True coincidence summing

The problems caused by true coincidence summing (TCS) can be demonstrated by referring to the calibration 

The upper curve, measured with the source on the detector cap, is not at all satisfactory. The points do not lie on an orderly line and it would be difficult to draw an acceptable curve through them. The reason for this dramatic difference is TCS. 

Practical Gamma-ray Spectrometry - 2nd Edition Gordon R. Gilmore 2008 John Wiley Sons, Ltd. ISBN 978-0-470-86196-7 

As with random summing, the event results in loss of counts from the full-energy gamma-ray peaks and a loss of efficiency. However, unlike the random summing that I discussed in Section 4.8, the summed pulse will not be misshapen and cannot be rejected by pile-up rejection circuitry. 

A rough and ready estimate of the likelihood of summing of two photons emitted at the same time, P, can be estimated by using the following equation  

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Gilmore, G. and Hemingway, J. D. 1995. True coincidence summing in Practical Gamma-Ray Spectrometry. Chapter 7. West Sussex, England John Wiley. 

The instructions with the software packages indicate how to determine / and a, how to measure the parameters of the efficiency calibration of the detector and convert it to specific counting geometries, and how to convert the peak areas into the mass firactions of the elements. The software packages have libraries of ko values, Qo values, mean resonance energies, half-lives, decay types, and the details of the decay schemes needed for true coincidence summing calculations. 

Relevant mechanisms that cause loss of counts from the photopeak include partial conversions of the incident energy event with part of the energy escaping the detector, true coincidence summing, random. summing of pulses, also known as pile-up, and dead time. While the first two effects are part of the detector s efficiency and are the same for all sample and standard counts, random summing and dead time are dependent on a sample s activity. ... 

Decay schemes give vital information on whether gammas are in cascade . This has great significance in true coincidence summing. 

Another type of summing, referred to as true coincidence summing, is a function of the nuclide decay scheme and the source/detector geometry and will be dealt with in some detail in Chapter 8. All of the other features in the spectrum can be attributed to unavoidable interactions of gamma-rays from the source with the surroundings of the detector - the shielding, cryostat, detector cap, source mount, etc. 

The latter restriction is a consequence of lost counts due to true coincidence summing. I will discuss this fully in the next chapter. For a nuclide emitting a single gamma-ray, such a restriction would not necessarily apply. In general, the use of corrections of this type is best avoided. It is much more satisfactory to standardize on a small number of counting positions and create a separate efficiency calibration at each one. If it does become necessary to make mathematical corrections, it should be borne in mind that. 

In deriving Equation (7.16), a number of simplifications have been made and one would not expect to be able to correct for gross changes in geometry in this manner. It should also be noted that changes in true coincidence summing are not accounted for explicitly although the empirical manner in which the correction factor is derived would tend to do this if the nuclide used were the same as that to be measured in practice. 

True coincidence summing is of such great importance that Chapter 8 has been devoted in its entirety to the problem. 

It is worth noting that, for a given solid angle, the number of true coincidence summing events per second (but not the ratio of lost/total counts) will be directly proportional to the sample activity. On the other hand, random summing losses are a function of the square of the sample activity. In the situation in Figure 8.1, we can be quite sure that the problem with the top-of-detector count is due to TCS, rather than random summing, because the measurements had almost the same count rate. 

Figure 8.12 Simple illustrative decay schemes liable to true coincidence summing...

Not all programs will perform all tasks and not all tasks will be relevant for aU analyses but one might expect a typical commercial analysis program to be able to cope with the majority. In this chapter, I will discuss all of these items individually with the exception of true coincidence summing, which was discussed separately in Chapter 7. In general, a full computer spectrum analysis will consist of three phases ... 

In Chapter 7, where the problems caused by true coincidence summing in close geometry measurements were discussed, we saw how TCS can make nonsense of an efficiency curve and strongly recommended comparative analysis, particularly for environmental measurements. 

GammaVision provides a Umited means for performing a comparative analysis in that there is an option to provide an interpolative efficiency curve. If the efficiency calibration data is provided for each gamma-ray of each nuchde to be measured, then each request for an efficiency value would return the actual calibration data derived from the standard spectrum. If true coincidence summing were a problem, then as long as the standard spectra were of the same nuclides measured under the same conditions as the sample spectra, the summing errors would cancel out. The procedure is not elegant, but as far as I can see, should work satisfactorily. 

The larger the detector, the greater is the degree of true coincidence summing. This was discussed at length in Chapter 8. 

Much of the sample within a Marinelli beaker is close to the detector. That means true coincidence summing (TCS) errors. With a larger beaker, more of the sample will be further away from the detector and, consequently, TCS errors will be lessened. 

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