You can think of a photomultiplier tube (PMT) as essentially a light amplifier which is sensitive to individual photons, typically in the infrared to near ultraviolet portion of the electromagnetic spectrum. Fig. 1 shows a schematic view of a PMT which consists of the following:

1. a glass window with a thin layer of metal deposited on the inside surface which is referred to as the photocathode. A visible light photon entering the PMT will likely knock off an electron from the photocathode via the photoelectric effect;
2. a series of metal plates called dynodes. When struck by an electron with sufficiently high kinetic energy, several more electrons will be knocked off of a dynode; and
3. an anode at the opposite end of the tube from the photocathode.

Figure 1: Schematic drawing of the electron cascade inside a photomutiplier tube.

The photocathode, dynodes, and anode are electrically connected in series. A high voltage potential, typically 1000 to 2000 volts, is applied across these elements. The resulting electric field gradient accelerates electrons produced at the photocathode onto the first dynode in the chain. Electrons which are liberated at the first dynode are accelerated onto the second dynode producing an average of three new electrons for each electron that was ejected from the first dynode. This process continues until the end of the dynode chain where all of the electrons strike the anode creating an output pulse. The size of the output pulse is proportional to the total number of electrons ejected from the last dynode. A PMT with 10 dynodes will produce in excess of 1×105 electrons at the anode for each electron produced at the photocathode. The number of electrons in the output pulse generated by a single photoelectron is called the gain of the PMT, and a PMT's gain increases with the the number of dynodes and the voltage potential applied to the tube.

Assuming a fixed gain, more light entering the front of the PMT will produce more photoelectrons and thus larger output pulses.

PMTs are very efficient devices for detecting fast pulses – on the order on nanoseconds – of visible light photons. By measuring the size of the output pulse, one gains information about how much light entered the PMT.

PMTs are not effective for detecting photons with energies higher than a few electron volts (eV). Higher energy photons have an increasingly low probability of interacting with the photocathode and thus tend to pass through the PMT without generating an output pulse. In order to detect x-ray and gamma-ray energy photons, one needs use a scintillator to absorb the energy of the photon and convert some of that energy into visible light photons which can then be detected by the PMT.

X-ray and gamma-ray energy photons interact with electrons in the NaI scintillator, most probably by Compton scattering at higher energies and/or photoelectric effect at lower energies. A typical sequence of events goes as follows:

1. The high energy photon enters the NaI crystal and Compton scatters off of an electron.In the process, it loses some of its energy to the electron.
2. The electron moves through the crystal, losing energy and producing visible light via the scintillation process.
3. The scattered photon, now with reduced energy, continues through the crystal until it either interacts with another electron or leaves the crystal. If it interacts with another electron, the possibilities are:
   1. another Compton scatter, in which case steps 2 and 3 repeat; or
   2. it is absorbed via the photoelectric effect, in which case all of the remaining energy of the photon is converted into kinetic energy of an electron (which proceeds as in step 2). At this point all of the energy of the original x-ray/gamma-ray has been lost to electrons which have then gone on to produce visible light.

Now consider a NaI scintillator which is optically coupled to the front of a PMT. The sides and back of the NaI crystal are wrapped with a light-tight material which will reflect visible light leaving the crystal back into the crystal. Now, when an x-ray or gamma-ray energy photon enters the NaI crystal, it will lose its energy to electrons which produce visible light as described in Sec. 1.2 above. These visible light photons enter the PMT where they are converted into an electrical pulse as described in Sec. 1.1.  The size of the output pulse from the PMT is proportional to the number of visible light photons from the NaI crystal which strike the photocathode. The number of visible light photons produced in the NaI crystal is proportional to the energy of the incident x-ray/gamma-ray. Thus, through a chain of connected events the size of the output pulse from the combined PMT+NaI detector is proportional to the energy of the incident x-ray/gamma-ray.

Usually one uses a NaI+PMT detector to measure the energy and or intensity of x-rays/gamma-rays in order to study some physical process. In the lab, you will look at the output pulses from the PMT on a pulse height analyzer (PHA). The pulse height analyzers used in the lab measure the size of each output pulse from the NaI+PMT detector, and counts the number of pulses of different sizes. Depending on how the PHA is set up, pulse size is defined as either the total current in the pulse (Direct Input mode) or the maximum voltage of the pulse (Pre-Amp Input mode). In both methods, the pulse size is proportional to the energy of the incident x-ray/gamma-ray as described in Sec. 1. In either mode, the total range of pulse sizes which can be measured by the PHA are is divided in to a number of equal size bins. Usually, 512, 1024, or 2048 bins are used. The PHA software displays a real-time histogram of the number of pulses (along the y-axis) which fall into each bin (along the x-axis).

