Area CPM Calculator User's Guide
1. Introduction
The Area CPM Calculator is a field screening tool provided to help determine a detector instrument response, in counts per minute (cpm), equivalent to a prescribed level of surface contamination, in pCi/cm2.
The calculator can be used on surfaces contaminated with one or more radionuclides. For multiple radionuclides the remedial allowance of each radionuclide is compared to its ratio in the mixture according to here. Remedial activity can be calculated using the PRG, BPRG, SPRG, DCC, BDCC, and SDCC calculators.
It is important to note that the Area CPM Calculator does not replace the need for lab-based sampling, but may help reduce the amount of intermediary sampling. Final sample-based surveys are required to prove successful remediation.
2. Model Assumptions
2.1 Uniformity
The model assumes that the source surface is uniformly contaminated, such that the radionuclides of interest are in constant ratio to each other, and the contamination source is infinite in lateral extent. As a result, if the ratios of the nuclides vary spatially, such as separate spills or cross-contaminated sites, this tool will not provide an accurate assessment and the user must rely on other methods of sampling to ascertain the extent and level of contamination.
2.2 Gamma Emitters
The model addresses only gamma emitters. Nuclides that emit alpha and beta radiation are difficult to measure with any accuracy in the field and are omitted from this model unless the radionuclide also emits a qualifying gamma particle. Nuclides with a gamma yield less than 0.1% are omitted from the selection list.
Nuclides that emit alpha and beta radiation are difficult to measure with any accuracy in the field and are omitted unless the nuclide also emits a qualifying gamma particle.
2.3 Shielding and Attenuation
The model assumes the source surface is free from all substances (oil, moisture, etc.).
2.4 Background Radiation
Background radiation is not accounted for in the model. The user is responsible for adding any background radiation to the final goal detector response.
2.5 Omitted Shielding Factors
The Area CPM Calculator does not account for backscatter or buildup in the surface material.
3. Model Inputs
3.1 Radionuclide Specific Parameters
Radionuclide specific parameters used in the model include: mode of radioactive decay, principal photon yield (%), and principal photon energy (MeV). This data can be viewed here.
3.2 Preliminary Remediation Goals (PRGs)
Tools for calculating the preliminary remediation goals for soil and water, inside buildings, and outside hard surfaces are available.
3.3 Dose Compliance Concentrations (DCC) Calculators
Tools for calculating the dose compliance concentrations for soil and water, inside buildings, and outdoor surfaces are available.
3.4 Linear Attenuation Coefficients of Photons in Air
The linear attenuation coefficient is calculated from the approximation of three equations fit to a graph of the linear attenuation coefficient per energy of photon in air found here. See Section 4.2 for more information.
4. Equations
4.1 Geometric Attenuation and Linear Attenuation Coefficient
Geometric attenuation is the loss of source intensity due to the divergence of particles as they travel away from a source. As the distance between the source and the detector increases, fewer particles are counted by the detector.
The linear attenuation coefficient is the loss of source intensity due to the interaction of the particles in a medium. The linear attenuation coefficient (μ) is dependent on the density of the medium through which the particles are travelling, in this case air, and the principal photon energy (T).
To estimate the linear attenuation coefficient for any given energy a table of linear attenuation coefficients (Eckerman, 2006) was plotted and broken into three best fit equations. The table and resulting graph can be viewed here.
For the following energy ranges of T (MeV) the linear attenuation coefficient, μ (1/cm), can be found as follows:
| T ≤ 0.03 | μ = 2 x 10-8T-2.832 |
| 0.03 < T ≤ 18 | μ = 8 x 10-5T-0.436 |
| 18 < T | μ = 2 x 10-5T-0.0349 |
To calculate the total effect of the geometric attenuation and linear attenuation on the detector reading, the following equation, derived from Eq. 6.38 (Shultis, J., Faw, R., 2000) is used:
where
Θmax is the maximum angle created between the perpendicular of the detector to the outside of the infinite disk source;
r is the radius of the disk source; and
h is the height from the disk source to the detector
This integral is further derived (Eq. 6.43, Shultis, J., Faw, R., 2000) as:
For 0 ≤ μ*h ≤ 1 the exponential function, E, is numerically evaluated:
and for 1 ≤ μ*h ≤ 1,
4.2 Converting Remedial Activity to Detector Response
The remedial activity (pCi/cm2) is the maximum radionuclide activity permitted that meets the cumulative risk assessment for a single radionuclide of interest. This value can be looked up using the PRG, BPRG, SPRG, DCC, BDCC, and SDCC calculators.
