Theory of Soliton Generation and Lattice Relaxation in Polyacetylene (I) General Formalism

This series of papers is devoted to the theory of soliton and polaron generation in polyacetylene by both radiative and non-radiative processes. In the first paper of this series a general formalism is presented which combines the Lattice relaxation approach for the multiphonon process developed by Huang and many others with the consistency condition in terms of the Bogoliubov-de Gennes equation and the gap equation. The exact adiabatic electron wave functions consistent with the different lattice symmetry breaking in the initial and final states are used to calculate the transition probability between these multi-electron states. The formalism presented is illustrated by deriving a general expression for the non-radiative decay rate using the steepest descent method in the case of strong coupling. The theory developed here can be applied to treating the quantum transitions between states of differnet symmetry breaking when the multi-electron background effect and the consistency condition are essential. The applications of the general formalism to polyacetylene and the comparison with numerical results and the recent experiments wi11 be given in the succeeding papers.