Field sampling has the potential to be an extremely time-consuming and expensive
portion of a radiological site remediation. Collected samples must be
shipped to an off-site laboratory or counted in an on-site mobile unit in
order to establish areas of contamination and to ensure that acceptable
residual levels of contaminants remain.
The Area CPM Calculator is a web-based calculator that estimates a gamma detector response for a target level of surface contamination. This calculator provides a rapid, exceptionally cost-effective assessment of contamination and cleanup standards based on field instrument data, which minimizes the use of more expensive sample collection and laboratory analysis. A correction factor for cpm analysis established between this calculator's results and lab sampling analysis may be needed to account for ground truthing and other field nuances. The user should verify calculator results with lab sampling.
Additional features of the Area CPM Calculator include:
Section 2 provides the user with a step by step guide for each page of the CPM calculator and highlights potential issues that may be encountered.
Daughter products that reach secular equilibrium in a hundred to a thousand years are automatically added. Adding a parent and it's daughter will automatically deselect the daughter as it is inherently included. To calculate the parent and daughter activities manually, deselect the box "Include daughter products." Chains with very long-lived daughters have been truncated at the typical 'parent' radionuclides for man-made purposes. To select one of three natural decay series find the parent with the suffix of 'n'. See Section 3.3 for more information.
Select primary (parent) radionuclides of interest by clicking on a radionuclide in the "Radionuclides (and daughter progeny)" list to highlight it and then clicking on the ">>" button to add it to the "Radionuclides of Interest" list. When one or all radionuclides have been selected, click "Next".
The TAC is analogous to PRG and DCC concentrations which can be calculated using the PRG, BPRG, SPRG, DCC, BDCC, and SDCC calculators. The TAC may also be based on an ARAR such as the 5 pCi/g over background standard from 40 CFR 192.
Enter the target activity concentration (TAC) in pCi/cm2 for each radionuclide in the table. If multiple radionuclides are selected, enter the Field Activity Concentrations (FACs). Click "Next".
The CPM calculator is only valid with the use of "0.5"x1", 1"x1", 2"x2", and 3"x3" NaI crystal detectors. For further guidance see Section 3.1.
Select the size of the gamma scintillation detector. Enter the estimated distance between the source and the detector in centimeters. Click "Next".
The results table lists the primary selected radionuclides and their daughters, each daughter's fractional activity and the number of photons from each daughter. For reference the field activity (if more than one primary is selected) and the target activity concentrations (TAC) are reprinted next to their individual conversions to cpm. At the bottom, the detector size and distance are followed by the Gross Detector Response (GDR) in cpm.
The results are displayed. Click on the number of photons for a list of a radionuclide's photon energies and yields. Click the "Back" button to go back a page or click "Start Over" to begin another calculation.
Section 3 details the detector-specific and radionuclide-specific parameters utilized for the consequent calculation of Gross Detector Response. Information required from the user about the radionuclides of interest, the detector used, and the geometry of the site are discussed in this section. Each step of the model is outlined in order to aid the user and ensure transparency.
Detector data is based on three sizes of gamma scintillation
detectors by Ludlum Measurements
Inc. The models are the 44-2,
NaI(Tl) crystal gamma scintillation detectors of sizes 0.5"x1", 1"x1",
2"x2", and 3"x3" NaI crystals.
The detector sensitivity (S), a constant that converts exposure to cpm,
and the detector response, a coefficient dependent on the detector's
cataloged response to the photon energy are fed into the Area CPM
The response coefficient is found in a graph of photon energy and
response from the detector user manual. Datathief, a shareware program, was used to
visually trace the graphs and convert the values to text for the three
detector sizes. The graphs and text files for the detectors can be seen below:
0.5"x1" graph and text,
1"x1" graph and text,
2"x2" graph and text.
3"x3" graph and text.
By default, the Area CPM Calculator estimates the detector response for the primary radionuclide in one hundred to one thousand years of secular equilibrium with its daughters. This is meaningful, especially in the common case of Cs-137 (the well-known 662 keV gamma of Cs-137 is actually produced by its metastable daughter, Ba-137m). However, this feature can be deactivated by deselecting the check box beneath the radionuclide selection list. The three main natural decay chain series have been truncated for use with manmade or purified radionuclides of U-238, U-235 and Th-232. For example, selecting U-238 will only include the immediate three daughters. The next sequential daughter, U-234, being so long lived, is considered a new radionuclide. To calculate for the natural state of the above three chains, as in calculating for uranium ore, select from the radionuclide list the natural instance of the parent radionuclide, denoted by the suffix, n: U-238n, U-235n, and Th-232n. Selecting one of these radionuclides will include the contribution of the entire natural chain.
