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Coincidence summing corrections for gamma-ray spectrometry.

Contents

Introduction

True Coincidence Summation occurs when two gamma-rays are emitted during the same decay event of the nucleus, so that they appear to be emitted instantaneously. This seemingly instantaneous emission of separate gamma-rays is known as coincidence. In this situation the detector will see both of the gamma-ray energies as one larger energy deposited in the detector. A tell-tale sign of coincidence is a summation peak that appears at the combined energy of the two characteristic gamma-rays of the source.

Advantages of the web application:

  • The advantages of the web application are that there is no software to install and it is available worldwide - only a web browser and an internet connection are required
  • Time consuming calibrations avoided
  • Easy to use
  • User friendly interface


Theoretical Background

True coincidence summing occurs whenever two (or more) different gamma-rays emitted from the same decay are registered simultaneously by the detector. As such, it should always be distinguished from the random coincidence summing, which involves two gamma-ray from two different decays registering simultaneously. The rate of random coincidences is proportional to the activity of the sample, whereas the rate of true coincidences is not. Rather, it is a feature of the geometry of the measurement setup, i.e., the detector size and the distance between the detector and the sample.

As an example, let us consider a radionuclide like Co-60 decays with a two-step cascade in which two gamma-rays are always emitted. When the first of these interact with the detector and deposits all of its energy in it, the corresponding count would end up in its full-energy-peak if Co-60 were a single-gamma emitter. But in reality, the second gamma ray can also interact with the detector, resulting in an increase in the deposited energy in the detector and causing the count of the first gamma-ray to be “lost” from its full-energy-peak.

Cascade gamma emission in Co-60.


What exactly do we mean by that? One has to bear in mind that the full-energy-peak efficiency is defined with reference to single-gamma emitters. Here is the basic formula of gamma-ray spectrometry, which is used in the calibration process and in the analysis of the spectrum and the determination of the activities of the radionuclides in the sample:


N = A b t ε


In this equation, N is the number of counts in a full-energy-peak, A is the activity of the radionuclide emitting the gamma-ray, t is the life-time and b the emission probability of the gamma ray. The full-energy-peak efficiency is denoted by ε. To calibrate the detector, the formula is used with known values of N, A, b and t to determine ε, and in the analysis phase the unknown activity A is determined from the known quantities N, t, b and ε In both cases it is assumed that the radionuclide in question is a single-gamma emitter. This is clearly necessary in order to keep the definition of the full-energy-peak efficiency radionuclide independent, i.e., to make the efficiency a function of gamma-ray energy only.

In the case of Co-60, however, the formula no longer applies, because not all the events with a full deposition of the energy of the first gamma-ray end up in its full-energy-peak, as discussed above. We therefore need to introduce a correction factor C, which is radionuclide dependent and also has a different value for each of the gamma-lines of a given multi-gamma radionuclide:


N = A b t ε C


The value of C is a complex function of the detector and sample size, composition, density and relative distance, as well as the entire decay scheme of the radionuclide. In practice it can therefore only be calculated using a computer code. The only alternative is to prepare a standard that matches the measured sample in all of its characteristics, including the radionuclide vector, and carry out a simple relative measurement.

The correction factor should be applied both in the calibration and in the analysis phase.

EFFTRAN offers the possibility of calculating the coincidence summing correction factors for a large number on radionuclides and for virtually any detector and sample size, density and composition. The results are given gamma-line by gamma-line, with the unaffected lines having a correction factor of 1.


The general characteristics of the true coincidence summing effect to bear in mind are as follows:

  • Is also called “cascade summing” or “true summing”
  • Does NOT depend on the activity of the source
  • Depends on the decay scheme (cascading gamma-rays)
  • Depends on the geometry
  • Is only important for close distance between source and detector
  • Is less important for smaller detectors
  • Well-type detectors suffer most coincidence summing
  • Summing with X-rays can be very important (n-type detectors) – use an absorber
  • Generally results in a lower detection efficiency for a specific peak (summing-out)
  • Sometimes results in a higher detection efficiency for a specific peak (summing-in)
  • Is the main reason for errors of 10-50% in gamma-ray spectrometry
  • Is almost always present with complex decay schemes
  • Affects calibration, as well as sample analysis


Source / Detector Configuration

The basic Source (Sample) / Detector configuration in the Coincidence Summing Corrections++ application is shown below. Here the Source / Sample is shown on top of the Detector. A detailed description of the Source / Sample and the Detector can be setup in My Detectors and My Source described below.

Source / Detector configuration showing the source on top of the detector.


