Can I use independent component analysis if I have two discrete populations of signal sources mixed together?
Conceptually, for ICA to work, it requires N observations of the SAME phenomenon and it will attempt to decompose these signals (the mixtures) to &lt; N components. 

From your description each detector is counting a different energy particle. That is, the "Mixtures" are actually already three different signals. Consider the example where you use the recordings of 4 different microphones to try and distinguish between 2 different (mutually independent) sound sources. In this case each microphone is recording a (different) sum of BOTH sound sources. In your case, because of the phenomenon you are observing, each "microphone" (detector) is NOT recording a (different) sum of BOTH sources, but rather it records each source separately (most of the times).

As you describe, sometimes, the SAME event might be recorded by more than one detectors (spill-over). In this case, if you insist with ICA then it would attempt to decompose THAT sum.

Therefore, perhaps you should consider something simpler, like obtaining the cross correlation between the events recorded by each one of the three different detectors as an indicator of the amount of spill-over.

But in this case, instead of examining 1000 "triplets" of observations, you create three different time series. One time series per detector describing the events (in time) of each detector.

If your detectors and aparatus are fast enough, this signal will look like a series of exponentially decaying pulses. If not, your signal will look like a train of pulses convolved with the impulse response of the system (a smoothed version). In either case, if the same event has been detected by more than one detectors then the output of these detectors will simultaneously rise in level (and increase the cross - correlation or some other form of correlation metric). It will be easier to detect that rise in the first case (fast system).

Therefore, the problem now becomes one where you have to decide which detector to assign that event to for it to be counted correctly. There is a number of ways that you can do this (not using ICA) but you will have to know the spectral response of your detector (Pulse amplitude VS energy or Voltage output VS energy). You would then be able to create a weighted sum of the counted particles by looking up the "weight" for each pulse on your detector's response. Or you could apply a "window" to the pulses. That is, consider a sharp threshold around the peak response of the detector and only count events that generate such (usually high) pulses. Considering a short region around the peak performance of the detector will reject the (lower) pulses created by spill-over.

I hope this helps. I hope to have understood your configuration correctly.