  The hole-state random phase approximation (hRPA) and the particle-state
random phase approximation (pRPA) for systems like odd $A$ nuclei are
discussed. These hRPA and pRPA are formulated based on the Hartree-Fock ground
state. An extension of hRPA and pRPA based on a correlated ground state is
given using time-dependent density-matrix theory. Applications to the
single-particle states around $^{16}$O are presented. It is shown that
inclusion of ground-state correlation affects appreciably the results of hRPA
and pRPA. The question of the coupling of the center of mass motion of the core
to the particle (hole) is also discussed.
