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

Marko M. Ninkovic1 and Feriz Adrovic2 *1Institute of Nuclear Sciences – Vinca, Belgrade, 2University of Tuzla, Faculty of Science, Tuzla, 1Serbia 2Bosnia and Herzegovina* 

#### **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:

$$
\Gamma\_{\delta} = \frac{l^2}{A} \left( \frac{dK\_{air}}{dt} \right) \delta
\tag{1}
$$

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 m2 kg-1 which, when the terms gray and becquirel are used, becoms Gy m2 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, 1992,1993; Sabol & 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.

#### **2. Derivation of the equation for calculation of**

The kerma Kair , for interaction of X-rays and gamma rays with air is given by:

Air Kerma Rate Constants

**4. Results** 

applications.

**of for selected radionuclide** 

**4.1 New recalculated values of** 

in column 2 the half-life,

given the following data:

for Nuclides Important to Gamma Ray Dosimetry and Practical Application 5

In the calculation, instead of gamma ray total transition intensities, the gamma ray

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

Table 1, lists recalculated air kerma rate constants for the 35 radionuclide used most often in gamma ray dosimetry and practical applications. For every radionuclide in the table are

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 m2 GBq-1 h-1) 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

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

Bremsstrahlung radiation contributes to the total air kerma rate constant by, for exam≤≤le, for 60Co, 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

**4.2 Examples of our previous measurements of photon spectra and calculation** 

selected radionuclides ( 182Ta, 192Ir and 226Ra in equilibrium with its decay products).

**4.2.1 Photon spectra and recalculated of for 182Ta 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

As can be seen from Table 2, the entire of photon ray spectrum of 182Ta is divided into five characteristic groups of photon lines. The air kerma rate constant was calculated for every

intensities corrected for internal conversion of gamma rays were used.

in column 1 the symbol of gamma-emitting nuclide,

and many others applications of point gamma radiation sources.

photon spectra and intensity of omitted bremsstrahlung radiation.

 in column 3 the low- energy photon spectra limit, in column 4 the high-energy photon spectra limit ,

was used to calculate the coefficient , where photon spectrum data are available.

$$K\_{\rm air} = \left. \Phi \frac{\mu\_k}{\rho} \right| E \tag{2}$$

where is the flunce, *E* the photon energy, and the energy-dependent mass energytransfer coefficient for air.

The kerma rate, d*K /*d*t,* is obtained from the kerma by substituting the flux density for the fluence in Equation 2:

$$\frac{dK\_{air}}{dt} = \psi \frac{\mu\_k}{\rho} E\tag{3}$$

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:

$$\psi = \frac{A}{4\pi l^2} \tag{4}$$

By inserting Equation 4 in Equation 3, the following equation is obtained:

$$\frac{d\,K\_{air}}{dt} = \frac{A}{4\pi l^2} \frac{\mu\_k}{\rho} E$$

If photons with energy *Ei* are emitted per decay event with yield *pi,* Equation 5 becomes:

$$\frac{dK\_{air}}{dt} = \frac{A}{4\pi l^2} \sum\_{i} \left(\frac{\mu\_k}{\rho}\right) p\_i E\_i \tag{6}$$

By inserting Equation 6 in Equation 1, the following equation is obtained for

$$
\Gamma\_{\delta} = \frac{1}{4\pi} \sum\_{i} \left(\frac{\mu\_k}{\rho}\right)\_i p\_i E\_i \tag{7}
$$

#### **3. 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.

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.
