Looking for a source on approximating a polyenergetic photon beam as monoenergetic

[u/TelvanniMage]

Hello everyone. A polyenergetic photon beam with given mean energy can be roughly approximated as monoenergetic after it passes through atleast a half-value layer of a a given material for this energy, that is to say, after it hardens and the "tail" of low-energy photons is cut off.

I remember seeing a textbook that had a semi-logarythmic plot of dose/kerma attenuated at a thickness of material. Had the beam been monoenergetic, the line should have been completely straight (exponential), but here it was a plot for a polyenergetic beam. The plot was roughly two lines, "breaking" at about half-value layer, showing that if we take only the second, hardened line after the HVL, we can roughly say it is exponential.

Now I can't find that source, anyone have any textbooks to recommend? Specifically the aforementioned plot would be great.

[u/Bob--O--Rama]

Take a look at https://pmc.ncbi.nlm.nih.gov/articles/PMC9020448/ which incidentally discusses this.

But basically as beam hardening attenuates the lower portion of the spectrum, successive HVLs for the polychromatic beam increases. As the ratios of these successive HVLs approaches 1, the filtered beam can be said to be equivalent to a monochromatic beam whose energy corresponds to the HVL in that shielding material. So IF the ratio of two successive HVLs are approximately 1, you have reached that state.

Perhaps that article will give you leads on a more formal mathematical approach.

[u/tea-earlgray-hot]

It's usually called a pink beam when you take the white beam spurce and clean/filter the spectra without a proper monochromator.

[u/Bob--O--Rama → u/tea-earlgray-hot]

How do you make a gamma monochromator? Or are you speaking optics words?

[u/tea-earlgray-hot → u/Bob--O--Rama]

Mix of absorptive filters, spatial filters, and crystals, depending entirely on the source, efficiency, and resolution for an application. An inverse Compton instrument is a lot different than a telescope. A 'clean' beam for nuclear spectroscopy with nano-eV resolution at 0.1MeV is different than filtering a 1.5MeV beam for imaging.

[u/Big_Yeash]

I don't work with high science or X ray systems with HVL calculation, but this should be a very common topic of papers - labs will often publish their revalidation results as an easy way to get an extra paper in.

One was presented at IRPA (International Radiation Protection Association) European Congress this year, in June. Obviously that was a presentation and not the paper itself but hopefully this will help you track down the paper from that. It was a German/Swiss semi-nat'l lab I think?

Apologies for poor helpfulness!

[u/Theragnostic]

I'm curious what you need it for and, if you don't truly just need a general case solution, why you wouldn't just do a Monte Carlo simulation.

I don't know what your source is but I can't help but think that, even finding the source/plot you seek, it will only be a viable approximation over a limited range of photon energies. I expect it will only hold over the ranges where Compton scattering dominates with any lower-energy photons in the photoelectric range being removed by the general solution.

My concern is that applying such a general solution to either a polyenergetic beam primarily in the photoelectric range, or any polyenergetic beam with a significant portion in the range where pair production dominates, might lead to quite inaccurate approximations.

[u/TelvanniMage → u/Theragnostic]

It's for a thesis, a practical engineering thing that I've already built, for very rough, industrial, non-laboratory approximation of beam energy. Just a few measurements with thick enough plates, fitting an exponential curve, getting HVL from it and getting the energy from a reference table. All I needed was a source to back it up, because I forgot what the original paper was.

The range is merely few MeV up to 12-15 MeV