A STRONG COUPLED ACOUSTIC DEFORMATION POLARON IN ONE DIMENSION

A study is undertaken of the system comprised of an electron interacting with acoustic phonons via the deformation potential in one dimension. A strong coupling adiabatic perturbation theory is developed in which an effective-phonon Hamiltonian is generated and determined by the solution of an iterative equation. Modified phonon modes are obtained which represent excitations of the deformed lattice. One of the modes is a translation which is interpreted as a polaron. The effective mass of the polaron is determined. The density of modified phonon modes is obtained by a Green's function method and the shift from the constant unperturbed density is computed. The energy, to the next order in inverse coupling constant beyond the strong coupling limit, involves this shift in the density of modes due to the electron-phonon interaction. Interpretation of this shift is facilitated by the introduction of a scattering phase shift. The behavior of this scattering shift clearly indicates the presence of a bound state, the polaron, and a resonance