The geometry of the model is a disc source above which a detector is suspended. The height (h) of the detector is the user's estimate of the distance in centimeters between the detector and the source of contamination. The maximum radius of the disc (R) is calculated such that the distance from the detector to the outer circumference of the circle is seven mean free paths (7/μ) of the greatest photon energy, a distance at which the photon is safely assumed to be attenuated. See the exposure derivation.
The target activity concentration (TAC) is converted to detector
response in cpm using an equation for exposure, the radionuclide-specific gamma
constant and detector-specific parameters. If multiple primary radionuclides
are selected each TAC is converted separately and then summed with a
risk-weighted equation using ratios established from the field activity
concentrations, or FACs.
The FAC is the actual activity of each primary radionuclide in the contamination. FACs are used to establish field ratios for multiple radionuclides. The target detector responses, in cpm, are then figured together to obtain the Gross Detector Response (GDR). First, the theoretical exposure rate at the detector is calculated for each TAC. The exposure rate is then multiplied by the detector sensitivity to convert to detector response in cpm and then corrected for the energy-specific detector response of the radionuclide's energy spectrum. Finally, a sum-ratio equation from MARSSIM that accounts for the contamination ratios and restrictive radionuclide concentrations is applied.
The exposure rate at the detector is calculated as follows:
where Χ is the exposure rate in μR/hr,
Γ is the gamma coefficient in μR hr-1 cm2 pCi-1,
A is the surface activity in pCi/cm2,
h is the distance from the detector to the surface in cm, and
R is the radius of the contamination boundary.
R is designed so that the range from the detector to the boundary is 7 mean free paths and is defined:
3.4.2 Normalized, Weighted Response Factor
The detector response varies by the energy of the incident photon. A normalized and weighted detector response factor, RFnorm, is calculated to correct the response for the photon spectrum:
where Y is the yield of each photon of each radionuclide,
dfrac is the emitting radionuclide's fractional activity based on the primary parent's activity, and
RF is the response factor correlating to the energy of each photon.
The detector response in cpm is found by multiplying the exposure rate at the detector by the detector's sensitivity and response factor, RFnorm, resulting in cpm corrected for the spectrum's energy variance:
where S is the sensitivity of the detector in cpm / (μR/hr), and
RF is the energy response factor of the detector.
For a single radionuclide of interest, the user may skip to section 3.4.5.
3.4.4 Relative Fraction
The relative fraction, fi, is the fraction of the total activity contributed by each radionuclide, i. The field activity concentrations are used to find the relative fractions of each radionuclide which are then applied to the Gross Detector Response. MARSSIM Chapter 4 (U.S. EPA, 2000)
Where cpmFACj is the field activity concentration of each radionuclide, j, in units of detector cpm.
3.4.5 Gross Detector Response
The Gross 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 "Gross Activity DCGL" (U.S. EPA, 2000) is applied to find the gross detector response and can be seen in an edited form below:
Where fj is the relative fraction of each radionuclide, j, and cpmSACj is the target activity concentration for each radionuclide, j, in units of detector cpm.
3.5.1 The Model
The Area CPM Calculator is designed around a model that converts surface activity in pCi/cm2 to detector response in cpm. The model is basic, involving a contaminated surface and a detector suspended a specified distance above. Differences between the model and field characteristics may introduce error into calculator estimates. The Area CPM Calculator does not replace the need for lab-based sampling or MARSSIM final status survey requirements; however, it may provide a reasonable starting point from which to work.
The model source surface assumes uniform contamination, such that the radionuclides of interest are in constant ratio to each other, and that the source surface is essentially infinite in lateral extent. Incongruity of the radionuclide ratios, such as separate spills or cross-contaminated sites, will diminish the effectiveness of the calculator.
3.5.3 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.
3.5.4 Shielding and Attenuation
The model calculator assumes the source surface is free from all shielding from materials or substances coating or between the detector and source, such as and including paper, oil or moisture.
3.5.5 Background Radiation
The model calculator does not account for background radiation. The user is responsible for adding or subtracting any background counts to the GDR.
3.5.6 Omitted Exposure Factors
This calculator does not account for backscatter or buildup in the surface material.
A correction factor may be designed and applied to correlate a few lab sampling analyses to the results of this calculator.
Guidance on circumstances where it may be appropriate to conduct real-time methods in addition to risk estimates based on slope factors is provided in Radiation Risk Assessment At CERCLA Sites: Q&A. Instances where it may be beneficial to also use direct measurments for assessing risk from external exposure to penetrating radiation include:
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, 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
ICRP, 2008. Nuclear Decay Data for Dosimetric Calculations. ICRP Publication 107. Ann. ICRP 38 (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.
B. Tummers, DataThief III. 2006 http://datathief.org/