Issues when comparing data collected from a high density detector with theoretical predictions

I am working on data analysis for an X-ray spectrometer on a satellite. The student working on the project before me built the instrument in Geant, and now we are trying to validate that everything with the simulation is working as expected before moving on to data analysis.

For validation, we removed most of the geometry from the instrument so that we were just left with a flat plate (the detector). We are firing particles through the plate and dividing the energy deposited by the distance it traveled through the detector (either to first interaction or the whole thickness if there are no secondary events) to get the linear stopping power of the material for that energy and comparing that to the theoretical linear stopping power found from the Bethe Formula. We are binning energies and averaging dE/dx within bins and comparing the average to Bethe, so outlier events are not the issue.

So far, things are looking good for low density materials. The actual detector is made out of silicon, and the data for silicon is lining up nicely with the theoretical calculation. The issue arises with higher density materials. For example, I ran the test for Uranium (density~18.95 g/cm^3), and I am getting deviation from Bethe-Bloch up to 35% at <10 GeV for positive muons (well within the range Bethe-Bloch should be applicable, we limit primary energy to 10 GeV). The error lessens for heavier particles (protons/deuterons), but still gets up to 10% for deuterons and 15% for protons. Lowering Uranium’s density in the detector lowered the error, and bringing it down to around Silicon’s density (~2.329 g/cm^3) gives very low error. I tried the same test for other high density materials with similar results, so I think the issue arises with high densities. I have the higher order density corrections for the Bethe formula accounted for, so that is not the issue.

I am not sure if the issue is with the Bethe calculation or the simulation. I don’t think the issue is with the theoretical calculation unless there is something strange with higher densities that I am not familiar with. Any advice would be greatly appreciated.


Bethe-Block formula and linear energy transfer in real simulation are two different values. They should be different for about 20 % depending on density.


Dear Vladimir,
I would like to ask you what you propose as a starting point to validate this kind of simulations ?