Variations on four - neutrino

We make a model-independent analysis of all available data that indicate neutrino oscillations. Using probability diagrams, we connrm that a mass spectrum with two nearly degenerate pairs of neutrinos separated by a mass gap of ' 1 eV is preferred over a spectrum with one mass eigenstate separated from the others. We derive some new relations among the four-neutrino mixing matrix elements. We design four-neutrino mass matrices with three active neutrinos and one sterile neutrino that naturally incorporate maximal oscillations of atmospheric and explain the solar neutrino and LSND results. The models allow either a large or small angle MSW or vacuum oscillation description of the solar neutrino deecit. The models predict (i) oscillations of either e ! or e ! s in long-baseline experiments at L=E 1 km/GeV, with amplitude determined by the LSND oscillation amplitude and argument given by the atmospheric m 2 , and (ii) the equality of the e disappearance probability, the disappearance probability, and the LSND ! e appearance probability in short-baseline experiments.