Recommendations on Dose Coefficients for Assessing Doses From Accidental Radionuclide Releases to the Environment

Appendix B: Considerations For Radionuclide Decay Chains And Example Calculations

Considerations for Radionuclide Decay Chains

In assessing doses from environmental exposures to radionuclides, it is important to realise that, in general, dose coefficients for radionuclides do not include any contribution to dose due to ingrowth of decay-chain members in the environment, although coefficients for internal exposures do reflect the contribution to dose from ingrowth in the body. In some cases, it is reasonable to assume that the parent and progeny are in equilibrium in the environment following release from the source. Decay chains where this assumption is often valid include:

¹⁰⁶Ru - ¹⁰⁶Rh ¹³²Te - ¹³²I ¹³⁷Cs - ¹³⁷mBa ¹⁴⁴Ce - ^144/144mPr

In these cases, it is almost always reasonable to assume that secular equilibrium between parent and progeny is maintained both in the plume and following deposition, due to the short half-lives of the daughters (less than a few hours). In Table 2 , external dose coefficients listed for the parent radionuclides of these four decay chains were obtained by multiplying the dose coefficient for the progeny by the decay-branching fraction and adding to the coefficient for the parent.

For most cases, it is not reasonable to assume secular equilibrium between the parent and its chain members. Examples include the complex decay chains of long-lived actinides, those involving noble gases and nuclides with non-zero deposition velocities, such as ⁸⁸Kr - ⁸⁸Rb, and those in which the parent and daughter are reasonably long-lived with similar half-lives (e.g. ⁹⁵Zr - ⁹⁵Nb). The contribution from each must be explicitly calculated by considering its production and decay, and any difference in environmental behaviour before dose coefficients for a radionuclide and its progeny can be combined (Kocher 1983).

The activity of a decay-chain member at any time, t, due to radioactive decay and ingrowth can be described by the Bateman equations (CRC 1982, CSA 1991, Eckerman and Ryman 1993). Using these equations, the activity at time t of the various chain members, A_i (t), from the decay of an initial quantity of the parent, A₁⁰, is given by (Eckerman and Ryman 1993) 3

For exposures due to either submersion in, or inhalation of, the radioactive plume, the activities calculated using equation B.1 can be multiplied by the appropriate cloudshine dose coefficients, or the inhalation dose coefficients and breathing rates, to give the effective dose rate from each radionuclide at time, t. The effective dose is the integral of the dose rate over the period of interest. If it is assumed that radionuclide concentrations remain constant over the exposure period (the time for the radioactive plume to pass), the effective dose can be determined by multiplying the dose rate by the exposure time, T, and summing over the contribution from each radionuclide.

For ground contamination, where radioactive decay and ingrowth are more important due to the potentially longer exposure period, it is usually not justified to assume that radionuclide concentrations remain constant. In this case, the effective dose can be calculated by integrating equation B.1 over the exposure period, and applying the appropriate groundshine dose coefficients. For a single contamination event resulting in a ground surface activity concentration of A₁⁰, the effective dose, E (Sv), over exposure period T, is given by (Eckerman and Ryman 1993)

where DC_ext,i is the groundshine dose coefficient for radionuclide i.

Under the more general scenario where the initial activities of the progeny A₂⁰, A₃⁰...A_n⁰ ≠ 0, the contribution due to each non-zero member, A_i⁰, can be calculated from equation B.1 and B.2 by replacing A₁⁰ with radionuclide A_i⁰ as the parent of the sub-chain. Information on nuclear decay characteristics, including radioactive decay products and fractional yields is available from several sources, including ICRP (1983), Eckerman et al (1993), and Eckerman and Legett (1996).

Equations B.1 and B.2 apply to the specific scenarios described above, and only take account of changes in activity concentration due to nuclear decay transformations. As stated previously, changes due to differences in environmental behaviour should also be accounted for, where appropriate. Recommendations on this topic were beyond the scope of the Working Group.

Example Calculations

The following examples are intended to illustrate the how the information contained in this report may be used in the evaluation of effective doses to exposed individuals.

Example 1:

The concentration of ¹³⁷Cs in the atmosphere following an accidental release from a facility is estimated to be about 100 Bq m^-3. The time of exposure is estimated to be 3 hours. Estimate the effective doses to an adult from inhalation and submersion in the plume, assuming equilibrium between ¹³⁷Cs and its daughter, ^137mBa.

