Gamma Spectrometry Forum

Compton Experiment
Some of you guys here might be familiar with the Compton scatter experiments often carried out by studends in the physics lab. Essenially it involves exposing a metal rod with a collimated beam of gamma rays (Cs137) and then with a scintillation detector counting the scattered gamma rays at various angles between 10˚ and 110˚. The objective of the experiment is to show how the scattered gamma energy varies with the angle.

When we view a typical Cs137 gamma spectrum, the compton plateau is very obvious and we all know what it is, it starts with the backscatter peak at around 200 keV and tapers off at around 400 keV.

The common explanation for this phenomenon is that a gamma ray collides with an electron in one of the outer shells and transfers some of it's momentum to the electron which in turn emits a photon with energy less than 511 keV depending on the scattering angle.

An easy observation anyone can do is to look at the number of counts in the compton plateau and check that there are more counts in each bin on the left than there is towards the right, i.e. it slopes upwards towards the left.

What you might also obswerve is, if you view the spectrum in energy per bin mode (PRA or IMPULSE) the compton plateu looks flat.

Hypothesis
Consequently I hypothesise, a body exposed to a beam of gamma rays will radiate scattered energy isotropically, i.e. the total energy radiated should be the same in all directions. It basically shines with equal brightness in all directions but not with equal number of photons.

Experiment
This experiment is reasonably easy to do if you have a strong enough source, but it is even possible with a weak source if you use two detectors in coincidence mode.
If anyone is interested in the student experiment paper, please email me. I would rather not post it here as it has a University logo.

How is this useful?
Maybe it is not immediately obvious to everyone, but all those counts that we recognise as the compton plateau arent supposed to be there, they all belong to the main photopeak, but just never made it that far up because they lost some energy through the sides of the detector. (an infinitely large crystal would solve the problem).

If my hypothesis is correct it should be theoretically possible to put the counts back where they belong. This would involve a function which loops through each bin in the compton region, calculates the number scattered counts, and moves them to the photopeak.

The amount of scatter is highly dependant on crystal size and gamma energy, the smaller the crystal the more energy lost to scatter, so a program which does this would have to have an input factor for crystal efficiency and energy of the gamma peak you want to repair.

I am still thinking about how to write this function, but it seems plausible. I imagine it to be a filter which one would apply after recording a spectrum.

Anyone have any thoughts to add?

Steven

Steven

I think that idea works in principle, and is sometimes applied in gamma-spectroscopy. But it is not easy as I'll describe below.

First of all, the angular distribution of photons after a single Compton scattering event can be theoretically calculated with the Klein-Nishina formula https://en.wikipedia.org/wiki/Klein%E2% ... na_formula.
Angular distributions of scattered photons are forward peaked for high energy incident photons, and non-isotropic even for very low energy photons.
But the Klein-Nishina formula describes only a single collision. A sequence of Compton scattering events can smooth the angular distribution and it might appear more isotropic.

The add back of counts from the compton continuum is still possible, but it requires a detailed measurement (or simulation with a tool like Geant4) of the shape of the compton continuum for all energies. Whenever I've seen people using this technique, they created a functional description of the complete shape of the detector response (compton continuum plus corresponding peak, for all energies). This function was then used to fit a recorded spectrum. The downside is, that all peaks have to be fitted simultaneously, because all functions are overlapping. I don't think this procedure can be generalized, because it depends on the precise detector geometry and construction, and also on the position of the source.

Michael

Michael,

Thanks for reply and yes I understand it can become quite complicated, however based on my hypothesis that energy is roughly isotropic, I did some very crude tests running a simple python script, and even a very small correction seems to enhance the spectrum.

Essentially what I did in this test was to assume the Compton shine from the crystal was energy isotropic and constant.

I then looped through all bins in the Compton region (peak_energy - - electron_energy) and subtracted an integer number of counts equal to the shine from each bin and added the same number to a lost_count variable.

The counts in the photo peak were then grossed up by a factor so the total counts in the spectrum remained constant.

Below are screen captures taken of the spectra and four levels of correction.

The method is relatively uncomplicated and since the count correction in the Compton region is based on energy and not counts it won't affect other peaks in the region.

