Abstract
Various properties are investigated in the ground state of the system which consists of localized states with local electron-phonon interactions in a degenerate electron gas. The phase diagram for the occupation number of the localized state is presented as a function of relevant physical parameters. It is shown that the occupation number increases abruptly as the Fermi energy exceeds certain thresholds under the assumption of strong interaction between electrons and local phonons. The effects of interaction between two localized states are also examined. It is found that the negative- U interaction due to localized electrons is suppressed by the transfer interaction between two localized states.
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