Formation of Large Bipolarons

A variational approach is presented to calculate the ground-state energy of large bipolarons in two and three dimensions. The values of the critical coupling constant α_c above which the bipolaron is stable and the critical ratio of dielectric constants η_c below which the bipolaron is stable are approximately evaluated. It is found that the stability region of bipolarons in the (l/α, η )-plane becomes larger with decreasing dimensionality.