Coincidence Summing Corrections Web Application

My Detectors

Coincidence Summing Corrections: my Detectors Enlarge


  • The window-to-crystal gap is the distance between the top dead layer of the crystal and the detector window.
  • The crystal diameter includes its side dead layer. Similarly, the crystal length includes its top dead layer.
  • The upper edge of the crystal may be rounded. The amount of rounding is given in terms of the bulletization (cystal rounding) radius.
  • The crystal hole (cavity) is the central void drilled in the crystal, which contains the cooling pin (cold finger). The latter is not part of our model. The cavity diameter should include the surrounding germanium dead layer, which is also not modelled explicitly.
  • The absorber is assumed to be placed directly onto the detector window.
  • The crystal mount cup (holder) keeps the detector crystal in place.
  • The term end cap (housing) refers to the the detector cryostat, sometimes also called the detector can.


My Sources

Coincidence Summing Corrections: My Sources Enlarge


  • To simulate a point source, set all the numerical parameters to zero (except the container-to-absorber-gap) and all the materials to "vacuum"
  • The container-to-absorber gap is the distance between the top of the detector absorber and the bottom of the sample container.
  • The sample filling height refers to the sample material only, excluding the container bottom thickness.
  • The container diameter includes (both) its side walls.
  • The source material is assumed to tightly fill the space in the container in its radial dimension.


Coincidence correction

Coincidence Summing Corrections Enlarge


How is the actual efficiency curve corrected with the correction factors?

The measured efficiency should simply be multiplied with the appropriate coincidence summing correction factor. This refers to the calibration phase of the analysis and is described in more detail in the following section.

When determining the unknown activities in a measured sample (using a calculated or measured efficiency curve from the calibration phase), the activities obtained from the uncorrected peaks should be multiplied with the appropriate coincidence summing correction factor.


Example: Calibration Curve Correction for Coincidence Summing Effects

In this section an example of the data and the plots for a HPGe calibration curve corrected for the coincidence summing effects are given. This data was provided by the gamma-rays spectrometry laboratory of the SCK•CEN.

The efficiency curve (raw data) was established by measuring a calibrated filter of 11 cm in diameter containing Cd-109, Cs-137, Pb-210, Am-241, Co-57, Te-123m, Sn-113, Cr-151, Sr-85, Co-60 and Y-88 directly on the detector window of a medium-size, low-energy HPGe detector. The efficiency (raw) data is show in in the figure below.

Efficiency (raw) data before correction Enlarge


The corrections computed with the EFFTRAN code are shown below.

Correction factors, uncorrected and corrected efficiences as a function of energy Enlarge


The above corrections factors have been calculated using the stand-alone version of EFFTRAN. The correction factors can, however, be calculated using the web application. In this case the calculation should be done for each of the nuclides (Cd-109, Cs-137, Pb-210, Am-241, Co-57, Te-123m, Sn-113, Cr-151, Sr-85, Co-60 and Y-88) individually. This will result in small changes to the values given above for the correction factors due to the statistical process of Monte Carlo integration employed, and the fact that the version of EFFTRAN used is not exactly the same as the one for Nucleonica.

Finally the efficiency data are corrected using the results in the table. The final efficiency (corrected) data are shown below.

Efficiency data after correction Enlarge


We see that the energy dependence of the efficiencies is now a smooth one, as expected.

It should be noted that the energy of a gamma line as such does not have anything to do with the magnitude of its coincidence summing correction, at least not directly. And neither does, indeed, the emission probability, except if lines overlap. It all depends on the entire decay scheme of a given radionuclide, and on the efficiency values, especially total efficiencies.

References

Coincidence Summing Basics

Advanced gamma-ray spectrometry dealing with coincidence and attenuation effects

True Coincidence Summing Corrections

True Coincidence Summing Corrections - Theory

Cascade summing corrections for HPGe spectrometers by the Monte Carlo method

Arnold, D. and Sima, O., 2004. Application of GESPECOR software for the calculation of coincidence summing effects in special cases. Applied Radiation and Isotopes 60, 167–172.

Berger, M. J. and Hubbell, J. H., 1987. XCOM: Photon Cross Sections on a Personal Computer. NBSIR 87-3597, National Bureau of Standards (former name of NIST), Gaithersburg, MD.

Vidmar, T., 2005. EFFTRAN - a Monte Carlo efficiency transfer code for gamma-ray spectrometry. Nuclear Instruments and Methods A 550, 603-608.

Vidmar, T., et al., 2010. Testing efficiency transfer codes for equivalence. Applied Radiation and Isotopes 68, 355-359.

Vidmar, T., Kanisch and G., Vidmar, G., 2011. Calculation of true coincidence summing corrections for extended sources with EFFTRAN. Applied Radiation and Isotopes 69, 908-911.

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