Area CPM User's Guide

1. Introduction

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:

  • option to calculate the Gross Detector Response for a single radionuclide or multiple radionuclide mixtures according to MARSSIM guidance
  • option to include daughter (+D) ingrowth
  • truncated decay chains in order to allow for man-made decay spectrum
  • three natural decay series
  • three gamma NaI crystal detector sizes to choose from
  • ability to specify the exact distance between the detector and the source
  • option to choose specific target activity

2. Step by Step User Guide

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.

2.1 Radionuclides of Interest

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".
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.

2.2 Activity Concentrations

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 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.

The FAC is based on laboratory analysis. The FAC is the activity of each primary radionuclide on the contaminated surface and are used to find the radionuclide ratios in mixtures.

2.3 Detector Information and Geometry of the Site

Select the size of the gamma scintillation detector. Enter the estimated distance between the source and the detector in centimeters. 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.

2.4 Gross Detector Response

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.
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.

Detector response for photons outside the energy range of the detectors, 40 keV to 2 MeV, cannot be reliably ascertained. If a radionuclide in the list emits a photon outside this range, a list of photon outliers will appear below the results table. A correction factor between lab sampling results and the Area CPM Calculator may be appropriate.

3. Design

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.

3.1 Gamma Scintillation Detectors

Detector data is based on three sizes of gamma scintillation detectors by Ludlum Measurements Inc. The models are the 44-2, 44-10, 44-62, and the 44-20 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 Calculator equations. 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.

3.2 Daughters and Chains

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.

3.3 Model Geometry

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.

3.4 Equations

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.

3.4.1 Exposure

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.

3.4.3 CPM

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 Limitations

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.

3.5.2 Uniformity

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.

3.6 Correction Factors

A correction factor may be designed and applied to correlate a few lab sampling analyses to the results of this calculator.

3.7 Guidance

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:

  • During early site assessment efforts when the site manager is attempting to communicate the relative risk posed by areas containing elevated levels of radiation,
  • As a real-time method for indicating that remedial objectives are being met during the conduct of the response action. The use of exposure rate measurments during the conduct of the response actions should not decrease the need for a final status survey.
Direct radiation exposure rate measurements may provide important indications of radiation risks at a site, particularly during early investigations, when these may be the first data avaіlable. However, such data may only reflect a subset of the radionuclides and exposure pathways of potential concern (e.g., only external exposure from gamma-emitting radionuclides in near-surface soil), and may present an incomplete picture of site risks (e.g., risk from internal exposures, or potential increased future risk from radionuclides in subsurface soils). In most cases, more accurate estimation of radiation risks will require additional site characterization data, including concentrations of all radionuclides of concern in all pertinent environmental media. The principal benefits of utilizing direct exposure rate measurements is the speed and convenience of analysis, and the elimination of potential modeling uncertainties. However, these data should be used in conjunction with, rather than instead of, characterization data of radionuclide concentrations in environmental media to obtain a complete picture of potential site-related risks. Exposure rate measurements should be correlated with actual scanned data by co-locating them to ensure that modeled assumptions about the correlation between exposure rate and sample concentrations is accurate.

4. FAQs

  • How does the Area CPM Calculator address daughter ingrowth (+D)?
    The gamma coefficient is a nuclide-specific exposure rate. To calculate daughter ingrowth at secular equilibrium, a special gamma coefficient (+D) that includes the exposure contribution by the chain is used. Then a normalized and weighted detector energy response is used to correct the detector response to account for the photon energy spectrum of the chain.
  • What assumptions does the Area CPM Calculator make?
    The Area CPM Calculator model makes several simplifying assumptions that are not likely to exist in the field. It assumes the surface is infinite in area, flat, and free from shielding by grass, oil, or water, and that the surface is uniformly contaminated such that the radionuclides are in a constant ratio to each other throughout the surface. Altering any of these assumptions may contribute to inaccurate results of the Area CPM Calculator.
  • Why doesn't the Area CPM Calculator address alpha and beta 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.
  • Why are some gamma emitters excluded from the calculator?
    Restrictions on energy range are due to the manufacturer's specifications on energy response, which references five sources between 60 keV to 1.25 MeV. This range was increased to include energies between 40 keV and 2 MeV, for which the expanded energies are bundled into the closest response coefficient. This allows for a significantly greater number of nuclides without greatly damaging confidence in the results. Nuclides that have emissions with energies outside this range are ignored and a notice to the user is displayed. It may be appropriate to apply a correction factor based on lab sampling.
  • How does the calculator address the energy ranges associated with radionuclide decay?
    The Area CPM Calculator addresses a nuclide's energy spectrum in two ways. The gamma coefficient is a nuclide-specific exposure rate that integrates all the exposure due to that nuclide. Then a normalized and weighted detector energy response is used to correct the detector response to account for the photon energy spectrum of the chain.

