A $\beta$-spectrometer for searching effects of finite neutrino masses

A detailed description of a Tret'yakov-type magnetic$\beta$--spectrometer with electrostatic acceleration is presented.The instrument is being used for high precision measurements of the$ \beta $--spectra of various isotopes and to search for neutrinomixing and heavy neutrinos with masses up to $100 \,$keV$/c^2$.The relative momentum resolution, obtained with an extendedsource ($ 3 \times 2 \,$cm$^2$) and a large silicon stripdetector, is $ \delta p/p = 6.9 \times 10^{-4} $ (FWHM).The width of the energy band, which can simultaneously be measuredwith this resolution, is typically 50 times larger than thecorresponding width of the energy resolution.The detector delivers pulse-height and one-dimensional positioninformation. The read-out electronics provides a seperate channelfor each detector strip, allowing measurements to be madewith high count rate and small dead-time losses.The detection of scattered electrons was minimized by thearrangement of baffles and by the use of materials with smallatomic number. Experimentally, scattering in the spectrometerwas investigated by accelerating photoelectrons up to $ 60 \,$keV energy. A system for measuring the corresponding high voltageis described.Extensive Monte Carlo simulations of scattering in the spectrometerhave been performed. Good agreement with the experimental datawas obtained and there was no need to adjust any scatteringcross section to the particular experimental situation. Weconclude that calculated scattering probabilities can reliablybe used in the analysis of experimental $ \beta $--spectra,which is important as otherwise scattering would constitute amajor uncertainty.