By means of a new Cooper pair mean field approximation, an effective phonon-Cooper pair interaction is derived for electron-phonon systems. It is demonstrated that through exchange of virtual Cooper pairs, phonons with opposite wave vectors can feel an effective attractive force and bound into phonon pairs, which leads to a new superconducting phonon state. It is found that the electron Cooper state and the superconducting phonon state consist of the stable and symmetric superconducting ground state with high critical temperature. In the weak coupling limit of phonon-Cooper pair interactions, the ground state symmetry breaks down and becomes the traditional BCS state.
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