  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 RPA (SCRPA) 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 the 1D Hubbard model give very good
results.
