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This question is an attempt to complement this other question about fluctuations in radiactive decay.

This question is completely experimental though: in general, suppose i have certain sample of a radiactive substance. My goal is to gather experimental data about fluctuations in net momenta of all decay products. I certainly would have to set the sample temperature near to zero Kelvin in order to reduce or eliminate thermal contributions to net momenta. However, what is the experimental setup one would have to have?

Should one only consider individual events where all decay products have been detected and their individual momenta obtained?

How do you make sure that a set of decay product events are associated to the same event? time correlation? does this mean that the sample size needs to be small enough so overlapping decay events are percentually few and can be filtered out?

what other considerations are required?

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That's a hard experiment.

The remnant nucleus generally has a very low (non-relativistic) velocity{*}, making it difficult to detect and characterize.

Should one only consider individual events where all decay products have been detected and their individual momenta obtained?

This is the formal definition of an "exclusive" event, but experimentally we (that's the nuclear and particle physics "we") almost always relax it with respect to the remnant nucleus.

How do you make sure that a set of decay product events are associated to the same event? time correlation? does this mean that the sample size needs to be small enough so overlapping decay events are percentually few and can be filtered out?

Where possible you set your event rate slow compared to the DAQ latch and report rate. So almost all reported DAQ events are associated with only one physics event. There is a bit of art and science in this.

If I was really going to do it, I'd consider measuring the transverse direction only at a radioactive beam accelerator{**}. That won't make it easy, mind you, just less horribly difficult. That simplifies your life in the sense that the remnant is now a ionizing particle with a macroscopic track length, so you can ID it, but of course you no longer have good information on exactly where the decay occurs and may not be able to extract a good value for the longitudinal component of the momentum due to the decay {+}.


{*} Momentum of a few MeV, and mass of multiple to hundreds of GeV. You might ask the AMO people about this, they are more used to working with just barely ionizing energies than particle physicists and may have an answer. Perhaps it is a good application for a multi-channel plate.

{**} They do exist.

{+} Lost in the noise of the much larger component due to the beam momentum.

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