Abstract
In the limit of strong electron-phonon coupling, we use either a Pekar-type or an oscillator wave function for the center-of-mass coordinate and either a Coulomb or an oscillator wave function for the relative coordinate, and are able to reproduce all the results from the literature for the large-bipolaron binding energy. Lower bounds are constructed for the critical ratio ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$ of dielectric constants below which bipolarons can exist. It is found that, in the strong-coupling limit, the stability region for bipolaron formation is much larger in two dimensions (2D) than in 3D. We introduce a model that combines the averaging of the relative coordinate over the asymptotically best wave function with a path-integral treatment of the center-of-mass motion. The stability region for bipolaron formation is increased compared with the full path-integral treatment at large values of the coupling constant \ensuremath{\alpha}. The critical values are ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\approxeq}9.3 in 3D and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\approxeq}4.5 in 2D. Phase diagrams for the presented models are also obtained in both 2D and 3D.
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