  We propose a time-independent method for finding a correlated ground state of
an extended time-dependent Hartree-Fock theory, known as the time-dependent
density-matrix theory (TDDM). The correlated ground state is used to formulate
the small amplitude limit of TDDM (STDDM) which is a version of extended RPA
theories with ground-state correlations. To demonstrate the feasibility of the
method, we calculate the ground state of 22O and study the first 2+ state and
its two-phonon states using STDDM.
