Self-Trapping of an Electron by the Acoustical Mode of Lattice Vibration. I

The importance of the acoustical mode of lattice vibration for self-trapping of an electron is emphasized. It is shown that when the coupling constant between the electron and the acoustical mode vibration exceeds a certain critical value, the effective mass of the electron changes discontinuously to such an enormous value that it is practically allowed to take a localized self-trapping state as an eigenstate, in contrast to the case of polaron, in which the effective mass changes continuously with coupling constant. This diffrence is attributed to the different force range of electron-lattice interaction in the two cases.