We discuss an experiment to search for a massive admixed neutrino in nuclear beta decay via detection of the recoil nucleus as well as the electron, and hence a complete kinematic reconstruction of the final state.PACS number(s): 23.40. Bw, 12.15.Ff, 14.60.Gh, 27.10. + h The issue of possible nonzero neutrino masses remains a fundamental and unresolved one. A natural concomitant of such masses is lepton mixing [I]. Strangely, although the awareness of possible lepton mixing led to numerous exgeriments to search for neutrino oscillations, experimental studies of weak decays yielding neutrinos continued to assume implicitly that the weak and mass eigenstates of neutrinos were the same. In 1980, one of us suggested tests for massive neutrinos which could occur, via mixing, in various weak decays including nuclear beta decay, and set the first upper limit on the emission of massive, admixed neutrinos in nuclear beta decay, and in rr, K, and p decay [ 2 ] . Writing the weak eigenstate Y, as a linear combination of mass eigenstates, v , = x i Uljv,, the limit given in Ref.[2] for nuclear beta decay was / U,, I2 < 0.1 for m ( vj ) in the range from 0.1 keV to -3 MeV.The suggestion to carry out searches for the kinks in Kurie plots due to possible emission of massive, admixed neutrinos led to the first experiments directed toward this goal. These initially set limits [3], but in 1985, an experiment on 3~ beta decay [4] reported observing a spectral excess at low electron energy, which was attributed to the emission of a 17 keV neutrino with mixing strength / U,, l3 -0.03, replaced later by / U I J ' = 0 . 0 1 from measurements on both 3 5~ and 'H beta decays [5]. A similar spectral excess had actually been observed much earlier [6], but the massive neutrino emission via mixing had not been considered as a possible explanation; indeed, no experiments searching for massive neutrino emission via mixing in weak decays were performed until after 1980.A number of subsequent experiments on 3 5~, 6 3~i , and 3~ found no evidence for any emission of a massive neutrino [7], while other experiments on I4c, 3 5~, and 6 3~i beta decays [8] (and "~e electron capture with inner bremsstrahlung [9]) have found evidence confirming Ref. 151. *Electronic address: sbhep1::finocchiaro. '~lectronic address: shrock@dirac.physics.sunysb.edu.In view of this unsettled situation, it would be valuable to use a fundamentally different experiment to try to resolve the issue. Here we shall discuss an experiment in which one detects and measures not only the electron but also the recoil nucleus, together with the angle between them. This information suffices, in principle, to reconstruct the kinematics of the final state completely and thus to determine, on an event-by-event basis, the mass of the emitted (antilneutrino. The real question is whether an experiment using this method would be feasible in practice and would have sufficient sensitivity to help resolve the current controversy. We have carried out an investigation of this question for several ...