The region of existence of the three-dimensional continuum bipolaron

The ranges of ɛ * /ɛ ∞ and of the electron-phonon coupling constant in which the three-dimensional bipolaron exists are determined. The limits of these ranges correspond to the emergence of the first bound state of two polarons. The criteria for the first bound state to arise are found by solving an integral equation, which corresponds to a Schrödinger equation describing internal vibrations of a bipolaron. The Hamiltonian describing these vibrations is separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.