Collisional incoherence in neutrino line emission

The collisional broadening of neutrino line emission in stellar cores is analyzed. In a Lorentz model for impact broadening the linewidth is determined by the neutrino wavelength and by the thermal velocity and the collision frequency of the emitting nucleus. The general expressions are applied for the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ electron-capture reaction in the Sun. The resulting collisional coherence time of 5×${10}^{\mathrm{-}17}$ sec yields an upper limit of ${10}^{\mathrm{-}7}$ ${\mathrm{eV}}^2$ on the difference in the neutrino mass squared for observable neutrino oscillations on Earth.