Isotope Effect on the Formation Energy of Soliton in t-Polyacetylene

The formation energy of a soliton was derived in the TLM model to be 2\Delta_{0}/\pi which is independent of the masses of the polymer atoms. We estimate effects of the electron-phonon coupling on the soliton formation energy, particularly, through modifications of the harmonic oscillations of (CH) groups. A model based on the amplitude mode formalism is used and the electron-phonon coupling is taken into account to make the effective potential of lattice vibration. Among dynamical degrees of freedom in the lattice vibration, a translational mode of the soliton is separately examined, since it corresponds to a zero-energy mode. We get a difference in the formation energy between the two isotopes of about 0.03eV. Soliton trapping around defects or impurities changes the formation energy and enlarges the isotope difference.