Intermediate Coupling Theory: Padé Approximants for Polarons

A general method is presented for obtaining an accurate intermediate-coupling theory from weak- and strong-coupling perturbation theory. The method uses two-point Pad\'e approximants to extrapolate (low-order) expansions about the weak- and the strong-coupling limits into the intermediate-coupling regime. The method is used to evaluate the ground-state energy and effective mass of the polaron with gratifying success. In addition, the weak-coupling perturbation theory of the polaron dispersion relation, ground-state energy, and effective mass are extended to fourth, sixth, and fourth order, respectively. A scheme based on two-point Pad\'e approximants is used to obtain an optimal polaron dispersion relation.