Taking 16O as an example of realistic nuclei, we demonstrate that a correlated ground state can be obtained as a long time solution of a time-dependent density-matrix formalism (TDDM) when the residual interaction is adiabatically treated. We also study in TDDM the E2 giant resonance of 16O built on the correlated ground state and compare it with that built on the Hartree-Fock ground state. It is found that a spurious mixing of low frequency components seen in the latter is eliminated by using the correlated ground state.Taking 16O as an example of realistic nuclei, we demonstrate that a correlated ground state can be obtained as a long time solution of a time-dependent density-matrix formalism (TDDM) when the residual interaction is adiabatically treated. We also study in TDDM the E2 giant resonance of 16O built on the correlated ground state and compare it with that built on the Hartree-Fock ground state. It is found that a spurious mixing of low frequency components seen in the latter is eliminated by using the correlated ground state.

Progress of Theoretical PhysicsJul 1, 19954 citations

Correlated ground state of 16O and E2 giant resonance built on it

M. Tohyama

A correlated ground state of ${}^{16}\mathrm{O}$ and an $E2$ giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix (TDDM) theory. The Skyrme III force is used as an effective interaction for the calculation of both a mean field and two-body correlations. It is found that a TDDM calculation with the Skyrme force gives reasonable ground-state correlations and a large spreading width of the $E2$ giant resonance.A correlated ground state of ${}^{16}\mathrm{O}$ and an $E2$ giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix (TDDM) theory. The Skyrme III force is used as an effective interaction for the calculation of both a mean field and two-body correlations. It is found that a TDDM calculation with the Skyrme force gives reasonable ground-state correlations and a large spreading width of the $E2$ giant resonance.

Physical Review COct 1, 19987 citations

Damping of collective states in an extended random-phase approximation with ground-state correlations

M. Tohyama

Applications of an extended version of the Hartree-Fock theory and the random-phase approximation derived from the time-dependent density-matrix theory (TDDM) are presented. In this TDDM-based theory, the ground state is given as a stationary solution of the TDDM equations and the excited states are calculated using the small-amplitude limit of TDDM. The first application presented is an extended Lipkin model in which an interaction term describing a particle scattering is added to the original Hamiltonian so that the damping of a collective state is taken into account. It is found that the TDDM-based theory well reproduces the ground state and excited states of the extended Lipkin model. The quadrupole excitation of the oxygen isotopes $^{16,20,22}\mathrm{O}$ is also studied as realistic applications of the TDDM-based theory. It is found that large fragmentation of the giant quadrupole resonance in $^{16}\mathrm{O}$ is reproduced, and it is pointed out that the effects of ground-state correlations are quite important for fragmentation. It is also found that the quadrupole states in neutron-rich oxygen isotopes have small spreading widths.Applications of an extended version of the Hartree-Fock theory and the random-phase approximation derived from the time-dependent density-matrix theory (TDDM) are presented. In this TDDM-based theory, the ground state is given as a stationary solution of the TDDM equations and the excited states are calculated using the small-amplitude limit of TDDM. The first application presented is an extended Lipkin model in which an interaction term describing a particle scattering is added to the original Hamiltonian so that the damping of a collective state is taken into account. It is found that the TDDM-based theory well reproduces the ground state and excited states of the extended Lipkin model. The quadrupole excitation of the oxygen isotopes $^{16,20,22}\mathrm{O}$ is also studied as realistic applications of the TDDM-based theory. It is found that large fragmentation of the giant quadrupole resonance in $^{16}\mathrm{O}$ is reproduced, and it is pointed out that the effects of ground-state correlations are quite important for fragmentation. It is also found that the quadrupole states in neutron-rich oxygen isotopes have small spreading widths.

Physical Review CApr 24, 200724 citations

Relation between Density-Matrix Theory and Pairing Theory

M. Tohyama, Satoshi Takahara

The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the quasi-particle RPA satisfy the TDDM and STDDM equations, respectively, when only pairing-type correlations are taken into account in TDDM and STDDM.The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the quasi-particle RPA satisfy the TDDM and STDDM equations, respectively, when only pairing-type correlations are taken into account in TDDM and STDDM.

arXiv:nucl-th/0405070Progress of Theoretical PhysicsSep 1, 20044 citations

Extended RPA with ground-state correlations

Tohyama, M, Takahara, S, Peter Schuck

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.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.

Nov 6, 20037 citations

Extended RPA with ground-state correlations in a solvable model

Satoshi Takahara, M. Tohyama, Peter Schuck

The ground states and excited states of the Lipkin model Hamiltonian are calculated using a new theoretical approach that has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix (TDDM) theory. TDDM theory 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.The ground states and excited states of the Lipkin model Hamiltonian are calculated using a new theoretical approach that has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix (TDDM) theory. TDDM theory 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.

arXiv:nucl-th/0408042Physical Review CNov 19, 200419 citations

A correlated ground state of

{}^{16}\mathrm{O}

and an

E2

giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix (TDDM) theory. The Skyrme III force is used as an effective interaction for the calculation of both a mean field and two-body correlations. It is found that a TDDM calculation with the Skyrme force gives reasonable ground-state correlations and a large spreading width of the

E2

giant resonance.

^{16,20,22}\mathrm{O}

is also studied as realistic applications of the TDDM-based theory. It is found that large fragmentation of the giant quadrupole resonance in

^{16}\mathrm{O}

is reproduced, and it is pointed out that the effects of ground-state correlations are quite important for fragmentation. It is also found that the quadrupole states in neutron-rich oxygen isotopes have small spreading widths.