Recoilless resonant emission and detection of electron antineutrinos

Abstract

Recoilless resonant capture of monoenergetic electron antineutrinos (Mössbauer antineutrinos) emitted in bound-state β -decay in the system 3 H -3 He is discussed. The recoilfree fraction including a possible phonon excitation due to local lattice expansion and contraction at the time of the nuclear transition, homogeneous and inhomogeneous line broadening, and the relativistic second-order Doppler effect are considered. It is demonstrated that homogeneous line broadening is essential due to stochastic magnetic relaxation processes in a metallic lattice. Inhomogeneous line broadening plays an equally important role. An essential issue which has been overlooked up to now, is an energy shift of the resonance line due to the direct influence of the binding energies of the 3 H and 3 He atoms in the lattice on the energy of the electron antineutrinos. This energy shift as well as the second-order Doppler shift exhibit variations in a non-perfect (inhomogeneous) lattice and may seriously jeopardize the observation of Mössbauer antineutrinos. If successful in spite of these enormous difficulties, Mössbauer antineutrino experiments could be used to gain new and deep insights into the nature of neutrino oscillations, determine the neutrino mass hierarchy as well as up to now unknown oscillation parameters, search for sterile neutrinos, and measure the gravitational redshift of electron antineutrinos in the field of the Earth.

Neutrino oscillations: quantum mechanics vs. quantum field theory

“…In [27], a comparison of the QM and QFT approaches was presented for the special case of Mössbauer neutrinos, i.e. neutrinos produced and detected recoillessly in hypothetical Mössbauer-type experiments (see, e.g., [26,28,29] and references therein). The new results obtained in the present work include a more advanced and general study of the QFT-based derivation of the neutrino wave packets (including the possibility that some of the external particles are not detected), matching of the QFT and QM expressions for the neutrino wave packets, study of the general properties of the wave packets describing the neutrino states (including their energy uncertainties in the case when neutrinos are produced in decays of unstable particles) and clarification of the issue of normalization of the oscillation probabilities in QM and QFT.…”

Mössbauer antineutrinos: Recoilless resonant emission and absorption of electron antineutrinos

“…where θ is the effective Debye temperature, k B is the Boltzmann constant, and E 2 2M c 2 is the recoil energy which would be transmitted to a free atom of mass M. With θ ≈ 800K for the 3 H -3 He system [7], f 2 r ≈ 0.07 for T → 0.…”

“…They lead to sudden, irregular transitions between hyperfine-split states originating, e.g., from magnetic moments (spins) of many neighbouring nuclei. Thus the wave function of the emitted particle (photon,ν e ) is determined by random (in time) frequency changes which cause line broadening characterized by the time-energy uncertainty relation [7]. As a consequence, the broadened line cannot be decomposed into multiple sharp lines.…”

“…As a consequence, the broadened line cannot be decomposed into multiple sharp lines. [7], [13], [14].…”

“…Since, in the nuclear transformations, theν e energy is directly affected by E B , one has to expect that the variations of theν e energy are much larger than 10 −12 eV, probably in the 10 −6 eV regime. Thus, inhomogeneous line broadening is estimated to give Γ Γexp i ≪ 10 −12 [7], [13], probably Γ Γexp i ≈ 10 −18 [14].…”