Peak search in a gamma-ray energy spectrum

In this post, a method for finding peaks in energy spectra obtained in high resolution gamma-ray spectroscopy is presented. The method is straightforward and involves no iterative procedures and is widely used in many software packages. The basic idea is to study the derivatives of the spectrum to find out where the peaks are located.

The method is presented by an example. We use one HPGe spectrum from the 2002 IAEA inter-comparison spectra. This spectrum, identified by the name "mix2eq", was acquired during one hour with the detector aimed at at mixture of nuclides.

Channel

The peak positions are located at places where the 1^st derivative of the spectrum is zero and the 2^nd derivative is negative. The 1^st and 2^nd derivative is approximated by finite differences as follows. In our spectrum, we have h = 1 since we are dealing with channels.

If you were to plot the 1^st or the 2^nd derivative and zoom in, you would notice a lot of noise where the data fluctuates around zero. To avoid detecting false peaks, we will only use 1^st derivative data that are within a band around zero and only use 2^nd derivative data that are below a certain negative threshold. For this example, you can experiment with the limits using the sliders below:

1^st derivative limit:

2^nd derivative limit:

Plotting the 2^nd derivative data only for those channels that fulfill these limits provides a visual tool to see where the peaks are located. This plot is updated when the sliders above are moved.

Channel

The dynamic updating of the plot demonstrated above may not be necessary for your application. As it is implemented here, it may cause a bad flickering effect especially on slower computers.

This post contained one example of how peaks may be located in a high resolution gamma-ray energy spectrum. The interested reader may find the following list of references useful for further study:

• A. Likar and T. Vidmar; "A peak-search method based on spectrum convolution"; J. Phys. D: Appl. Phys. 36 (2003) 1903–1909.
• K. Debertin and R. Helmer; "Gamma- and X-Ray Spectrometry with Semiconductor Detectors"; North-Holland, 1988. ISBN-10: 0444871071, ISBN-13: 978-0444871077