About the Problem of Existence of a Three-Dimensional Bipolaron

The range of existence of a translation invariant continuum three-dimensional bipolaron in space of two variables: of electron–phonon coupling constant and the dielectric parameters of polar medium is investigated. The critical values of the electron–phonon coupling constant are found. The possibility of existence of metastable bipolaron formations is scored. On the basis of definition of bipolaron existence the requirement of existence of a bound condition in a bipolaron potential well is necessary. It is shown, that use of a rigider requirement, than positivity of dissociation energy, namely presence of even one bound state narrows the range of existence of a bipolaron. The criteria for a bound state to arise are found by solving an integral equation, which corresponds to a Schrödinger equation describing internal states of a bipolaron.