Intermediate Coupling Theory of a Polaron in External Fields

Abstract

A new extension of the Lee, Low and Pines (L–L–P) method to the problem of a polaron weakly bound in a Coulomb potential and/or in a weak magnetic field is developed. The effective Hamiltonian of a polaron bound in a Coulomb potential is derived exactly to order P⁴. The validity of replacing P² by [P_z²+eHh(2n+1)⁄c] in the field-free polaron energy E(P²) within the framework of the L–L–P method is shown in the limit of a weak magnetic field H along the z axis in the intermediate coupling case. The energies of a polaron in a Coulomb potential and subject to a weak magnetic field are also discussed.