Steven

Steven

The Compton continuum ranges from 0 to E_compton, where E_compton depends on the incident gamma energy ( the formula is here https://en.wikipedia.org/wiki/Compton_edge ) and can be larger than m_electron*c^2.
I think your suggested method is too simple: By scaling the photopeak such that the area compensates for the subtracted Compton continuum will not improve the statistical properties of the peak, i.e. relative fluctuations from bin to bin will not improve by doing that.

Here is a paper describing the process of spectral deconvolution using the full detector response function (in this case calculated using Geant4 and an empiric analytical formula). They are doing it for a large range of gamma energies (up to 8 MeV gammas), but the basic principle is what you initially suggested: Take the Compton continuum into account instead of treating it as background.
https://nopr.niscpr.res.in/bitstream/12 ... 27-430.pdf

Michael

Michael,

Sometimes physicists are like lawyers, overcomplicating things to make their work look important 😱, nothing like partial differential functions and monte Carlo simulations to get a paper past the journal editors 😂

With a background in manufacturing, I go straight for the cheapest most direct solution to a problem,......this is why we now have a GS-PRO instead of the NIM crate.
I am familiar with the compton formula, and I don't see how E Compton can exceed 511 KeV when (1-cos0) can't be more than 1.

\[ \frac{1}{E'} - \frac{1}{E} = \frac{1}{m_e c^2} * (1-cos(\phi) \]

If we compare the same spectrum presented in counts per bin vs energy per bin we can see how the Compton area is almost perfectly horizontal, indicating as I suggest that Compton shine is near energy isotropic.

We can expect some deviation as a result of crystal geometry, but in this case a 2x2" crystal is for calculation purposes an ideal sphere.
Since we are now confident about the distribution of Compton counts, we can reduce each bin in the area( peak - e-electron) by a fixed energy amount and consequently factor up the counts in the photo peak.

Since nothing was invented or added, the end result is a spectrum that looks like it came from a more expensive detector.

Furthermore, this process can be executed for multiple peaks as long as one peak is processed at the time.

Steven

Steven

NIM standard is from 1964, people didn't have computers with sound cards back in the day.

I'm not saying that this is not working, I'm saying that people have done this already and one can learn from their experiences.

Maybe I misunderstood what you mean by E_compton. Normally, E_compton is the maximum energy that the scattered electron can have after the scattering process (this the upper end of the Compton continuum in the spectrum). It can be calculated as \[ E_{compton} = E_{\gamma} \left( 1 - \frac{1}{1+2E_{\gamma}/(m_e c^2)} \right) \]
For a 1.4 MeV gamma, E_compton is 1.115 MeV, which is larger than 511 keV.

A spectrum with Intensity*Energy says nothing about the angular distribution of the Compton shine. In order to see the angular distribution of the Compton shine, you need to measure it. That could be done with a coincidence setup (as you already said), where a photon is scattered from one detector into a 2nd one (at various angles). What you will find when comparing the intensities at different angles is, that the Compton shine is non-isotropic.

Michael

Michael,

Yes that makes sense, I was referring to the photon leaving the detector and you were referring to the absorbed energy, so my terminology was wrong.

I have done the coincidence experiment with my weak sources, but the counts are low and statistically unreliable. I might ask a friend at University of Sydney to get some data for me, I know they have a strong collimated source. Something to consider is how many counts are attenuated by the detector housing in the low energy region.

Steven

A bit off topic, the calculator below graphs recoil electron energy (Compton edge) and scattered photon energy (backscatter peak) based on incident photon angle and energy. You can play with it and see why Compton plateau features aren't seen below 250 keV, and why visible light (2-2.6 eV) and low energy x-rays scattering is coherent. Fortunate, I guess, because it would be hard to look yourself in the mirror otherwise.

https://www.sciencecalculators.org/nucl ... cattering/

Michael,

Thanks for the link, definitely on the topic, but like almost all Compton experiments it focuses entirely on the photon energy and does not consider intensity.

The Compton experiment is a classic example of how students are given some ingredients, a recipe and instructions to find a known outcome.

I guess a student would be in trouble if he or she actually experimented with something unknown....

Steven