A bipolaron in a spherical quantum dot with parabolic confinement

A theory of bipolaron states in a spherical parabolic potential well is dev eloped applying the Feynman variational principle. The basic parameters of the bipolaron ground state (the binding energy, the number of phonons in th e bipolaron cloud, and the bipolaron radius) are studied as functions of th e radius R of the potential well. Analytical expressions for bipolaron para meters are obtained at large and small sizes of the quantum well. It is sho wn that at R >> 1 (where R is expressed in units of the polaron radius), th e influence of confinement on the bipolaron binding energy W(R) is describe d by the function similar to 1/R-2, while at small sizes this influence is more complicated: W(R) passes through a maximum in the region R < 1.