A Electrostatic Spectrometer for Neutrino Mass Measurements Using Frozen Molecular Tritium.

The electrostatic spectrometer described in this thesis measures the integrated energy distribution of the electrons emitted from a frozen molecular tritium beta-decay source for the purpose of setting limits on the mass of the electron anti-neutrino |nu_{e}. The unique features of this spectrometer include a frozen tritium source and a purely electrostatic spectrometer. The resolution is essentially a step function with a 10%-90% rise over 3.1 eV for 18.6 keV electrons with no low energy tail. The hardware has been thoroughly tested and shown to work as designed. The ultimate sensitivity of any neutrino mass measurement is dominated by systematics. Our spectrometer is designed to achieve a few eV statistical sensitivity with reasonably short data runs to allow study of possible systematic effects. The electrostatics are well understood. Systematic error on the fitted value of m_sp{ nu}{2} due to uncertainties in the resolution model will be less than 5 eV ^2. The signal rate from tritium near the endpoint is very low. This limits the statistical sensitivity to m_sp{nu}{2} because the neutrino mass effect on the energy spectrum is largest near the endpoint. Our experiment has an advantage over some others because it measures the integral spectrum, not the differential spectrum. In the integral spectrum, the decay rate climbs as (Q - E_{beta })^3 while the differential decay rate only climbs as (Q-E_{beta}) ^2. Therefore statistical sensitivity is increased for a given source strength. The increased sensitivity allows us to do the measurement in the last few hundred eV of the spectrum. Even with the integral spectrum, the data rates near the endpoint are small. Because of the low rates, it is important to optimize the set of times and energies at which to take data for sensitivity to the neutrino mass. I introduce a method for choosing the data set based on maximizing the curvature of < chi^ {2}>. It uses all of the information available about the source, the resolution and the background. I estimate that the statistical error on m_sp {nu}{2} will be less than 25 eV^2 for a 50 hour data run with 200 mCi of tritium if data sets generated with this method are used.