5. Glossary

  • activity concentration: The activity per surface area (pCi/cm2).
  • alpha particle: A positively charged particle comprised of a helium nucleus emitted by some radioactive materials during radioactive decay. Alpha particles expend their energy quickly and are easily attenuated. They have a very short range in air and will not penetrate the dead skin layer. They are difficult to detect in the field. The main hazard due to alpha particles is from ingestion or inhalation, such as gaseous radon and its particulate daughters.
  • attenuation: The loss of energy or intensity of a photon particle or beam as it passes through and interacts in a medium. The loss can be quantified with the use of the linear attenuation coefficient.
  • background radiation: Surrounding radiation that is present in the environment, emitted from a variety of natural and artificial sources, including cosmic sources and fallout. The user must account for and add the background radiation to the Gross Detector Response.
  • Becquerel (Bq): The International System (SI) unit of radioactivity equal to one disintegration per second. 1 curie = 3.7 x 1010 Becquerels.
  • beta particle: An electron emitted from the nucleus during radioactive decay. Beta particles have a relatively short range in air. Although very high energy betas can be easily measured, most beta radiation is difficult to measure with accuracy in the field. The main hazard from beta particles is exposure to eyes and skin.
  • counts per minute (cpm): The number of counts a radiation detector records in a minute.
  • curie (Ci): A unit of radioactivity defined as 3.7 x 1010 Becquerels, or decays per second, which is approximately equal to the decay rate of one gram of Ra-226.
  • detector: An instrument that detects radiation.
  • detector response curve: A graph of a gamma detector response to photons of multiple energies.
  • detector response factor (RF): A coefficient for correcting for a gamma detector's varied response due to incident photons of multiple energies.
  • exposure rate: The amount of ionization produced per unit time in air by X-rays or gamma rays. The unit of exposure rate is Roentgen/hour (R/h).
  • Field Activity Concentration (FAC): The current concentration of parent nuclides in the field. This is used primarily to ascertain contaminant ratios.
  • fractivity: The fractional activity of a daughter compared to the primary parent nuclide in secular equilibrium. This fraction is multiplied by the primary parent activity to find the daughter activity.
  • gamma constant/coefficient: The gamma constant is a nuclide-specific exposure rate due to photons. The gamma coefficient differs from the gamma constant in that the coefficient includes annihilation photons as contributing to exposure. The gamma coefficient was compiled from the output of the DECDATA software of ICRP Publication 107 (ICRP, 2008).
  • gamma radiation: Penetrating high-energy, short-wavelength electromagnetic radiation emitted from the nucleus during radioactive decay. Gamma rays are very penetrating and require dense materials, such as lead or steel, for shielding. Gamma particles are also called photons.
  • Gross Detector Response: The final cpm result.
  • half-life (T1/2): The interval in which the activity of a radionuclide will decay to half of its initial value. The half-life is related to the decay constant λ as T1/2= ln(2) / λ .
  • isotope: Atoms of the same atomic number, the number of protons, but with more or less neutrons, which often contributes to the stability, or radioactivity, of the atom.
  • linear attenuation coefficient: A function of particle energy, the linear attenuation coefficient, μ, is the probability that a particle will interact or attenuate in a medium.
  • MARSSIM: The Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM) provides guidance to federal agencies, states, site owners, contractors, and other private entities on how to demonstrate that their site is in compliance with a radiation dose or risk-based regulation, otherwise known as a release criterion.
  • mean free path: The average distance traveled by a projectile prior to an interaction and the inverse of the linear attenuation coefficient, μ. The intensity of a beam of photons will be diminished to 37% in one mean free path of material. At seven mean free paths the intensity of the beam is negligible and considered to be completely attenuated.
  • nuclide: A general term used to describe the full range of elements and their family of isotopes.
  • picocurie (pCi): A unit of radioactivity defined as 1 x 10-12 curies.
  • primary nuclide: A term used to denote a nuclide selected by the user as opposed to a daughter nuclide. Not all primary nuclides have daughter nuclides.
  • radionuclide: see nuclide.
  • relative fraction (f): The fraction of the total activity contributed by one nuclide of a mixture.
  • Roentgen (R): The unit of photon exposure in air equivalent to 2.58 x 10-4 C/kg.
  • sensitivity (S): The detector signal output per unit exposure (cpm / (μR/hr)).
  • shielding: Any material or substance that blocks or attenuates radiation.
  • Target Activity Concentration (TAC): The surface activity concentration that meets the cumulative risk assessment for a radionuclide of interest, although any level of surface activity can be used for investigative purposes.
  • yield: particles emitted per nuclide decay.

6. Appendix (data and links)

Preliminary Remediation Goal (PRG) Calculators

Tools for calculating the preliminary remediation goals for soil and water, inside buildings, and outdoor surfaces are available.

Dose Compliance Concentrations (DCC) Calculators

Tools for calculating the dose compliance concentrations for soil and water, inside buildings, and outdoor surfaces are available.

Nuclide Data File

This table was built from the data included in ICRP 107.

Response Curves

The detector response curves are generated from graphing the responses of a number of commonly used check sources. The curves can be found here.

7. 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). National Institute of Standards and Technology, Gaithersburg, MD.

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