Effect Of Ground State Correlations Research Articles

Number conservation in odd-particle number random phase approximation and extensions

Abstract The number conservation law in the odd-particle number random-phase approximation (oRPA) and its extension (EoRPA) is studied by applying them to a pairing model and 16O. It is found in the application to 16O that the number conservation law is not fulfilled in oRPA or EoRPA and that it is drastically improved in EoRPA due to the inclusion of ground-state correlation effects. PACS numbers: 21.60.Jz

Extended random-phase-approximation study of the fragmentation of the giant quadrupole resonance in O16

The damping of isoscalar giant quadrupole resonance in $^{16}\mathrm{O}$ is studied using extended random-phase-approximation approaches derived from the time-dependent density-matrix theory. It is pointed out that the effects of ground-state correlations bring strong fragmentation of quadrupole strength even if the number of two-particle--two-hole configurations is strongly limited.

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Description of ν and ν¯ scattering within quantum hadrodynamic theory

In this paper we develop a model to describe $\ensuremath{\nu}$ and $\overline{\ensuremath{\nu}}$ scattering in the GeV region by nuclei within a nuclear matter quantum hadrodynamics approach that is fully relativistic. We simplify it as much as possible, keeping the most relevant effects and trying to describe the greatest number of observables. We introduce explicitly the effect of ground-state correlations through a momentum distribution calculated perturbatively, and also final-state interactions using a perturbed nucleon propagator dressed by a relativistic self-energy containing nucleon-nucleon and $\mathrm{\ensuremath{\Delta}}$-nucleon correlations. Also, primary $\mathrm{\ensuremath{\Delta}}$ excitations are considered within a consistent approach. All these mentioned effects are built on together, into the Lehmann representation of the propagator. Within our model we take into account the effect of 2p2h and 3p3h excitations in addition to the quasielastic 1p1h ones, needed to describe the experimental data. The obtained results are promising, showing that the model works quit well and thus putting to disposal a simple but powerful approach developed within the context of nuclear matter field theory.

Effects of ground-state correlations on dipole and quadrupole excitations of 40Ca and 48Ca

The effects of ground-state correlations on the dipole and quadrupole excitations are studied for $^{40}$Ca and $^{48}$Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Large effects of the ground-state correlations are found in the fragmentation of the giant quadrupole resonance in $^{40}$Ca and in the low-lying dipole strength in $^{48}$Ca. It is discussed that the former is due to a mixing of different configurations in the ground state and the latter is from the partial occupation of the neutron single-particle states. The dipole and quadrupole strength distributions below 10 MeV calculated in ERPA are in qualitatively agreement with experiment.

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.

Effective restoration of dipole sum rules within the renormalized random-phase approximation

The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in $^{48, 52, 58}$Ca and $^{90, 96, 110}$Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, causing the violation of the corresponding energy-weight sum rules (EWSR). It is shown that this sum rule violation can be eliminated by taking into account the contribution of the particle-particle and hole-hole excitations together with the particle-hole ones in a simple and perturbative way. Consequently, the ratio of the energy-weighted sum of strengths of the pygmy dipole resonance to that of the giant dipole resonance increases.

Application of extended random-phase approximation with ground-state correlations to collective excitations of 16O

The ground-state correlation effects on the octupole excitation of 16O are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. ERPA includes the effects of ground-state correlations through the fractional occupation of single-particle states and a correlated two-body density matrix. The coupling to two particle – two hole configurations is also included in ERPA. It is found that the first 3− state calculated in the random phase approximation (RPA) is shifted upward when the self-energy contributions due to ground-state correlations are included in particle – hole pairs and that the coupling to two particle – two hole states plays a role in shifting the first 3− state down to the right position.

Three-body force effect on nuclear symmetry energy and single-particle properties of asymmetric nuclear matter

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.

Effects of ground-state correlations on collective excitations of16O

The effects of the correlations in the ground state of $^{16}$O on the octupole and dipole excitations are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. It is found that the ground-state correlation effects are significant especially in the octupole excitation. It is shown that the first $3^-$ state calculated in the random phase approximation (RPA) is shifted upward when the self-energy contributions are included in particle - hole pairs. The coupling to the two particle - two hole states plays a role in shifting the first $3^-$ state down to the right position. It is also found that the dipole strength is fragmented due to the partial occupation of the single-particle states and that the peak position of the giant dipole resonance calculated in ERPA is little changed from that in RPA due to the above-mentioned competing effects: the increase in particle - hole energy and the coupling to two particle - two hole configurations.

