Understanding Pulse-height Analysis in a β Counter

We are occasionally asked about the significance of window settings with our flow-through detector. "What does a setting of 200 mean and how is it related to the reality of isotope energy?" Here, we'd like to provide a brief explanation. The discussion is restricted to β-measurement though it is equally applicable to alphas, positrons, and soft-gammas when counted under comparable conditions.

For β-measurement, with constant chemistry -- the same solutions, scintillator concentration, chemical species, etc. -- the scintillation process is reasonably linear in terms of light output vs. decay energy, i.e., a β-particle having twice the kinetic energy of another produces about twice as many photons. However, that may not be true when comparing light output from one solution to another, from one chemistry to another, from one scintillator composition to another. Then, global differences in energy transfer and scintillator performance often result in somewhat different light outputs for β-particles of the same energy.

Under the best conditions -- the best scintillators, the best solvents, colorless sample materials that do not inhibit the scintillation process -- photon output for a liquid scintillator, is perhaps 5 photons per keV of β-particle energy given up to the surrounding solution; solid scintillators and Cerenkov phenomena produce less. Deleterious phenomena lumped under the heading of "quenching" also reduce light output.

Therefore, with liquid scintillator the most energetic H-3 event (Emax = 18 keV) produces a maximum of about 90 photons. But, that same energy particle in a different solution, or with solid scintillator, or if quenching is present, produces fewer photons, sometimes so few that counting is not possible. At the other extreme there is P-32 (Emax = 1710 keV). In the ideal liquid scintitillator solution, we might expect the most energetic event to give about 8500 photons. However, under Cerenkov counting conditions {B Flow-Through Measurement Without Scintillators: Cerenkov and Bremsstrahlung Counting}, even though there is essentially no quenching, the maximum energy decay event gives rise to just 210 photons.

The function of the photomultipliers is to convert these photons first to electrons at the photocathode ("photoelectrons") and then to multiply (amplify) their number down the dynode string until an output pulse is produced at the anode. That is then followed by sufficient electronic amplification to provide signals suitable for pulse height analysis. By adjusting the high voltage and/or the electronic gain we are able to bring the pulse heights into a workable range. Lower- and upper-level discriminators ("window settings") allow selection of an energy range particular to each isotope.

In a system such as our β-RAM, pulse height analysis is performed over a range of 0 to 10 volts. That range is arbitrarily divided into 1000 equal parts ("divisions"). By adjusting the high voltage and/or the amplifier gain and employing an ideal H-3 sample in liquid scintillator, we might see to it that there are no pulses (other than an occasional background count) having an amplitude greater than 200.

We know that the maximum energy H-3 event produces an 18 keV β-particle. Rather than label the H-3 endpoint "200" we might as easily label it "18". Then, it could be said that we are working directly in energy units. But, that would be misleading. Whether the H-3 sample is quenched or not, whether liquid scintillator or solid scintillator is used, the maximum energy event is always 18 keV but the light output is not always 90 photons and the pulse size varies accordingly. And, for P-32, the 1710 keV β-particle gives 8500 photons with liquid scintillator but only 210 under Cerenkov conditions, again resulting in an enormous difference in pulse heights.

So, a scale in energy units can only be meaningful for a constancy that is not possible. The 18 keV pulse height for one sample is not the same as the 18 KeV pulse height for the next.

Having said that, it is necessary to remark that the same is not the case for gamma counting with solid state or sodium iodide detectors. Here, sample quality does not come into play, nor are there different scintillators with different light outputs as there are in β-counting. Assuming stable electronics, under any condition the photopeak will convert to pulses of the same amplitude. With the energy of the photopeak known, it is possible to establish a baseline in meaningful energy units.