Pulse-Height Spectrometry

1

The Ideal Pulse-Height Spectrum

Suppose that a monoenergetic γ-ray source is placed in front of a radiation detector. Assume, further, that the energy of the γ rays, E _γ , is less than 1.022 MeV, so that pair-production interactions do not occur. The principle γ-ray interactions with the detector will be by photoelectric absorption and Compton scattering. Most of the photoelectric interactions result in full deposition of the γ-ray energy in the detector (the characteristic x ray usually is also absorbed in the detector). Pulse amplitudes from these events are proportional to E _γ ( Fig. 10-2A ). With an ideal radiation detector, this would produce a single narrow line in the pulse-height spectrum, called the photopeak , at a location corresponding to the γ-ray energy E _γ ( Fig. 10-2B ). In Compton scattering, only a part of the γ-ray energy is transferred to the detector, via the Compton recoil electron. If the scattered γ ray also is absorbed in the detector, the event produces a pulse in the photopeak, whereas if the scattered γ ray escapes, the energy deposited in the detector is less than E _γ . According to Equation 6-14 , the energy deposited in the detector in a single Compton scattering event ranges from near zero (small-angle scattering event), up to a maximum value E _ce , corresponding to the energy of the recoil electron for 180-degree Compton scattering events

where E _γ and E _ce are in MeV. The ideal spectrum therefore includes a distribution of pulse amplitudes ranging from nearly zero amplitude up to some maximum amplitude corresponding to the energy given by Equation 10-1 . As shown in Figure 10-2B , this part of the spectrum is called the Compton region. The sharp edge in the spectrum at E _ce is called the Compton edge.

Another possibility is that a Compton-scattered γ ray may experience additional Compton-scattering interactions in the detector. Multiple Compton scattering events produce the distribution of pulses with amplitudes in the “valley” between the Compton edge and the photopeak.

2

The Actual Spectrum

In practice, the actual spectrum obtained with a NaI(Tl) spectrometer is quite different from the ideal one shown in Figure 10-2B . For example, Figure 10-3 shows a spectrum obtained from a ¹³⁷ Cs radiation source, which emits 662-keV γ rays and ~30-keV barium x rays. The spectrum was recorded with a multichannel analyzer, 0.01 V per channel, with the amplifier gain adjusted so that 662 keV of energy corresponds to 6.62 V of pulse amplitude. Thus the horizontal axis has been translated from pulse amplitude (~0-8 V) into energy (~0-800 keV).

The first feature noted is that the spectrum is “smeared out.” The photopeak is not a sharp line, as shown in Figure 10-2B , but a somewhat broadened peak, and the Compton edge is rounded. This is caused by the imperfect energy resolution of the NaI(Tl) detector, discussed in Section B.7.

Another structure that may appear in the spectrum is a backscatter peak. This is caused by detection of γ rays that have been scattered toward the detector after undergoing a 180-degree scattering outside the detector. Certain detector configurations enhance the intensity of the backscatter peak. For example, in the well counter ( Chapter 12 , Section A), a γ ray may pass through the detector without interaction, then scatter back into the detector from the shielding material surrounding it and be detected.

Note that the energy of the backscatter peak, E _b , is the energy of the scattered γ ray after 180-degree scattering, whereas the energy of the Compton edge, E _ce , is the energy given to the recoil electron in a 180-degree scattering event. Therefore

Equation 10-2 is helpful for identifying backscatter peaks.

Another structure that may appear is an iodine escape peak. This results from photoelectric absorption interactions with iodine atoms in the NaI(Tl) crystal, followed by escape from the detector of the characteristic iodine K-x ray, which has energy of approximately 30 keV. The iodine escape peak occurs at an energy approximately E _γ – 30 keV; that is, about 30 keV below the photopeak. Iodine escape peaks may be prominent with low-energy γ-ray emitters, for example, ¹⁹⁷ Hg ( Fig. 10-4 ). Low-energy γ rays are detected by absorption primarily in a thin layer close to the entrance surface of the NaI(Tl) crystal where there is a reasonable probability that the iodine x ray will escape from the detector. With increasing γ-ray energy, the interactions tend to occur deeper within the detector, and there is less likelihood that the x ray will escape. Also, the relative difference between the photopeak and escape peak energies becomes smaller, and it becomes more difficult to distinguish between them.

Lead x-ray peaks sometimes are seen in spectra acquired with systems employing lead shielding and collimation. These peaks are caused by photoelectric interactions of the γ rays in the lead. These interactions are followed by emission characteristic 80- to 90-keV lead x rays, which may be recorded by the detector.

If the γ-ray energy exceeds 1.022 MeV, pair production interactions can occur. The kinetic energy given to the positive-negative electron pair is E _γ – 1.022 MeV (see Chapter 6 , Section C.4). In most cases, the entire kinetic energies of both particles are deposited in the detector. When the positron comes to rest, it combines with an electron to create a pair of 511-keV annihilation photons. If both of these photons are absorbed in the detector, the event is recorded in the photopeak. If only one is absorbed, the event is recorded in the single escape peak, at energy E _γ – 511 keV ( Fig. 10-5 ). If both escape, the event is recorded in the double escape peak, at E _γ – 1.022 MeV.

Scattering within or around the radiation source, or object scatter, changes the distribution of radiation energies striking the detector. This is especially important in counting measurements in vivo and in radionuclide imaging because substantial scattering of radiation occurs within the patient. Figure 10-6 shows spectra for ¹³¹ I with and without scattering material around the source. The general effect of object scatter is to add events in the lower-energy region of the spectrum. It is possible to discriminate against scattered radiation by using a pulse-height analyzer to count only events in the photopeak, as shown in Figure 10-6 .

Coincidence summing can occur when a radionuclide emits two or more γ rays per nuclear disintegration. Figure 10-7 shows spectra recorded with a NaI(Tl) well counter for ¹¹¹ In, which emits a 173-keV and a 247-keV γ ray simultaneously. The peak at 420 keV seen when the source is inside the well counter results from simultaneous detection of these two γ rays. Summing between x rays and γ rays also can occur. With positron emitters, coincidence summing between the two 511-keV annihilation photons also may be observed. Coincidence summing is especially prominent with detector systems having a high geometric efficiency (see Chapter 11 , Section A.2), that is, systems in which there is a high probability that both γ rays will be captured by the detector [e.g., well counters ( Chapter 12 , Section A)].

3

Effects of Detector Size

The larger the detector crystal size, the more likely it is that secondary photons (i.e., Compton-scattered γ rays and annihilation photons) will be absorbed in the crystal. Thus with increasing crystal size, the number of events in the photopeak versus Compton regions increases. Figure 10-8 shows this effect on the spectrum for ¹³⁷ Cs. Figure 10-8 also shows that the “valley” between the Compton edge and the photopeak at first increases with increasing detector size, due to greater likelihood of an incident photon undergoing multiple Compton interactions within the detector. However, the number of counts in this region eventually decreases due to greater likelihood of complete absorption of the incident photon’s energy within the detector, thereby producing an event in the photopeak rather than in the valley. For γ-ray energies greater than 1.022 MeV, the size of annihilation escape peaks also decreases with increasing crystal size.