Nucleon effective mass in symmetric nuclear matter from the extended Brueckner-Hartree-Fock approach

We have calculated the nucleon effective mass in symmetric nuclear matter within the framework of the Brueckner-Bethe-Goldstone (BBG) theory, which has been extended to include both the contributions from the ground-state correlation effect and the three-body force (TBF) rearrangement effect. The effective mass is predicted by including the ground-state correlation effect and the TBF rearrangement effect, and we discuss the momentum dependence and the density dependence of the effective mass. It is shown that the effect of ground state correlations plays an important role at low densities, while the TBF-induced rearrangement effect becomes predominant at high densities.

Nucleon Effective Mass in Asymmetric Nuclear Matter within Extended Brueckner Approach

The on-shell properties of the nucleon effective mass in asymmetric nuclear matter are investigated in the framework of an extended Brueckner—Hartree—Fock (BHF) approach. The proton and neutron effective masses in neutron-rich nuclear matter are predicted by including both the effect of ground state correlations and the three-body force (TBF) rearrangement contribution. Within this framework, the neutron effective mass is predicted to be larger than the proton one in neutron-rich nuclear matter, i.e., m*n ≥ m*p. The effect of ground state correlations turns out to be dominated at low densities and it leads to a strong enhancement of the effective mass. The TBF rearrangement contribution becomes predominant over the effect of ground state correlations at high densities and it reduces remarkably the absolute magnitude of the isospin splitting of the neutron and proton effective masses in neutron-rich matter at high densities.

Effects of ground-state correlations on high energy scattering off nuclei: The case of the total neutron-nucleus cross section

With the aim at quantitatively investigating the longstanding problem concerning the effect of short-range nucleon-nucleon correlations on scattering processes at high energies, the total neutron-nucleus cross section is calculated within a parameter-free approach which, for the first time, takes into account, simultaneously, central, spin, isospin, spin-isospin, and tensor nucleon-nucleon correlations, and Glauber elastic and Gribov inelastic shadowing corrections. Nuclei ranging from $^{4}\mathrm{He}$ to $^{208}\mathrm{Pb}$ and incident neutron momenta in the range 3 GeV/$c$--300 GeV/$c$ are considered; the commonly used approach which approximates the square of the nuclear wave function by a product of one-body densities is carefully analyzed, showing that $\mathit{NN}$ correlations can play a non-negligible role in high energy scattering off nuclei

Effects of ground state correlations on the structure of odd-mass spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the quasiparticle and phonon operators, used to describe them, are built of fermions and as a consequence they are not ideal bosons. The correct treatment of this problem requires calculation of the exact commutators between the quasiparticle and phonon operators and in this way to take into account the Pauli principle corrections. In addition to the correlations due to the quasiparticle interaction in the ground-state influence the single-particle fragmentation as well. In this article, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned above. As an illustration of our approach, calculations of the structure of the low-lying states in the odd-mass nuclei $^{131\ensuremath{-}137}\mathrm{Ba}$ have been performed.

Extended random-phase approximation with three-body ground-state correlations

An extended random-phase approximation (ERPA) which contains the effects of ground-state correlations up to a three-body level is applied to an extended Lipkin model which contains an additional particle-scattering term. Three-body correlations in the ground state are necessary to preserve the hermiticity of the Hamiltonian matrix of ERPA. Two approximate forms of ERPA which neglect the three-body correlations are also applied to investigate the importance of three-body correlations. It is found that the ground-state energy is little affected by the inclusion of the three-body correlations. On the contrary, three-body correlations for the excited states can become quite important.

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.

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

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.

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.

Ground state correlations in deep inelastic scattering and the Drell-Yan process

Non-perturbative corrections to the LO cross section formulae for DIS and the Drell-Yan process were calculated. The interaction of partons was taken into account via dressing the incoming quark lines with spectral functions. We found the effect of ground state correlation in DIS to be large in the region of small Bjorken x and low momentum transfer Q. For a quark width of the order of 200 MeV, the deviation from parton model cross section reaches as much as 50% for Q^2=10 GeV^2. On the other hand, for the values of Q well above the resonance region, the effect of ISI turned out to be small in DIS, but still substantial for the triple differential Drell-Yan cross section. Our calculations show that the shape of the high mass Drell-Yan pair transverse momentum distribution is fully determined by quark off-shellness. From comparison to the resent data on the Drell-Yan cross section from NuSea collaboration, we obtained for the quark width in the nucleon the value about 200 MeV.

Extended random-phase approximation and Lipkin-Nogami method

The Lipkin-Nogami method, which makes it possible to take more accurately into account the law of particle-number conservation, is incorporated in the extended scheme of the random-phase approximation. The effect of ground-state correlations on the transition charge density of the lowest quadrupole state is investigated for the example of the 68Zn nucleus.