 1.0156 0.9987 0.9967
0.0002 0.0010
479
Table 6 Ratio of the air kerma rates determined with the PK400 to those of the HRK3 using the three different sets of s¯ca values Quality
N300
N350
N400
u
s¯ca (IC ¼ 78 eV) s¯ca (IC ¼ 86 eV) s¯ca (IC ¼ 87 eV)
0.979 0.997 0.999
0.985 1.002 1.004
0.987 1.004 1.006
0.003 0.003 0.003
4. Results and discussion The ratios of the air kerma rates obtained by the PK400 and the HRK3 chamber in the fields of N300, N350 and N400 are shown in Table 6. If one omits the uncertainty contribution from the s¯ca values, the relative uncertainty of the air kerma rate ratios is 0.3%. Please bear in mind that W/e, and hence its uncertainty, is cancelled out in the ratio because it is assumed to be the same value for both cavity and free-air chambers. In a first approach, the air kerma rates of the HRK3 were determined according to Eq. (2)using the s¯ca values based on the ICRU 37 [8] stopping-power values shown in Table 5. It was found that the air kerma rates measured with the HRK3 were significantly higher than those obtained with the PK400, by up to 2%. Different s¯ ca values were then calculated based on graphite stopping-power values computed with different I-values of graphite (see Table 5). By trial and error, a good agreement within a range of 0.4% between the air kerma rates of both chambers was achieved when I ¼ 86 eV was chosen (see Table 6). This value is within the uncertainties of I ¼ 86.9(1.2) eV, which was obtained by Bichsel et al. [9] from proton energy loss measurements in graphite. The results of this work strongly support the use of graphite stopping power values computed according to the methods described in ICRU 37 but with a different I-value of graphite close to the value measured by Bichsel et al. [9]. This result is of fundamental importance for primary standards dosimetry laboratories because all of them employ graphite cavity chambers to realize the unit of air kerma for 137Cs- and 60Co-g-radiation [1]. Problems arising from different values in the stoppingpower ratios were addressed in the past by Rogers and Kawrakow [10]. Moreover, the evaluation of the widely used W value for electrons arising from 60Co radiation in dry air [11] also relies on calculated graphite stopping-power values. Bu¨ermann [12] reported about discrepancies in the comparison of the calculated and the measured air kerma response of graphite cavity chambers for 30 to 300 kV X-ray beams, which could also partly be caused by the use of incorrect stopping-power values. This topic will be analyzed in a future study and is going to be published in a forthcoming paper.
ARTICLE IN PRESS 480
L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
References [1] L. Bu¨ermann, I. Csete, in: International Symposium on Standards and Codes of Practice in Medical Radiation Dosimetry: proceedings of an international symposium held in Vienna, Austria, 25–28 November 2002, vol.1;STI/PUB: 1153, 2003, p. 125. [2] J. Borg, I. Kawrakow, D.W.O. Rogers, J.P. Seuntjens, Med. Phys. 27 (2000) 1804. [3] I. Kawrakow, D.W.O. Rogers, Technical Report PIRS-701, National Research Council of Canada, Ottawa, 2000. [4] ICRU Report 31, Washington, DC, 1979. [5] I. Csete, L. Bu¨ermann, H.M. Kramer, PTB Report PTB-DOS-40, 2002, ISBN:0172-7095.
[6] D.W.O. Rogers, I. Kawrakow, J.P. Seuntjens, B.R.B. Walters, Technical Report PIRS-702, National Research Council of Canada, Ottawa, 2000. [7] M.J. Berger, NIST Report NISTIR-4999, Washington, DC, available online at /http://physics.nist.gov/StarS, 1992. [8] ICRU Report 37, Washington DC, 1984. [9] H. Bichsel, T. Hiraoka, Nucl. Instr. and Meth. B 66 (1992) 345. [10] D.W.O. Rogers, I. Kawrakow, Med. Phys. 30 (2003) 521. [11] M. Boutillon, A.-M. Perroche-Roux, Phys. Med. Biol. 32 (1987) 213. [12] L. Bu¨ermann, in: J.P. Seuntjens, P.N. Mobit (Eds.), Recent Developments in Accurate Radiation Dosimetry, Medical Physics Publishing, Madison, WI, 2002, p. 53.
Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480 www.elsevier.com/locate/nima
Significant discrepancies in air kerma rates measured with free-air and cavity ionization chambers L. Bu¨ermann, G. Hilgers Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany Available online 18 May 2007
Abstract Air kerma rates were measured in the same narrow X-ray beams in the range 300–400 kV with a free-air ionization chamber and a graphite cavity ionization chamber. The graphite-to-air stopping-power ratios that are necessary to determine the air kerma rates according to the cavity theory were calculated by means of Monte Carlo methods based on measured energy distributions of the photon fluence and the ICRU 37 stopping-power values. As a result, it was found that the air kerma rates obtained with the cavity chamber were significantly higher, by up to about 2%. The discrepancies disappeared when different stopping-power values for graphite were used in the calculation of the graphite-to-air stopping-power ratios. The ICRU 37 values were calculated on the basis of a mean excitation energy in graphite of I ¼ 78 eV, in contrast to I ¼ 86 eV used for the calculation of those values solving the discrepancies obtained in the first approach. The results are of fundamental interest for primary standard dosimetry laboratories because all of them employ graphite cavity chambers to realize the unit of air kerma for 137Cs- and 60Co-g-radiation. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Dq; 06.20.Fn; 87.50.Gi Keywords: Primary air kerma standards; Free-air ionization chamber; Graphite cavity chamber; Cavity theory
1. Introduction Primary standard dosimetry laboratories maintain air kerma standards using free-air ionization chambers (FACs) for kilovoltage X-rays in the range 10–300 kV and graphite cavity ionization chambers for 137Cs- and 60 Co-g-radiation [1]. FACs become impractical for measurements in photon beams with energies higher than approximately 400 keV because the ranges of the secondary electrons in air become too large and, therefore, graphite cavity chambers are used in this energy range [1]. Recently, Borg et al. [2] have shown that the cavity theory holds for photons with energies down to approximately 150 keV. This implies that there is a small intermediate photon energy range where the two types of standards can be used for air kerma rate measurements. A comparison of both types of measurements is of fundamental interest in dosimetry because they rely on different physical princiCorresponding author. Tel.: +49 531 592 6620; fax: +49 531 592 6015.
E-mail address: [email protected] (L. Bu¨ermann). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.144
ples. In this work, the air kerma rates were measured in the same narrow X-ray beams in the range 300–400 kV with both free-air ionization chamber and graphite cavity ionization chamber. 2. Theory For a free-air chamber of measuring volume VFAC, the air kerma rate is determined by the relation Y K_ a ¼ ðI=mÞFAC ðW =eÞ ki (1) i
where m ¼ raVFAC is the mass of dry air contained in the measuring volume, ra the density of dry air at temperature 293.15 K and pressure 1013.25 hPa I the ionization current under these conditions, W the mean energy expended by an electron to produce an ion pair in dry air, and e the elementary charge. ki are correction factors to be applied to the standard (see Section 3.3 and Table 3). Usually, relative standard uncertainties of the air kerma rates of about 0.25% can be achieved [1].
ARTICLE IN PRESS L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
478
For a graphite cavity chamber of cavity volume Vcav, the air kerma rate is determined by the relation Y ki (2) K_ a ¼ ðI=mÞcav ðW =eÞðmen =rÞac s¯ca i
where m ¼ raVcav is the mass of dry air contained in the cavity volume, ðmen =rÞac the ratio of air to graphite of the mean mass–energy absorption coefficients, and s¯ca the ratio graphite to air of the mean restricted mass collision stopping powers with the cutoff energy D ¼ 10 keV. ki are correction factors to be applied to the standard (see Section 3.4 and Table 5). Usually, relative standard uncertainties of the air kerma rates of about 0.2% can be achieved [1].
used to measure the energy distributions of the photon fluence at a distance of 1 m from the focal spot. 3.2. Radiation qualities The Cu half value layers (HVL) and other main characteristics of the radiation qualities used in the measurements, called N300, N350 and N400, are shown in Table 1. The measurements were performed at a distance of 1 m from the focal spot at mean air kerma rates of approximately 8 mGy/s. The diameter of the circular field in the reference plane was 8 cm. 3.3. Free-air ionization chamber
3. Measurements Air kerma rates were measured at the X-ray facility described in Section 3.1 and with the radiation qualities described in Section 3.2. Measurements were carried out at a distance of 1 m from the focal spot with the free-air chamber and the cavity chamber described in Sections 3.3 and 3.4, respectively. A transmission–monitor chamber was used to link the air kerma rates measured with the freeair and the cavity chamber. It is important to note that the diaphragm diameter of the FAC and the outer diameter of the pancake-type cavity chamber are nearly identical so that corrections for possible beam non-uniformities need not to be applied in the comparison.
