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Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent random-phase approximation equations already known from the literature. From the equations of the odd particle number case the single-particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and to the one-dimensional Hubbard model give very good results. [ABSTRACT FROM AUTHOR]