  The ground states and excited states of the Lipkin model hamiltonian are
calculated using a new theoretical approach which has been derived from an
extended time-dependent Hartree-Fock theory known as the time-dependent
density-matrix theory (TDDM). TDDM enables us to calculate correlated ground
states, and its small amplitude limit (STDDM), which is a version of extended
RPA theories based on a correlated ground state, can be used to calculate
excited states. It is found that this TDDM plus STDDM approach gives much
better results for both the ground states and the excited states than the
Hartree-Fock ground state plus RPA approach.

Nuclear Theory