A large primary standard parallel-plate free-air chamber, called PK400, which is suitable to measure air kerma rates for X-ray qualities generated with tube voltages of up to 400 kV (Table 2) was used. The correction factors to be applied for the PK400 are listed in Table 3. Corrections for ionization gain by scattered photons, electron loss and aperture edge transmission were calculated by means of Monte Carlo methods using the EGSnrc code system [3]. The air humidity correction factor was 0.9980(4) according to ICRU 31 [4]. The correction factors for wall transmission, field
Table 2 Main dimensions of the PK400 free-air chamber
3.1. X-ray facility The air kerma rate measurements were performed at PTB’s X-ray facility which is normally used for the routine calibration of secondary air kerma standards. The facility is under strong quality management system control and all measuring instruments, such as electrometers, thermometers, pressure gauges, are calibrated traceably to primary standards of PTB. The X-ray source used for the investigations was of the type MG452, manufactured by YXLON. The converter-type generator operates at a frequency of 40 kHz and yields a constant potential which can be varied between 20 and 450 kV in steps of 25 V. The bipolar X-ray tube MB 450/1 has a 7 mm beryllium window. The high voltage was measured invasively by means of a voltage divider traceable to the primary standard of PTB for DC high voltage, and non-invasively using a high-purity Ge-spectrometer. The latter was also
Aperture diameter (cm) Air path length (cm) Collecting length (cm) Electrode separation (cm) Electrode height (cm) Measuring volume (cm3) Applied voltage (V)
4.9999(10) 63.15(5) 5.0257(10) 58 60 98.675(44) 10,000
Table 3 Correction factors and uncertainties of the PK400 free-air chamber Quality
N300
N350
N400
u
Air attenuation Scattered radiation Electron loss Aperture transmission
1.0087 0.9953 1.0013 0.9988
1.0084 0.9955 1.0016 0.9984
1.0079 0.9962 1.0042 0.9976
0.0010 0.0005 0.0005 0.0005
Table 1 Main characteristics of the radiation qualities Quality
Tube voltage (kV)
Filtration mm Al
mm Sn
mm Pb
1st HVL mm Cu
Mean energy (keV)
N300 N350 N400
300 350 400
4.0 4.0 4.0
3.0 3.0 3.0
5.0 5.0 10.0
5.99 6.51 7.26
248.5 281.1 329.3
ARTICLE IN PRESS L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
distortion, ion recombination, polarity effect and bremsstrahlung loss were found to be equal to 1 within relative uncertainties of 0.05%. The relative standard uncertainty of the air kerma rate measurements with the PK400 was estimated at 0.26%. 3.4. Graphite cavity ionization chamber A pancake-type graphite cavity ionization chamber, called HRK3, normally in use as a primary air kerma standard for 60Co and 137Cs-gamma radiation [5], was used to measure the air kerma rate in the X-ray beams by applying the cavity theory (Table 4). The correction factors for ion recombination, stem scattering and polarity effect were 1.0011(5), 0.9990(5) and 1.0000(5), respectively. The air humidity correction factor was 0.9970(3) according to ICRU 31 [4]. The wall correction factors, kwall, the values of ðmen =rÞac and s¯ca were calculated by means of the CAVRZnrc, DOSRZnrc and SPRRZnrc user codes [6], respectively, using the measured energy distribution of the photon fluence as a photon source. Results are listed in Table 5. Values of s¯ ca were also calculated with different sets of graphite stopping-power values, generated with Berger’s ESTAR program [7] by using different mean excitation energies (I-values) of graphite. Values calculated with I ¼ 78 eV according to ICRU 37 [8] and those obtained with I ¼ 86 and 87 eV are shown in Table 5. If one ignores the uncertainty contribution from the values of s¯ca , the relative standard uncertainty of the air kerma rate determined with the HRK3 is 0.23%.
