Oscillating decay rate in electron capture and the neutrino mass difference

Reported oscillations in the rate of decay of certain ions by $K$-electron capture have raised questions about whether and how such oscillations can arise in quantum-mechanical theory and whether they can measure the neutrino mass difference. Here I show that simple principles of quantum mechanics answer some questions and clarify what must be performed theoretically or experimentally to answer some others. The principal result is that quantum mechanics does allow mass-difference-dependent oscillations in principle, but it imposes conditions not obeyed by the approximate dynamical models that have been put forth up to now. In particular, indirect coupling between two neutrino mass channels must be taken into account. What needs to be done experimentally and theoretically is discussed.