ABSTRACT
The inclusion of the neutrino interaction with matter particles will be the next stage of our analysis. The basic idea of our approach consists in the reduction of the totality of the neutrino interactions in matter to the motion in a field with a potential energy. Doubts because of the appearance of a potential energy coupled with forces acting on the neutrino in the problem under consideration may arise. These forces are caused by the presence of matter particles (electrons, neutrons, protons) and a consistent theory demands a quantumfield description of the whole system. In such a fundamental description the neutrino interaction with matter does not represent a direct process: it is realized by a quantized electroweak field, that is, it happens owing to exchanges of the electroweak interaction carriers. And we want to work within a phenomenological theory. We are interested in only the motion of the single particle, the neutrino, the action of matter particles being reasonably described with the help of an effective potential Ueff . We are already faced with the effective potential idea before. Recall the introduction of a refractive index in classical optics. It is well known, that in microscopic scale, the glass that consists of atoms is not an homogeneous medium. Describing the propagation of a light wave, a photon, within the fundamental theory, we would consider the light wave interaction with all atoms of the glass. However, if one is constrained by a phenomenological description of propagating a light through the glass, then the summary effect of elementary interactions could be changed by some effective refractive index. In nonrelativistic quantum mechanics, the particle evolution description is also based on the effective potential idea. However, the description of electromagnetic properties of a solid using the refractive index has its limitations. Analogously, interactions between elementary particles may not always be described by a potential function. It is possible only in the description of interactions with nonrelativistic particles providing the validity of the particle number conservation law.
