Gamma Spectrum

Let’s start with a brief summary of what we’ve learned so far in this section.

During radioactive decay, isotopes decay into other stable or also radioactive isotopes. During this decay, gamma radiation can be emitted. The energies of this gamma radiation are characteristic of the decaying isotope. With a suitable detector, the energy of the gamma radiation can be determined. Its distribution, i.e., how often gamma radiation of a certain energy has been measured, can be displayed in a spectrum. In individual channels, we will then see increases (lines), called peaks, that correspond to the characteristic energies of the respective isotopes.

Did you notice anything in the summary that we haven’t described precisely?

Take another look at the last sentence: it states that in certain channels, the lines appear that correspond to the characteristic energies of the respective isotope. That’s correct! However, our actual task in gamma spectrometry is that we usually do not know the isotope and want to determine it through gamma measurement.

The “problem” here is that we can choose the number of channels in the multichannel analyzer and the various settings in the detector electronics (Black-Box) almost freely. This means that depending on the chosen settings, the same characteristic lines will appear in different channels in the spectrum. Thus, we generally cannot say that, for example, the line at channel number 352 corresponds to an energy of 121 keV. We still lack a link between channel number and energy.

And that leads us to the calibration of a detector system, the energy calibration.

Energy calibration addresses the mentioned problem of assigning channels in a spectrum to energies. However, it should be noted that for any changes to the settings of the detector system, i.e., changing the number of channels, the settings of the detector electronics, etc., a new energy calibration is required.

In practice, most measurement sites are used for many weeks or months with unchanged settings. Therefore, a regular check of the energy calibration is sufficient.

But how does an energy calibration actually work?

If you have read the earlier explanations thoroughly, you should already know (or at least have an inkling). When you conduct measurements with known isotopes (e.g., commercially available calibration sources), you can extract the energies of the gamma radiations of the isotopes from the corresponding data sheets or databases.

It is easiest to evaluate the measurements if you use isotopes that emit only one or two characteristic lines, such as ²⁴¹Am (at 56 keV), ¹³⁷Cs (at 661 keV), or ⁶⁰Co (at 1173 keV and 1332 keV). You then perform a measurement (i.e., recording the distribution) with one of the isotopes and note the channel numbers where you “see” its lines.

We have already shown examples of what such spectra can look like in various ways. For a measurement with the nuclide ⁶⁰Co, we will show the spectrum again below.

Repeat this with the other isotopes and enter the respective values (energy and channel number) in a table.

The result of these measurements might look as follows (Note: the values indicated are not from the spectra shown above!):

The noted assignments of channel number – energy can now be plotted in a graph, as shown below. In the graph, the horizontal axis represents the channel number, and the vertical axis represents the energy in keV (the units of energy – here keV – and their significance will be discussed in a later section).

The dashed lines illustrate, for example, how the point for the gamma energy at 661.7 keV and the corresponding channel number 3582 is determined: first, a horizontal line (green dashed) is drawn, which intersects the energy axis (vertical axis) at 661.7 keV, then a vertical line (blue dashed) is drawn, which intersects the channel number axis (horizontal axis) at the value 3582. The intersection point of the two dashed axes is the sought point (marked in red). Similarly, further points can be generated.

Now, draw a straight line through the individual points, which will allow you to determine the corresponding energy for each channel number.

If you now “see” a characteristic line in a measured spectrum, determine its channel number and use the graph to find the corresponding energy. In the following diagram, this is shown for channel number 4500, which is assigned an energy of 829.4 keV.

In practice, such a diagram is “only” used for visualizing an energy calibration. The straight line (the so-called calibration line) is then described by a mathematical equation, whose parameters are automatically determined by fitting the values of the energy calibration. To determine an energy, only the channel number needs to be plugged into the formula. This is, of course, much faster, more precise, and thus more effective.

Since the relationship between channel number and energy is not always linear (i.e., a straight line), deviations in the relationships can also be described through mathematical formulations.

In gamma spectrometry, suitable gamma spectrometry programs are used for measurement and evaluation. These can take into account the results of existing energy calibrations in the representations of the measured spectra, i.e., the values on the horizontal axis, which originally contained the channel numbers of the multichannel analyzer, are automatically converted into the corresponding energy values. This way, the energy of a line can be easily extracted from the spectrum.

The following illustrations exemplify the representation of gamma spectra in various (commercial) programs.

Now you know how to establish the link between channel number and corresponding energy through energy calibration. We are now ready to begin with the identification of radionuclides based on their characteristic lines in the measured spectrum.