Table 4 Main nominal dimensions of the HRK3 graphite cavity chamber Outer height (mm) Outer diameter (mm) Inner height (mm) Inner diameter (mm) Wall thickness (mm) Density of wall material (g/cm3) Electrode diameter (mm) Cavity volume (cm3) Applied voltage (V)
8.5 48 4.5 44 2 1.775 20 6.138(5) 100
Table 5 Wall correction factor kwall, ratio of the mean mass–energy absorption coefficients of air and graphite, and ratio of the mean restricted mass stopping powers of graphite and air calculated for three different sets of stopping power values for graphite Quality
N300
N350
N400
u
kwall ðmen =rÞac s¯ca (IC ¼ 78 eV) s¯ca (IC ¼ 86 eV) s¯ca (IC ¼ 87 eV)
0.9866 1.0055 1.0159 0.9989 0.9969
0.9887 1.0024 1.0158 0.9988 0.9968
0.9912 1.0007 1.0156 0.9987 0.9967
0.0002 0.0010
479
Table 6 Ratio of the air kerma rates determined with the PK400 to those of the HRK3 using the three different sets of s¯ca values Quality
N300
N350
N400
u
s¯ca (IC ¼ 78 eV) s¯ca (IC ¼ 86 eV) s¯ca (IC ¼ 87 eV)
0.979 0.997 0.999
0.985 1.002 1.004
0.987 1.004 1.006
0.003 0.003 0.003
4. Results and discussion The ratios of the air kerma rates obtained by the PK400 and the HRK3 chamber in the fields of N300, N350 and N400 are shown in Table 6. If one omits the uncertainty contribution from the s¯ca values, the relative uncertainty of the air kerma rate ratios is 0.3%. Please bear in mind that W/e, and hence its uncertainty, is cancelled out in the ratio because it is assumed to be the same value for both cavity and free-air chambers. In a first approach, the air kerma rates of the HRK3 were determined according to Eq. (2)using the s¯ca values based on the ICRU 37 [8] stopping-power values shown in Table 5. It was found that the air kerma rates measured with the HRK3 were significantly higher than those obtained with the PK400, by up to 2%. Different s¯ ca values were then calculated based on graphite stopping-power values computed with different I-values of graphite (see Table 5). By trial and error, a good agreement within a range of 0.4% between the air kerma rates of both chambers was achieved when I ¼ 86 eV was chosen (see Table 6). This value is within the uncertainties of I ¼ 86.9(1.2) eV, which was obtained by Bichsel et al. [9] from proton energy loss measurements in graphite. The results of this work strongly support the use of graphite stopping power values computed according to the methods described in ICRU 37 but with a different I-value of graphite close to the value measured by Bichsel et al. [9]. This result is of fundamental importance for primary standards dosimetry laboratories because all of them employ graphite cavity chambers to realize the unit of air kerma for 137Cs- and 60Co-g-radiation [1]. Problems arising from different values in the stoppingpower ratios were addressed in the past by Rogers and Kawrakow [10]. Moreover, the evaluation of the widely used W value for electrons arising from 60Co radiation in dry air [11] also relies on calculated graphite stopping-power values. Bu¨ermann [12] reported about discrepancies in the comparison of the calculated and the measured air kerma response of graphite cavity chambers for 30 to 300 kV X-ray beams, which could also partly be caused by the use of incorrect stopping-power values. This topic will be analyzed in a future study and is going to be published in a forthcoming paper.
ARTICLE IN PRESS 480
L. Bu¨ermann, G. Hilgers / Nuclear Instruments and Methods in Physics Research A 580 (2007) 477–480
References [1] L. Bu¨ermann, I. Csete, in: International Symposium on Standards and Codes of Practice in Medical Radiation Dosimetry: proceedings of an international symposium held in Vienna, Austria, 25–28 November 2002, vol.1;STI/PUB: 1153, 2003, p. 125. [2] J. Borg, I. Kawrakow, D.W.O. Rogers, J.P. Seuntjens, Med. Phys. 27 (2000) 1804. [3] I. Kawrakow, D.W.O. Rogers, Technical Report PIRS-701, National Research Council of Canada, Ottawa, 2000. [4] ICRU Report 31, Washington, DC, 1979. [5] I. Csete, L. Bu¨ermann, H.M. Kramer, PTB Report PTB-DOS-40, 2002, ISBN:0172-7095.
[6] D.W.O. Rogers, I. Kawrakow, J.P. Seuntjens, B.R.B. Walters, Technical Report PIRS-702, National Research Council of Canada, Ottawa, 2000. [7] M.J. Berger, NIST Report NISTIR-4999, Washington, DC, available online at /http://physics.nist.gov/StarS, 1992. [8] ICRU Report 37, Washington DC, 1984. [9] H. Bichsel, T. Hiraoka, Nucl. Instr. and Meth. B 66 (1992) 345. [10] D.W.O. Rogers, I. Kawrakow, Med. Phys. 30 (2003) 521. [11] M. Boutillon, A.-M. Perroche-Roux, Phys. Med. Biol. 32 (1987) 213. [12] L. Bu¨ermann, in: J.P. Seuntjens, P.N. Mobit (Eds.), Recent Developments in Accurate Radiation Dosimetry, Medical Physics Publishing, Madison, WI, 2002, p. 53.