Air Kerma Rate Constants for Nuclides Important to Gamma Ray Dosimetry and Practical Application

It is often necessary to estimate the exposure rate at a distance from radionuclide emitting gamma or X rays. Such calculations may be required for planning radiation protection measures around radioactive sources, for calibration radiation monitoring instruments, for patient containing radionuclides or for estimating the absorbed dose to patients receiving brachytherapy. The factor relating activity and exposure rate has been various names: the k factor (Johns, 1961), the specific gamma ray constant (ICRU Rep. 10a, 1962), exposure rate constant (Parker et al., 1978) and gamma rate constant (Kereiakes & Rosenstein, 1980). Conversion to SI units required that this factor be replaced by the air kerma rate constant which is now defined as:  = 2 l A ( air dK dt )  (1)


Introduction
It is often necessary to estimate the exposure rate at a distance from radionuclide emitting gamma or X rays. Such calculations may be required for planning radiation protection measures around radioactive sources, for calibration radiation monitoring instruments, for patient containing radionuclides or for estimating the absorbed dose to patients receiving brachytherapy. The factor relating activity and exposure rate has been various names: the k factor (Johns, 1961), the specific gamma ray constant (ICRU Rep. 10a, 1962), exposure rate constant (Parker et al., 1978) and gamma rate constant (Kereiakes & Rosenstein, 1980). Conversion to SI units required that this factor be replaced by the air kerma rate constant   which is now defined as: where (dK air /dt)  is the air kerma rate due to photons of energy >at a distance l from a point source of activity A. The SI unit for  is J m 2 kg -1 which, when the terms gray and becquirel are used, becoms Gy m 2 s -1 Bq -1 .
In the process of analysing accessible data on the are kerma rate constants and its precursos for many radionuclides often used in practice (Nachtigal, 1969;Ninkovic & Mladenovic, 1970;NCRP Rep. 49, 1976;Ungar & Trabey, 1982;Aird et al., 1984;Attix, 1986;Ninkovic, 1987;Wasserman & Groenwald, 1988;Ninkovic & Raicevic, 1992,1993Sabol & Weng, 1995;Ninkovic et al., 2005) it was concluded that published data are in strong disagreement. That is the reason we decided to recalculate this quantities on the basis of the latest data on gamma ray spectra and on the latest data for mass energy-transfer coefficients for air.

Derivation of the equation for calculation of  
The kerma K air , for interaction of X-rays and gamma rays with air is given by: where is the flunce, E the photon energy, and    the energy-dependent mass energytransfer coefficient for air.
The kerma rate, dK /dt, is obtained from the kerma by substituting the flux density  for the fluence in Equation 2: where  is expressed in m -2 s -1 . The quantity  is derived from the activity A, of a radiation source in accordance with inverse square low:

Calculation of  
Starting from Equation 7, the air kerma rate constants,   were calculated using data on mass energy-transfer coefficients for air (Hubbell, 1969;Hubbell & Seltzer, 2001) and data on photon emission yield in the process of decay of the radionuclides (Firestone, 1996;Stabin & Luz, 2002). The subscript implies that only photons with energy > , in MeV are included in the calculation.
Concerning the radiation spectra emitted per decay of a radionuclide, there are three types of photons: the gamma ray photons, those characteristic X-ray photons, those from internal conversion of gamma rays and electron capture and those accompanying bremsstrahlung processes of electrons from   decay and internal conversion of gamma rays and X rays. In this calculation gamma rays and characteristic X-ray photons with energies >20 keV as value are only ones to have been taken into account. The contribution of bremsstrahlung radiation has not been included.

www.intechopen.com
Air Kerma Rate Constants for Nuclides Important to Gamma Ray Dosimetry and Practical Application 5 In the calculation, instead of gamma ray total transition intensities, the gamma ray intensities corrected for internal conversion of gamma rays were used.
The particular air kerma rate constants were calculated for each discrete line of the photon spectrum of the radionuclide, with effective yield per decay >0.01% and energy >20 keV. Since the energy structure of the photon spectra and accessible discrete numerical values of the mass energy-transfer coefficient for air are not the same, the cubic spline interpolation was used to calculate the coefficient , where photon spectrum data are available. in column 1 the symbol of gamma-emitting nuclide, in column 2 the half-life, in column 3 the low-energy photon spectra limit, in column 4 the high-energy photon spectra limit , in column 5 the calculated value of the constant in basic SI units, and finaly in column 6 the calculated value of the constant in practical units (Gy m 2 GBq -1 h -1 )

New recalculated values of  
The last unit, for air kerma rate constant, is the practical one especially, for radiation protection and safety calculations in nuclear medicine laboratories, industrial radiography and many others applications of point gamma radiation sources.
The accuracy of calculation of air kerma rate constants is not more than three significant figures. The major portion of the standard error associated with these calculated values of   arise from uncertainties in relative intensity measurements of the X ray and gamma ray photon spectra and intensity of omitted bremsstrahlung radiation.
Bremsstrahlung radiation contributes to the total air kerma rate constant by, for exam≤≤le, for 60 Co, not more than 0.4%, and this decreases markedly with decreasing photon energy (BCRUM, Br.J. Rad., 55, 1982). The contribution to   from the omitted photons of energies < 20 keV, varies from radionuclide to radionuclide, this is not interesting for the purposes of practical health physics, but is of interest in specific nuclear medicine radionuclide applications.

