Difficulties in using the sharp neutrino spectrum at short times

Final states produced by a decay have a much broader energy spectrum than the natural line width at times much shorter than the decay lifetime. This tends to render impossible the use for neutrino detection of the high value of the resonance absorption cross section at the peak of the resonance. Proposals to use the very sharp neutrino emission line for neutrino detectors have been discussed for a long time [1]. More recent proposals [2] frequently overlook the constraints imposed by energy-time uncertainty [3]. The width of the energy spectrum reduces to the natural line width only after times of the order of the lifetime of the state emitting the neutrino. For a shorter time δt after the emission of the neutrino, the observed energy width of the final state energy spectrum is much brader and given by [3] Γobs ≈ τ δt · Γnat (0.1) where Γobs is the observed width expressed as the second moment of the energy spectrum, τ is the lifetime of the decay and Γnat is natural line width observed at times longer than the lifetime. The effective cross section σeff(δt) observed at a time δt after the neutrino emission is then ∗Supported in part by U.S. Department of Energy, Office of Nuclear Physics, under contract number DE-AC02-06CH11357.