Intermediate Coupling Theory of a Polaron in External Fields

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 P ⁴ . The validity of replacing P ² by [\(P_{z}^{2}+eH{\hbar}(2n+1)/c\)] in the field-free polaron energy E ( P ² ) 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.