Symmetry of bipolaron bound states for small Coulomb repulsion
  We consider the bipolaron in the Pekar--Tomasevich approximation and address the question whether the ground state is spherically symmetric or not. Numerical analysis has, so far, not completely settled the question. Our contribution is to prove rigorously that the ground state remains spherical for small values of the electron-electron Coulomb repulsion. 
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer
math-ph cond-mat.str-el math.AP math.MP