Extended RPA Theories Research Articles

Role of small-norm components in extended random-phase approximation

The role of the small-norm amplitudes in extended RPA theories such as the particle-particle and hole-hole components of one-body amplitudes and the two-body amplitudes other than two particle - two holes components are investigated for the one-dimensional Hubbard model using an extended RPA derived from the time-dependent density-matrix theory. It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.

Second random phase approximation and renormalized realistic interactions

We examine the response of closed-shell nuclei using a renormalized interaction, derived with the Unitary Correlation Operator Method (UCOM) from the Argonne V18 potential, and a second RPA (SRPA) method. The same two-body interaction is used to derive the Hartree–Fock ground state and the SRPA equations. Our results show that the coupling of particle–hole states to higher-order configurations produces sizable effects compared with first-order RPA. A much improved description of the isovector dipole and isoscalar quadrupole resonances is obtained, thanks in part to the more fundamental treatment of the nucleon effective mass offered by SRPA. The present work suggests the prospect of describing giant resonance properties realistically and consistently within SRPA or other extended RPA theories. Self-consistency issues of the present SRPA method and residual three-body effects are pointed out.

Spurious states in extended RPA theories, part II

Using an extended RPA theory (ERPA) which contains the effects of ground-state correlations and preserves hermiticity, conditions that spurious modes have zero-energy solutions in extended RPA theories are investigated from a general point of view. The single and double excitations of translational motion are considered as illustrative examples.

Extended RPA with ground-state correlations in a solvable model

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.

Relation between Density-Matrix Theory and Pairing Theory

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.

Extended RPA with ground-state correlations

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 22 O and study the first 2 + state and its two-phonon states using STDDM.

Extended random phase approximation in a solvable model

We propose an extended Lipkin model that can describe decay processes of particle-hole states and is still solvable. We examine several RPA-type theories using the model. We show explicitly the roles played by the self-energies of particle-hole propagators, and clarify how the extended RPA theory describes collective states better than other RPA-type theories.

Spurious modes in Extended RPA theories

Necessary conditions that the spurious state associated with the translational motion and its double-phonon state have zero excitation energy in extended RPA (ERPA) theories which include both one-body and two-body amplitudes are investigated using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM provides us with a quite general form of ERPA as compared with other similar theories in the sense that all components of one-body and two-body amplitudes are taken into account. Two conditions are found necessary to guarantee the above property of the single and double spurious states: The first is that no truncation in the single-particle space should be made. This condition is necessary for the closure relation to be used and is common for the single and double spurious states. The second depends on the mode. For the single spurious state all components of the one-body amplitudes must be included, and for the double spurious state all components of one-body and two-body amplitudes have to be included. It is also shown that the Kohn theorem and the continuity equations for transition densities and currents hold under the same conditions as the spurious states. ERPA theories formulated using the Hartree-Fock ground state have a non-hermiticity problem. A method for formulating ERPA with hermiticity is also proposed using the time-dependent density-matrix formalism.

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 $^{24}$O 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.

Collectivity of double giant resonances in extended RPA theories

Collectivity of double giant resonances in extended RPA theories

The Coulomb sum rule in the extended RPA theory

We investigate in detail the Coulomb sum rule of 40Ca with momentum transfer q = 2.0 fm −1, in the framework of traditional nuclear many-body theory, i.e. by using the G-matrix and the extended RPA theory. We have separately evaluated the one-body part (total charge Z) and the two-body part (two-body correlation function) of the sum rule. A considerable part of the missing charge in the existing experimental data is shown to be explained by the ground-state correlations induced by the tensor force. It is also found that the one-body part is not fully observed in the existing experimental data. Problems left to be discussed are pointed out.

The Coulomb sum rule of 40Ca

We investigate the Coulomb sum rule of40Ca for the momentum transfer q=2.0 fm−1 in the framework of traditional nuclear many-body theory, namely, by using the G-matrix and the extended RPA theory. We have evaluated the one-body part (total chargeZ and the two-body part (two-body correlation function) of the Coulomb sum rule separately. A considerable part of the missing charge in the existing experimental data is found to be explained maily by the ground state correlations induced by the tensor force. It was also found that the one-body part (charge Z) is not in the existing experimental data.

Sum rules in extended RPA theories

Different moments m k of the excitation strength function are studied in the framework of the second RPA and of the extended RPA in which 2p2h correlations are explicitly introduced into the ground state by using first-order perturbation theory. Formal properties of the equations of motion concerning sum rules are derived and compared with those exhibited by the usual Ip1h RPA. The problem of the separation of the spurious solutions in extended RPA calculations is also discussed.

Effects of two-particle-two-hole correlations on the longitudinal quasielastic response in 12C

In an extended RPA theory which includes 1p1h as well as 2p2h excitations we have calculated the quasielastic charge response in 12C for momentum transfers of 200, 250 and 300 MeV c . Using a realistic G-matrix interaction in local density approximation we find reasonable agreement with the (e, é) data for 200 and 250 MeV c while at 300 MeV c , as a result of shell truncations, the agreement starts to degrade.