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

TL;DR

This paper derives exact analytical solutions for a three-body scattering problem with separable potentials, revealing new resonance states that could influence stellar cooling processes via electron capture and neutrino emission.

Contribution

It provides the first exact solutions for three-body problems with separable potentials and explores their implications for astrophysical phenomena.

Findings

Discovery of new three-body resonance states depending on inter-center distance.

Resonance widths can be zero at specific distances, enabling state transitions.

Potential role in star cooling through electron capture and neutrino emission.

Abstract

Exact analytic solutions are obtained in three-body problem for the scattering of light particle on two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new three-body resonance states that depend on distance between two fixed centers. In the case when two-body neutron-nucleus amplitudes have the Breit-Wigner's form and heavy nuclei fixed in nodes of crystalline lattice widths of new resonance states can be equal to zero at certain values of the distance. It gives the possibility of transitions between three-body resonance states 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.