Examples of our previous measurements of photon spectra and calculation of   for selected radionuclide
The next section of the text shows, as examle, the data of our previous measurement of the photon spectrum and the results of calculating the air kerma rate constants for the three selected radionuclides ( 182 Ta,192 Ir and 226 Ra in equilibrium with its decay products).

Photon spectra and recalculated of   for 182 Ta radionuclide
As can be seen from Bearing in mind that standard tantalum sources are usually packed into 0.1 mm of platinum, it was calculated the constant for this type of source also. For that goal, it was calculated the absorption of tantalum photons into 0.1 mm of platinum and obtained that in this way the air kerma rate constant is reduced by 4,46 %. After this correction, a value of (42.8  0.9) aGy m 2 s -1 Bq -1 was obtained for air kerma rate constant for standard packaged encapsulated tantalum source (Ninkovic & Raicevic, 1992).    (Ninkovic & Raicevic, 1992) (Ninkovic & Raicevic, 1993) As can be seen from Table 3, the entire of photon ray spectrum of 192 Ir is divided into five characteristic groups of photon lines. The air kerma rate constant was calculated for each discrete photon line with yield per decay event >0.05 % and starting with energy of 0.1363 MeV as the lowest energy. That means X-ray were not included. The air kerma rate constant for the groups and for the total were obtained by addition of partial or single photon lines constant. Finally, a value of ( 30.0  0.9 ) aGy m 2 s -1 Bq -1 for an unshielded 192 Ir source has been obtained. That value is in good agreement with a new recalculated value given in Table 1.

Photon spectra and calculated of   for 192 Ir radionuclide
Keeping in mind that standard iridium sources are usually packed into 0.15 mm of platinum, the constant for that type of source was also calculated. For that goal, it was calculated the absorption of iridium photons into 0.15 mm of platinum and found that in the air kerma rate constant is reduced by 7.33 %. After this correction, a value of (27.8  0.9)

www.intechopen.com
Air Kerma Rate Constants for Nuclides Important to Gamma Ray Dosimetry and Practical Application 13 aGy m 2 s -1 Bq -1 was obtained for the air kerma rate constant for standard packaged iridium source (Ninkovic & Raicevic, 1993).  Table 4. Data for calculation and calculated partial, proup`s and total air kerma rate constant of 226 Ra radionuclide in equilibrium with its decay products (Ninkovic, 1987) As it can be seen from this table , the entire of photon ray spectrum of 226 Ra (in equilibrium with its decay products) are divided into five characteristic groups of photon lines. The air kerma rate constant was calculated for each discrete photon line with yield per decay event >0.05 % and starting with energy of 0.1857 MeV as value. That means X-ray were not included. The air kerma rate constant for the groups and for the total were obtained by addition of partial or single photon lines constant. Finally, a value of ( 56.9  2.4 ) aGy m 2 s -1 Bq -1 for an unshielded 226 Ra source has been obtained.

Group of lines
Having seen that standard radium sources are usually packed into 0.5 mm of platinum, the constant for that type of source was also calculated. For that goal it was used analyses of Shalek and Stoval (Shalek & Stovall, 1969), which is in good accordance with the earlier estimate of Aglincev et al. (Aglincev et al., 1960), that 0,5 mm of Pt by absorption of gamma radiation of radium and its decay products, reduce the air kerma rate constant with 9.25 %. After this correction, a value of ( 53.4  2.2 ) aGy m 2 s -1 Bq -1 was obtained for the air kerma rate constant for standard packaged radium sources (Ninkovic, 1987). On the basis of this calculated value and experimentally measured value of Aglincev et al. (Aglincev et al., 1960) it was concluded (Ninkovic, 1987) that the real value of air kerma rate constant of 226 Ra in equilibrium with its decay product is smaller by about 1 to 2 %, than the value recommended by ICRU (ICRU, Handbook 86, 1963).

Conclussion
Presented process of recalculation the values for air kerma rate constants, for 35 of the most often used radionuclide in practice, was based on the newest appropriate decay data for every radionuclide and latest numerical data for mass energy-transfer coefficient. That is the reason why, according to the authors opinion, obtained values for   listed in the table 1, are the most accurate data that can be found in the literature available at present.
It has to be pointed out that to calculate the absorbed dose to soft tissue the air kerma rate has to be multiplied by the ratio of the mass energy-absorption coefficient of soft tissue to that of air, which can be taken as 1,11 between 2 and 0,1 MeV and drops to 1,04 at 0,02 MeV. Also, since the radiation-waiting factor for gamma rays and X rays is 1, by multiplying air kerma rate constants by a factor 1,11, the soft tissue-equivalent dose constant can be obtained.