Comment on the broadening of the $^7$Be neutrino line in vacuum oscillation solutions of the solar neutrino

Abstract

We consider the effect of thermal broadening of the $^7$Be neutrino on vacuum oscillation solutions of the solar neutrino problem and analyze the conditions under which the electron-neutrino survival probability must be averaged over neutrino energy. For "just-so" solutions with $\Delta m^2$ of order $5 \times 10^{-11}~{\rm eV}^2$ averaging is not necessary, but for much larger values, it is. We analyze the effective broadening due to the extended production region in the Sun and find similar results. We also comment on the possibility of seasonal variations of the $^7$Be neutrino signal.