Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator

Institute of Experimental and Theoretical Physics, Ave Tole-bi 154, Almaty, Kazakhstan

^a e-mail: teta@nursat.kz

Abstract

Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two fixed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei fixed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.