Some of the cosmic ray nuclei are radioactive; that means that they decay with some characteristic lifetime. For example, Beryllium-10 decays with an average lifetime of about 1.6 million years. If AMS sees a lot of Be-10 in cosmic rays, then, it suggests that the rays got here fairly quickly (not too much more than a few million years.); if AMS sees very little Be-10, we can infer that the Be-10 has decayed during the cosmic rays' long, long journey through the galaxy. For a really accurate, quantitative measurement, we figure out the ratio of (stable) Be-9 and Be-10 seen in distant stars (where Be-10 can be created by nuclear reactions), and see how that ratio has changed after the particles' long journey through space. This measurement has been done at lower energies by balloon experiments; AMS will extend it to much higher energies.
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