Asymptotic expansions in the path-integral approach to the bipolaron problem

Large bipolarons are studied in two (2D) and three (3D) space dimensions. The bipolaron energy is expanded in inverse powers of the electron-phonon coupling constant α, which leads to ${\mathit{E}}_{\mathrm{bip}}$=-(2${\mathrm{\alpha }}^2$/3π)A(u)-B(u)+O(${\mathrm{\alpha }}^{\mathrm{-}2}$), where u=U/α and U is the dimensionless Coulomb-repulsion coupling constant. We derive closed analytical formulas for the coefficients A(u) and B(u), which allow us to find the bipolaron stability region both in the scope of a model formulated in terms of Feynman path integrals and from fitting known results. Analytical expressions for the leading terms of the bipolaron effective mass and mean-square separation between electrons are also presented.