It is a well-established fact that the rate at which a collection of radioactive atoms decays itself decays exponentially over time. It's easy to see why: the number of decays is directly proportional to the number of radioactive atoms remaining in the sample; so the fewer active atoms there are left, the fewer decays will occur. That makes observations from Litvinov et al. in a paper in Physics Letters B, all the more surprising. Investigating β-decays of highly positive ions of heavy elements, these authors see a decay rate whose decline is not purely exponential, but which seems to be modulated up and down over time. They propose that the modulation arises from the 'mixing' of different types of neutrino-chargeless and almost massless particles produced in β-decays. That explanation would itself raise a host of further questions.
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