  Electron capture on $^{20}$Ne is thought to play a crucial role in the final
evolution of electron-degenerate ONe stellar cores. Recent calculations suggest
that the capture process is dominated by the second-forbidden transition
between the ground states of $^{20}$Ne and $^{20}$F, making an experimental
determination of this transition strength highly desirable. To accomplish this
task we are refurbishing an intermediate-image magnetic spectrometer capable of
focusing 7 MeV electrons, and designing a scintillator detector surrounded by
an active cosmic-ray veto shield, which will serve as an energy-dispersive
device at the focal plane.