The remedial levels of activity are converted to detector response (cpm) for each radionuclide i using the following equation:
Where
Cr,i (cpm) is the remedial detector reading for radionuclide i;
Ri (pCi/cm2) is the remedial activity for radionuclide i;
Yi (unitless) is the percentage photon yield of radionuclide i;
Di (unitless) is the detector efficiency for radionuclide i;
Ii is the attenuation; and
A (cm2) is the area of detector's surface
Ri, Di, and A are variables entered by the user.
4.3 Converting Present Activity to Detector Response
The present levels of activity or the ratios by activity (pCi/cm2) are converted to detector response (cpm) for each radionuclide i using the following equation:
where
Cp,i (cpm) is the present detector reading for radionuclide i;
Pi (pCi/cm2) is the present activity for radionuclide i;
Yi (unitless) is the percentage photon yield of radionuclide i;
Di (unitless) is the detector efficiency for radionuclide i;
Ii is the attenuation; and
A (cm2) is the area of detector's surface
Ri, Di, and A are variables entered by the user.
Then the ratio of each radionuclide i by detector response (cpm) is calculated according to the following equation:
These ratios are used in determining the goal detector response.
4.4 Calculating Goal Detector Response
The goal detector response is the total calculated response of the detector in cpm for the desired remedial activity of the particular radionuclides in the soil. MARSSIM Equation 4-4 (U.S. EPA, 1997) is used to find the goal detector response and can be seen below:
5. Using the cpm Calculator
Step by step instructions for the tool are given below.
5.1 Select Nuclides of Interest
Select and move the nuclide or nuclides of interest by first highlighting and then clicking >> to move the nuclides into the selection box or << to remove them.
Multiple radionuclides can be moved individually or all at once by using the SHIFT or CRTL key.
If you wish to clear the selected nuclides, click RESET.
5.2 Enter Detector Data
Enter the surface area (cm2) of the detector*. For a volumetric detector, such as a NaI detector, enter the surface area of the crystal, omitting the top disk, which is covered by the photomultiplier tube.
Enter the distance (cm) between the detector and the source surface.
Enter the detector efficiency (unitless) for each radionuclide. The efficiency must be between 0 and 1.
5.3 Enter Remedial Activity
Enter the remedial activity in pCi/cm2 for each radionuclide.
5.4 Radionuclide Concentrations or Ratios
The user may choose to enter the concentration of each radionuclide (pCi/cm2) or the ratio of each radionuclide by activity (pCi/cm2). If ratios are entered, they must add up to 1. If only one radionuclide was selected the ratio is 1 and the tool will skip this page.
5.5 Results
The results page displays information entered by the user and radionuclide-specific parameters needed to calculate the goal detector response (cpm). Hover the cursor over the column headers or decay mode for more information. To view a radionuclide's natural decay chain, simply click on the radionuclide name. The goal detector response is displayed in the bottom right most cell of the results table.
6. References
ITRC (Interstate Technology and Regulatory Council), 2006. Real-Time Measurement of Radionuclides in Soil: Technology and Case Studies. RAD-4. Washington, D.C.: Interstate Technology and Regulatory Council, Real-Time Radionuclide Team.
U.S. EPA, 1997. Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM).
U.S. EPA, 1999. Radiation Risk Assessment At CERCLA Sites: Q & A.
Shultis, J., Faw, R., 2000. Radiation Shielding. American Nuclear Society, La Grange Park, Illinois. ISBN: 0-89448-456-7
Berger, M.J. et al, 2005. XCOM: Photon Cross Section Database
(ver.y1.3).
Eckerman, K.F. et al, 2006. Radiological Toolbox User's Manual. ORNL/TM-2004/27R1.
International Commission on Radiological Protection (ICRP) Publication 107: Nuclear Decay Data for Dosimetric Calculations, 2009. ISBN: 978-0-7020-3475-6.