Coincident spectra from Compton scattering Cs-137

[pietkuip]

Your summary is completely correct. I do not quite understand what puzzling part remains?

Maybe it helps to look at it the other way around: if you add together the coincidence spectra of the plastic scintillator taken for different angles, the total will be the broad Compton continuum, the spectrum that one sees without coincidence.

The angle dependence of Compton scattering looks like classical collisions, because also here energy and momentum must both be conserved. So consider a projectile hitting a body that is initially at rest. In 2 or 3 dimensions, that body can get a wide range of energies (the Compton continuum). But if we know the angle of the projectile after the collision (because of the coincidence setup), we also know the energy and angle of the body that was at initially at rest.

It is really exciting that one can do such experiments with a soundcard and free software. Very inspiring. I can imagine lots of new experiments for my students to try: coincidences of gammas with x-rays, with alphas, with betas.

[Sesselmann]

Your summary is completely correct. I do not quite understand what puzzling part remains?

It's all about asking the right question, and as I was formulating my question for you, I ended up partially answering my own question.

Nice experiment, well done Tom and Pieter.

[toand]

Hello. I am not sure that I see the problem that you see Steven, but I will give it another try. If the energy transfer in the plastic detector is not sufficient, random coincidence will be (much) larger than any systematic coincidence. A coincident spectrum due to random coincidence is identical with the normal spectrum, a Compton continuum. A coincident spectrum due to true systematic coincidence, that is, complementary energy pulses, will instead reveal mutually dependent energy distributions (making up 662 keV). With a significant angle above zero and proper shielding, the systematic coincidence will be much larger (more frequent) than random coincidences. Consequently, with the angle fixed, the coincident spectra must show complementary peaks.

[Sesselmann]

Tom,

I think we all agree that it's not a problem, instead it looks as if two low resolution detectors can be used in this way to resolve an energy peak to a degree otherwise not possible.

If the energy deposited in each detector is a function of the scattering angle, then it should be possible to calculate the total energy and obtain a final spectrum with a far better resolution than either of the detectors could produce on their own.

Technically there is no reason why software couldn't do this automatically, in which case one could build stereo detectors with high resolution from relatively cheap materials. Such detectors would have to be directional and have within them two separate crystals and some kind of collimator at a fixed angle.

I think this is worth experimenting with.

[toand]

Yes. I wrote my last comment without first taking note of your and Pieter's last comments. After submitting it, I realized that there was a second page with your last comments, coming to a conclusion. Still, since I like statistics, I let it be. Agree. This is a very interesting area.

[toand]

A supplement to previous post, viewtopic.php?f=5&t=72, 2D plot of coincidence spectra of Compton scattering of Cs-137 gamma 662 keV.

[Sesselmann]

Tom,

I moved your post to the original thread, also could you please explain what we are looking at in the above coincidence plots. Most of us are not used to seeing spectra this way. Tell us how you got the raw data and what software you used to plot it.

[toand]

Ok Steven. I wasn't sure where to put it, precisely because it is different. Now I have edited the first page, putting it last, added explanations. I think that it summarizes the nature of the experiment and its results in an efficient way.

[pietkuip]

Steven, I agree, this deserves a bit more explanation. The 2-dimensional diagram is similar to the literature data that I showed in my earlier post in this thread (but rotated by 90 degrees, and zoomed out). I thought that one needed to extract this from the .pls-file, but it is much easier. There is an export option for coincidences in PRA, as Tom found out when he corresponded with Marek.

He then imported these data in Matlab as XY pairs: X for the gamma-prime energy of the event as detected by the NaI detector, Y for the energy of the Compton electron detected inside the plastic detector. The plotting routine is simple: just a dot for each XY pair. Color was used here to differentiate data taken with different scattering geometries. Which creates the atmosphere of a pointillist painting - I think this is beautiful to look at. To see the ridge with a slope of -1, due to energy conservation in Compton scattering. At every scattering angle the NaI detector shows the lead x-rays at 75 keV. Each gamma-prime also produces its own Compton continuum in the NaI scintillator.

One could also make a 2D histogram, with color coding for intensity. That would require better statistics and wider bins. We could do that: let spectra run overnight or during a weekend. With a 2D plot like this, one does not need well-defined angles to see the energy conservation. We could move the two detectors closely together again.