Answer to Question #8983 Submitted to "Ask the Experts"

I am testing the efficiency of a plastic scintillator personnel contamination monitor. Initially I optimized the unit with ⁵⁷Co to obtain the maximum sample to background ratio and then calibrated the unit with ⁶⁰Co. When I calculated the efficiency of the detector with the source (dimensions about 1 cm x 1 cm) in contact with the detector, I got an efficiency value (percentage that counts represent of source activity) over 50%. Theoretically it is impossible to get such a value. Measurement was repeated after optimizing the unit with ¹³³Ba and then it was calibrated with ⁶⁰Co. An efficiency that is higher than 50% was obtained. The experiment was repeated again after optimizing the unit with ⁶⁰Co and then calibrated with ⁶⁰Co. This time the obtained efficiency was around 37%, which is reasonable. We repeated the experiment one last time after having optimized the unit with ¹³⁷Cs, and again the value was reasonable.

Is there any suggestion of why we are getting an efficiency that is higher than 50% when optimizing the unit with ⁵⁷Co and ¹³³Ba and reasonable efficiency when optimizing the unit with ⁶⁰Co and ¹³⁷Cs?

Optimization here is referring to setting the gain on the PMT (photomultiplier tube).

Additional information provided upon request:

    Source        Optimization Voltage

       ⁶⁰Co             750 V
       ¹³⁷Cs            850 V
       ¹³³Ba           1,150 V
       ⁵⁷Co            1,275 V

Detector dimensions:

Volume: 5,260 in³
Surface area: 2,630 in³
Detector covering: 1mm steel    

We should note that these large-area, large-volume plastic scintillation detectors have relatively high detection efficiencies for photons, even high-energy photons as from ⁶⁰Co, especially when the source is in proximity to the detector. This is because the efficiency can be approximated by the quantity 1 – e^-µx, where µ is the linear attenuation coefficient for the photons of a specific energy in the detector material, and x is the available pathlength through the detector. This assumes that every interaction produces a detectable pulse, which will somewhat overestimate the efficiency. For these detectors, the thickness is two inches (the volume divided by the surface area), and when the source is close to the detector, the average pathlength through the detector is quite a lot larger than the detector thickness because many of the emitted photons take quite oblique paths through the detector. For a radionuclide such as ⁶⁰Co, which emits two photons per disintegration, when the source is in a 2p geometry with respect to the detector, it is possible to achieve a counting efficiency (counts per disintegration) that exceeds 50% if the individual photon detection efficiency exceeds 50%. This is not likely the case for these detectors, and we should now consider your observations pertaining to the efficiency determinations you have made.

First, we should note that even if the sources have sufficiently thin coverings that some beta particles and/or conversion electrons may escape, they will not be able to penetrate the 1 mm steel covering over the detectors. Therefore, the only response of the detectors should be to photons. For the three sources that you mention, the dominant mode of interaction for the important photons is Compton scatter. For a given energy photon it is easy to show, as long as pair production is not a significant interaction mechanism, that the average energy of the electron, E_e, set free by the initial photon interactions is given by

E = E_?µ_tr/µ,

where E_? is the photon energy, µ_tr is the linear energy transfer coefficient, and µ is the linear attenuation coefficient for the photons in the material of interest.

For ⁵⁷Co, ¹³³Ba,¹³⁷Cs, and ⁶⁰Co, respectively, the average photon energies of interest are about 125 keV, 266 keV, 662 keV, and 1,250 keV, and the respective average electron energies set free by photon interactions in a typical plastic are approximately 20 keV, 65 keV, 250 keV, and 600 keV. The point here is that the electrons are the particles that deposit their energies in the scintillator and produce the respective light pulses. For a given electronic gain that is below the point of amplifier saturation, the sizes of the light pulses from the system will be approximately in proportion to the original electron energies. Thus, the pulses from ⁶⁰Co would expectedly be about 30 times larger than those from ⁵⁷Co and almost 10 times larger than those from ¹³³Ba, but only about 2.3 times larger than those from ¹³⁷Cs.

When you used ⁵⁷Co as the nuclide for purposes of optimizing the system's performance, you required a relatively high voltage of 1,275 V to obtain the desired behavior. When you used⁶⁰Co for optimization, you found that an appreciably lower gain was necessary and the voltage was only 750 V. Thus, when you made measurements of ⁶⁰Co after having optimized with the ⁵⁷Co, the voltage of 1,275 V would have been much higher than the voltage you found actually best for the ⁶⁰Co. This can have a number of ill effects.

The much larger pulses from the ⁶⁰Co interactions would be even  more greatly exaggerated by the use of a much higher voltage than appropriate. This can produce various pulse shape distortions that may affect the observed count rate. It is possible that the pulses could saturate the amplifier; additionally, it is also possible for the excess amplification to produce pulse undershoot, where the tail of the pulse goes below the baseline before recovering. If you were counting in the bipolar mode, such undershoot events may be recorded as additional counts. In extreme cases, the electronic pulse tail may cross back again above the baseline and possibly add another count. Along with the pulse distortions, the excess high voltage also encourages the detection of electronic noise events that might otherwise have fallen below the discriminator. Similar events, but probably not quite as extreme, might also occur when counting ⁶⁰Co after optimization of operating parameters with ¹³³Ba, also leading to possible excess counts. When ¹³⁷Cs was used for optimization, the determined operating voltage was higher by only about 13% than what was optimum for ⁶⁰Co, not so far off that the secondary pulse effects noted above would be very significant.

You could assess possible pulse distortion effects by inspecting the pulses with the aid of an oscilloscope. If you look at pulses at different stages, such as out of the preamplifier and out of the amplifier, you may get a better feel for the kinds of events that might be occurring and how, or if, they are affecting the counts that you observe, especially as you change sources and applied voltages.

I hope this is of some help to you.

George Chabot, PhD, CHP