Published on Nov 30, 2023
A gamma-ray will interact with its medium in one of three different ways: photoelectric absorption, Compton scattering, and pair production. These different interactions change their probability of occurring depending on the energy of the gamma-ray and the atomic number of the material.
In the photoelectric absorption, the incident photon disappears and a photoelectron is produced from one of the electron shells of the absorber. The kinetic energy that this electron carries off is Ee− = h − Eb, where Eb is the binding energy of the liberated electron in its original shell. This empty spot in the electron shell is quickly filled by electron rearrange-ment. This process causes the binding energy, Eb, to be liberated as well. This energy is liberated in the form of a characteristic X-ray or an Auger electron.
The photoelectric absorption interaction is the ideal interaction for gamma-ray spectroscopy. The photoelectron carries away most of the gamma-ray energy and then an X-ray or Auger electron carries away the remaining kinetic energy. Assuming an ideal detector, the sum of these energies will equal the energy of the original gamma-ray.
This is desired for gamma-ray spectroscopy because we are interested in knowing the energies of the various gamma-rays that are emitted by a source. In Figure 3.3, we see what the ideal photopeak created by mono-energetic gamma-rays of a single energy looks like.
The Compton scattering interaction is the scattering of a gamma-ray off of a free or unbound electron, thus creating a scattered gamma-ray photon and a recoil electron. The energy of the incoming photon is divided between the scattered photon and the recoil nucleus by a relationship that is dependent on the scattering angle. There are two extreme cases dictated by this equation: When = 0, the scattered photon retains all of its energy and the recoil electron gains no energy. When = , the incident gamma-ray is backscattered and the recoil electron moves along the direction of incidence. This case is the case with the maximum energy transfer between the incoming gamma-ray and the electron.
In the detector, all scattering angles from 0 to will occur. Because of this, a continuum of energies can be transferred to the electron. This energy has a range from 0 all the way to the maximum.
Pair production is a gamma-ray that turns into an electron-positron pair. This occurs when the gamma-ray is in the intense electric field near the nuclei of the absorbing material. There is a minimum amount of gamma-ray energy that is required for this process to take place.
A block diagram for a typical scintillation detection system is shown in Fig. 1. The scintillation detector is illustrated in Fig. 2. Our detector has a 44 inch cylindrical NaI scintillation crystal which is activated with about 1 part in 103 thallium impurities. Through various processes, a gamma ray passing into the crystal may interact with it creating many visible and ultraviolet photons (scintillations). Oscilloscope Linear PM Base Amplifier NaI (Tl) Detector Source HV Power Supply Preamp Multi- Channel Analyzer Figure 1: Block diagram for a scintillation detector system.
To detect the scintillation photons, the crystal is located next to a photomultiplier tube (PMT) and the scintillator/PMT (detector) is enclosed in a reflective, light-tight housing. To minimize the effects of background gamma radiation, the detector is surrounded by a thick lead shielding tube with the desired gamma rays entering at the scintillator end of the tube. The PMT consists of a photocathode followed by a series of dynodes (6-10 is typical) followed by and ending with a collection anode. Scintillation photons striking the photocathode eject electrons via the photoelectric effect. A high voltage (HV) power supply and a resistor chain (not shown) bias the cathode, dynodes, and anode so as to accelerate electrons from the cathode into the first dynode, from one dynode to the next, and from the final dynode to the anode collector. Each incident electron strikes a dynode with enough energy to eject around 5-10 (secondary) electrons from that dynode. For each initial photoelectron, by the end of the chain, there are on the order of 106 electrons reaching the anode.
The anode is connected to a chargesensitive preamplifier which converts the collected charge to a proportional voltage pulse. The preamp pulse is then shaped and amplified by a linear amplifier before processing continues. Because the amount of light (number of photons) produced in the scintillation crystal is proportional to the amount of gamma ray energy initially absorbed in the crystal, so also are the number of photoelectrons from the cathode, the final anode charge, and the amplitude of the preamp and amplifier voltage pulses. The overall effect is that the final pulse height is proportional to the gamma ray energy absorbed in crystal.
As the name suggests, a pulse height analyzer (PHA) measures the height of each input pulse. Special circuitry, including a sample and hold amplifier and an analog to digital converter, determines the maximum positive height of the pulse—a peak voltage as might be read off an oscilloscope trace. From the pulse height, a corresponding channel number is calculated. For example, for a PHA having 1000 channel capability and a pulse height measurement range from 0 to 10 V, a pulse of height 1.00 V would correspond to channel 100, one of 2.00 V would correspond to channel 200, one of 8.34 V would correspond to channel 834, etc. After the correct channel for a given input pulse has been determined, the PHA then increments the count in that channel.
Our PHA can analyze pulse heights in the range 0-10 V and will be set up to sort them into 1024 channels. After many pulses of various sizes have been processed, a plot of the counts in each channel versus the channel number can be displayed to show the distribution of pulse heights. With some caveats to be described shortly, the pulse height distribution from a scintillation detector can be interpreted as a plot of the number of gammas versus the energy of the gammas from the source, i.e., a gamma ray spectrum of the (radioactive) source. Spectra from pure isotopes can be found in references and compared with a source spectra to determine the nuclear composition of the source.
To understand the pulse height distribution associated with the gamma rays from a radioactive source, it is important to realize that only a fraction of the gamma rays interact with the scintillator; many do not interact at all and simply pass right through. Furthermore, when a gamma does interact, the size of the pulse from the detector depends on whether all or only part of the gamma ray energy is deposited in the scintillator. For a given amount of energy deposited in the scintillator, the output pulse height will be well-defined but every pulse will not be exactly the same size. Because of statistical variations in light production, photon collection, photoelectron production, and electron multiplication, the pulse heights will show a distribution of values with some pulse heights larger and some smaller than the average. Typical variations with our detector are in the range of 5-10 percent.
The pulse height distribution for a source emitting only single energy gamma rays typically appears as in Fig. 3. The large peak at the far right is called the photopeak and arises when all the gamma ray energy is deposited in the scintillator. Note the 5-10% width of this peak due to statistical fluctuations. The most likely interaction to deposit 100% of the gamma ray energy is the photoelectric effect. The incident gamma essentially gives up all its energy to eject a bound inner shell electron from one of the crystal atoms. The ejected electron then has significant kinetic energy (the gamma ray energy less the small binding energy of the atomic electron, on the order of 10 keV) and loses this energy by exciting and ionizing more crystal atoms.
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