Detector for a Measurement of Shape Factors in Beta Decay

The search for a sterile neutrino, a viable candidate for dark matter, requires an improved understanding of the shape factors of non-unique forbidden beta decays. We present the design of a scintillation detector read out by mesh type photomultiplier tubes. It will be used in the PERKEO III spectrometer, which was initially developed for neutron beta decay, to measure electron spectra of various beta decays with high precision. We show the progress in designing the light guide form that yields the optimal performance with simulations using Geant4, and present a way of calibrating the detector with sufficient precision.