Interplay of nonrelativistic and relativistic effects in neutrino oscillations

A theoretical structure that involves neutrino mass eigenstates at nonrelativistic as well as relativistic energies is presented. Using this framework, we find that if the particle X, with a mass 33.9 MeV, of the KARMEN Collaboration anomaly is identified with the third neutrino mass eigenstate, then the present limit of 23 MeV upper bound on the tau neutrino mass implies \U-tau 3\<0.82.