Effect of Coulomb collisions on time variations of the solar neutrino flux

We consider the possibility of time variations of the solar neutrino flux due to the radial motion of the Earth and neutrino interference effects. We calculate the time variations of the detected neutrino flux and the extent to which they are suppressed by Coulomb collisions of the neutrino emitting nuclei. We treat the process of neutrino emission under the second quantization method. A neutrino emitting nucleus suffers random Coulomb accelerations in different directions. Thus, the positions and the velocities of the nucleus are different at different emission times. We properly calculate these emission times and emitted neutrino energies by making use of the method of stationary phase, which leads to the causality and Doppler shift equations. We average our results over the Holtsmark distribution of nuclear accelerations. To properly treat the collisions, it is necessary to simultaneously include in our analysis all other significant physical decoherence effects: the energy averaging and the averaging over the position of neutrino emission. We find that the collisional decoherence is not important (in comparison with other decoherence effects) in the case of neutrino line, but it may be important in the case of the continuous neutrino spectrum (or for high energy resolution explorations of the internal structure of the line). We find that the collisional decoherence averages out the time variations for the neutrino masses m2 −m1 ∼ 10−7 eV E 3/2 MeV. A simple and clear physical picture of the time dependent solar neutrino problem is presented and qualitative coherence criteria are discussed. Exact results for the detected neutrino flux and its time variations are obtained for both the case of a solar neutrino line, and the case of the continuous neutrino spectrum with a Gaussian shape of the energy response function of the neutrino detector. We give accurate constraints on the vacuum mixing angle and the neutrino masses required for flux time variations to not be suppressed. Pac(s): 26.65.+t, 14.60.Pq, 96.60.Jw Typeset using REVTEX 1