A new experiment shows how neutrino masses and mixing can be investigated by studying the behavior of a radioactive ion which decays by K-capture BEFORE and DURING its weak decay by K-capture. A new oscillation phenomenon providing information about neutrino mixing is obtained by following the ion before and during the decay. This normally neglected process is shown to be consistent with quantum mechanics and causality. Measuring the oscillation without detecting the neutrino avoids losses in conventional experiments due to the low neutrino absorption cross section. The normally unobservable long wave lengths are made observable by having the radioactive source move a long distance circulating around in a storage ring. The initial ion wave packet has a momentum spread required by Heisenberg and contains pairs of components with different momenta and energies. These can produce neutrino amplitudes in two mass eigenstates with different momenta which mix to produce a single $\nu_e$ state. In this typical quantum mechanics ``two-slit" or ``which path" experiment a transition between the same initial and final states can go via two paths in energy-momentum space with a phase difference producing interference and oscillations.