Now, let us consider the case of a monoenergetic beam of gamma-rays striking the NaI+PMT detector and ask what the spectrum of pulse heights from the PMT would look like. In an ideal world, we would expect that if the high voltage (HV) applied to the PMT is held constant, gamma-rays of the same energy will always result in output pulses of the same size. Therefore, all the pulses would end up in the same bin of the PHA and the pulse height spectrum (phs) would look like a delta function.  

However, nature is not so cooperative; the reality is a bit more complicated. (This is a good thing! If reality were simple, then anyone could do physics and we wouldn't be special  ).  For our purposes, there are two additional factors which need to be considered so that we can understand the features which appear in the pulse height spectrum (PHS) produced by a real NaI+PMT detector.

The first additional consideration is the statistical nature of the production of both the visible light photons in the NaI crystal, and the electron amplification in the PMT.  In the case of the NaI crystal, there is a well defined average number of visible light photons produced per unit energy deposited in the crystal. In the case of the PMT, a single photoelectron will produce on average a certain number of electrons at the tubes anode. The result is that x-rays/gamma-rays of a fixed energy will produce an average output pulse size, with fluctuations about the average given by normal counting statistics.

The second consideration is that every x-ray/gamma-ray which enters the NaI crystal does not necessarily deposit all of its energy in the crystal. Consider the two cases illustrated in Fig 2.

Figure 2: Two possible results when a gamma-ray enters a NaI crystal.

In the first case, (A), a gamma-ray with energy $E$ enters the NaI crystal, (1). It then Compton scatters off of an electron in the crystal, (2), losing some fraction of its energy to the electron so that the gamma-ray now has energy $E'<E$. The scattered electron moves off through the crystal rapidly losing the energy it gained from the gamma-ray and producing visible light as described in Sec. 1.2. The scattered gamma-ray – now with energy $E'$ – continues through the crystal until it interacts with another electron, (3), via the photoelectric effect, whereby all of the remaining energy of the gamma-ray is given to an electron which produces more visible light. In this example all of the energy of the incident gamma-ray ends up being transferred to electrons in the crystal. The output pulse sizes produced in this case will fall in the region of the PHS identified as the full energy peak in Fig 3. Note that the full energy peak consists of a narrow distribution of pulse sizes about an average value.

Another possible sequence of interactions is case (B). In this case, the gamma-ray of energy $E$ enters the NaI crystal, (1), and then Compton scatters off of an electron, (2). However, this time the scattered gamma-ray leaves the crystal before interacting with a second electron, (4), taking with it energy $E'$. Thus, only a fraction of the total energy of the incident gamma-ray – $E - E'$ – is transferred to an electron, resulting in a smaller pulse of light produced in the scintillator crystal and a correspondingly smaller output pulse from the PMT. How much smaller this output pulse is, (as compared to one where all of the gamma-ray energy is deposited in the crystal in case (A)), depends on the angle of the Compton scatter that precedes the gamma-ray leaving the crystal. Therefore, gamma-rays which Compton scatter out of the crystal produce a range of output pulse heights which fall into the region identified as the Compton shelf in Fig. 3. There is an edge to this Compton shelf (identified as the Compton edge in Fig. 3) given by the maximum amount of energy which can be transferred to an electron in a single Compton scatter. This maximum transfer occurs occurs when the scattering angle is $180^\circ$.

Finally, it is also possible, – and in fact, common, – for a full energy gamma-ray emitted by the source in a direction away from the NaI+PMT detector to scatter off of some other object and then enter the NaI crystal with a reduced energy. Gamma-rays with this reduced amount of energy which ultimately are absorbed via the photoelectric effect will produce a full energy peak, but at the position corresponding to their reduced energy. This peak is labeled as the backscatter peak in Fig. 3. Backscatter peaks are most common where there is a scattering surface located near or behind the detector. For example, an NaI+PMT detector in a vertical orientation above a table top will be subject to backscatter off the table surface, or a detector placed next to lead bricks will see scattering out of the bricks.

Figure 3: Pulse height spectrum of the 662 keV line of Cs-137.

In summary, a monoenergetic beam of gamma rays incident on a NaI+PMT detector will typically produce a pulse height spectrum with the following four distinct features:

• a full energy peak corresponding to the case where all of the energy of the incident gamma-ray was deposited in the crystal;
• a Compton shelf composed of output pulses generated when the incident gamma-ray Compton scatters out of the crystal, thus depositing only a fraction of its total energy;
• a Compton edge which corresponds to the maximum pulse size produced by a single Compton scatter at 180°; and
• a backscatter peak produced by gamma-rays which undergo a Compton scatter before entering the NaI crystal.

The most common detectors used in the instructional labs are 1.5“ x 1.5” sodium iodide crystals coupled to a PMT produced by the SpecTech company. (These are the type used in Introductory Lab: Gamma Cross Sections.) The specifications sheet is given below for more information.