Why are there still counts far from 180º angular separation?

[says]

I've added a graph of coincidence events vs. detector angular separation. This is for a electron-positron annihilation (gamma-gamma coincidence) experiment.

Why does the plot have a finite width and not look like a delta function? I'm assuming this is because the experimental conditions are not ideal. i.e. no infinitely small energy resolution, no infinitely small time resolution, not a perfect point source and point detectors aren't great.

Also, why are there still counts far from 180 degrees angular separation (past 130/230)? Shouldn't they only be registered within a small width?

thanks :)

 

[mfb]

You can have background from your detector, from random gamma decays, from two pairs annihilating nearly at the same time, and probably from some other sources. A three-photon annihilation is possible as well.

 

[says]

I should have mentioned the source was Na-22.

Can you elaborate on what you mean by background form your detector and random gamma decays?

I'm still not 100% sure how the overlap coincidence method works with this experiment. A pulse from the movable detector enables the linear gate of the multi-chan analyser, and then any corresponding pulse from the fixed detector that arrives within the gate interval will be considered coincident. If the Na22 decays via electron capture and a neutrino is ejected from the atom's nucleus into the movable detector, won't anything picked up within the gate (even background radiation) in the fixed detector be considered as a coincidence event, even though the 2 events are unrelated.

 

[mfb]

Your detector can see a signal for three reasons::
- photons from annihilation (what you are interested in)
- photons from gamma decays, cosmic rays or similar (background)
- without photons (noise)

Every pair of detections that happens close together in time will be recorded, even if the two photons don't have a common origin.

Only if both photons come from a single two-photon annihilation at the target volume you get an angle close to 180 degrees, otherwise you get some random angle.

 

[says]

So at angles other than 180 degrees the count measurements are a result of photons from background radiation and noise.

For angles close to 180 degrees there are a significant amount of counts registered. Is this because both detectors have a certain solid angle? If so, would the only way to reduce this be to reduce the solid angle of the detector?

 

[mfb]

So at angles other than 180 degrees the count measurements are a result of photons from background radiation and noise.

These things occur at all angles. They can also be reconstructed as 180 degrees.

For angles close to 180 degrees there are a significant amount of counts registered. Is this because both detectors have a certain solid angle? If so, would the only way to reduce this be to reduce the solid angle of the detector?

The solid angle of the detector elements is certainly relevant. The size of the sample is relevant as well. If the annihilation does not happen in the center of the detector, it can measure an angle that is a bit different from 180 degrees.

 

[says]

The size of the sample is relevant as well. If the annihilation does not happen in the center of the detector, it can measure an angle that is a bit different from 180 degrees.

I never thought of this! Thank you. The sample in my experiment was a small disk ~1cm radius.

 

[says]

I don't fully understand the energy resolution of a detector, but would a small energy resolution and time resolution also be why the plot has a finite width and doesn't look like a delta function (i.e. A straight line at 180 degrees)

 

[mfb]

It can lead to more background events (within the energy and time range where coincidences are counted) that don't show a peak, but I don't see how it would make the peak broader.