From Table 1 , the adult breathing rate is 22.2 m³ d^-1. From Table 2 , the adult inhalation and cloudshine dose coefficients for ¹³⁷Cs are:

• inhalation: 4.6×10-9 Sv Bq-1
• cloudshine: 2.55×10-14 Sv s-1 Bq-1 m3

The cloudshine dose coefficient includes the contribution from 137mBa in equilibrium with 137Cs.

The effective dose is given by the product of the dose rate and the exposure duration. For submersion, the effective dose received during passage of the plume is given by E_sub

• = (DC_sub C_Cs) t
• = 2.55×10^-14 Sv s^-1 Bq^-1 m³ x 100 Bq m^-3 x 3 h × 3600 s h^-1
• = 2.8×10^-8 Sv

If the assumption of equilibrium was not valid, the contributions to external dose from the two radionuclides would have to be calculated separately using the dose coefficients from Appendix C .

For inhalation, the effective dose committed during the passage of the plume is given by Einh

• = (DC_{inh_Cs} C_Cs B_adult ) t
• = 4.6×10^-9 Sv Bq^-1 × 100 Bq m^-3 × 22.2 m³ d^-1 × 3 h × 0.04167 d h^-1
• = 1.3×10^-6 Sv

Example 2:

Assume that deposition of ⁹⁵Zr from an airborne plume results in a uniform ground surface contamination of 1 000 Bq m^-2. Calculate the effective dose to an adult in the first month following deposition, assuming that the exposure is continuous, and that radioactive decay is the only mechanism by which the contamination is removed.

The effective dose is the integral of the dose rate due to the decay of ⁹⁵Zr and its progeny, ^95mNb and ⁹⁵Nb, which are assumed to be initially absent. The branching fractions for transformations (f _{j, j+1}) are 0.993 for ⁹⁵Zr ⁹⁵Nb, 0.007 for ⁹⁵Zr ^95mNb, and 1.0 for ^95mNb ⁹⁵Nb. This can be approximated by assuming that f = 1 for the transformation of ⁹⁵Zr to ⁹⁵Nb, and ignoring the contribution from ^95mNb.

In this example, the groundshine dose coefficients for ⁹⁵Zr and ⁹⁵Nb are treated separately. As given in Appendix C , the groundshine dose coefficients for adults are:

• ⁹⁵Zr: 7.04×10^-16 Sv s^-1 Bq^-1 m²
• ⁹⁵Nb: 7.28×10^-16 Sv s^-1 Bq^-1 m²

The decay constants for the two radionuclides are: λ _Zr95

•  = ln 2 / T_1/2
• = 0.693 / (63.98 d × 86 400 s d^-1)
• = 1.25 ×10^-7 s^-1

λ _Nb95

•  = ln 2 / (35.15 d × 86 400 s d^-1)
• = 2.28 ×10^-7 s^-1

From equation B.2, the effective dose from groundshine is given by

Substituting in the values defined above, the effective dose in the first 30 days following deposition is 1.97 × 10^-6 Sv. If the ⁹⁵Zr ^95mNb ⁹⁵Nb branch is explicitly included, additional terms appear in the above equation, which in this example are insignificant.

References

• CRC (1982) CRC Handbook of Radiation Measurement and Protection, Section A, Volume II: Biological and Mathematical Information. CRC Press Inc, pp 244-249.
• CSA (1991) Guidelines for calculating radiation doses to the public from a release of airborne radioactive material under hypothetical accident conditions in nuclear reactors. CAN/CSA-N288.2-M91. Canadian Standards Association, Toronto, Ontario.
• Eckerman K.F., Westfall R.J., Ryman J.C., and Cristy M. (1993) Nuclear decay data files of the Dosimetry Research Group. ORNL/TM-12350. Oak Ridge National Laboratory, Oak Ridge, TN.
• Eckerman K.F. and Ryman J.C. (1993) Federal Guidance Report No. 12: External exposure to radionuclides in air, water, and soil. EPA 402-R-93-081. U.S. Environmental Protection Agency, Office of Radiation and Indoor Air, Washington, DC.
• Eckerman K.F. and Leggett R.W. (1996) DCFPAK: Dose coefficient data file package for Sandia National Laboratory, ORNL/TM-13347. Oak Ridge National Laboratory, Oak Ridge, TN.
• ICRP (1983) Radionuclide Transformations: Energy and intensity of emissions. Publication 38. Ann. ICRP Vols. 11-13, Pergamon Press, Oxford.

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³ Equations B.1 and B.2 contain a correction in the subscript of term λ_j+1 from that found in Eckerman and Ryman (1993), equations A.2 and A.3.