One place where everyone can agree Poisson noise should appear is in the background spectra. So I have a question. Was the same background spectrum used for producing the the 2 background-subtracted spectra shown in Figure 1 of your ResearchGate manuscript?
The reason I ask is because I have realized that the noise that must be part of Wyttenbach's background spectra accounts for the small wiggles I see in Figure 1 of the ResearchGate paper. Wiggles such as the ones I have drawn a box around , here ...
I don't believe that these are peaks corresponding to separate gamma lines because they go up and down much faster than is compatible with the physics of the NaI crystal in the detector Wyttenbach uses. Instead, I think that these wiggles represent Poisson noise in the background samples and appear here because of the subtraction process. They are about the right size for Poisson noise.
If the same background sample was used for background subtraction in both the spectra seen in Figure 1, it would explain why each and every such wiggle is replicated in both spectra. Whether or not the same background was used repeatedly when preparing these spectra is undocumented.
It would be interesting to know whether Wyttenbach is interpreting each and every wiggle here as a separate spectral line.