Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2 + states in 24O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2 + states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory.