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Detecting nuetrinos is not easy of course but it seems that there are several interesting ways of playing with neutrinos using radioactive sources that can only decay by electron capture.

For example, maybe its possible to induce electron capture with a stream of neutrinos? Maybe its possible to test that a solar neutrino detector works by placing inside or near a detector a sample of material that decays in this way. Perhaps a combination of beta decay and electron capture (dont play terminology games, you know what I mean, emission vs capture) can lead to determining if a neutrino is its own antiparticle or not.

Fundamentally, Im interested in this and would like to know if there is any experiment that has used radioactive material that must decay by electron capture in order to study neutrinos?

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Yes, electron capture sources have been used as neutrino sources. For example, the GALLEX, GNO, and SAGE collaborations have all used such sources to calibrate their solar neutrino detectors. A simple web search will give you much further reading, e.g. this link for references from GALLEX under the "Radioactive Source Experiments" tab. The SOX experiment was the most recent one to attempt this feat, though unfortunately it had to be canceled after issues with the production of the source; since neutrinos interact weekly, you need a really, really strong source, so even just thermal heat from the decay becomes an issue.

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