Formation of polaron clusters

The formation of spherical polaron clusters is studied within the Fr$\ddot{o}$hlich polaron theory. In a dilute polaron gas, using the non-local statistical approach and the polaron pair interaction obtained within the Pekar strong coupling theory, the homogeneous phase results to be unstable toward the appearance of polaron clusters. The physical conditions of formation for the clusters are determined calculating the critical values of electron-phonon interaction for which bound states in the collective polaron potential develop. Finally the sequence in the filling of the states is found and the stability of the clusters is assessed.