Showing papers on "Random phase approximation published in 2002"
TL;DR: In this paper, the residual interaction between quasiparticles is determined consistently from the two-body force used in the Hartree-Fock-Bogoliubov (HFB) equations, while the continuum coupling is treated exactly.
Abstract: Quadrupole excitations of neutron-rich nuclei are analyzed by using the linear response method in the Quasiparticle Random Phase Approximation (QRPA). The QRPA response is derived starting from the time-dependent Hartree-Fock-Bogoliubov (HFB) equations. The residual interaction between the quasiparticles is determined consistently from the two-body force used in the HFB equations, while the continuum coupling is treated exactly. Calculations are done for the neutron-rich oxygen isotopes. It is found that pairing correlations affect the low-lying states, and that a full treatment of the continuum can change the structure of the states in the giant resonance region. (authors)
103 citations
TL;DR: In this paper, the total energy of solids is calculated by an ab initio method based on the Green's-function theory, which is constructed from one-body wave functions and eigenvalues obtained in the local density approximation (LDA) to density-functional theory, and the correlation energy is estimated within the random phase approximation.
Abstract: Total energies of solids are calculated by an ab initio method based on the Green's-function theory. Green's function is constructed from one-body wave functions and eigenvalues obtained in the local-density approximation (LDA) to density-functional theory, and the correlation energy is estimated within the random-phase approximation. The scheme is applied to Na and Si. In both cases, the equilibrium lattice constants are in reasonable agreement with experiments. The role of the exchange-correlation energy in the total-energy curve is discussed in detail in comparison with the LDA.
101 citations
TL;DR: In this paper, the isoscalar toroidal dipole strength distributions in spherical nuclei are calculated in the framework of a fully consistent relativistic random phase approximation, and the strong mixing between the toroidal resonance and the dipole compression mode might help to explain the large discrepancy between theory and experiment on the position of isoscarar giant dipole resonances.
Abstract: The isoscalar toroidal dipole strength distributions in spherical nuclei are calculated in the framework of a fully consistent relativistic random phase approximation. It is suggested that the recently observed “low-lying component of the isoscalar dipole mode” might correspond to the toroidal giant dipole resonance. Although predicted by several theoretical models, the existence of toroidal resonances has not yet been confirmed in experiment. The strong mixing between the toroidal resonance and the dipole compression mode might help to explain the large discrepancy between theory and experiment on the position of isoscalar giant dipole resonances.
72 citations
TL;DR: The fruitfulness of traditional many-body Green's function theory for calculating the total energy of real systems is demonstrated using the random phase approximation in the Luttinger-Ward formulation.
Abstract: The fruitfulness of traditional many-body Green's function theory for calculating the total energy of real systems is demonstrated using the random phase approximation in the Luttinger-Ward formulation. As the first application to a real system, the total energy of ${\mathrm{H}}_{2}$ is calculated as a function of nuclear separation and compared with the configuration interaction and the local density approximation results. While the local density result is in large error for large separations, the present approach gives satisfactory agreement with the configuration interaction results. The method is promising as an alternative to the quantum Monte Carlo technique.
70 citations
65 citations
TL;DR: In this article, the relativistic random-phase approximation (RRPA) is derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions.
Abstract: The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction. Their contribution is essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole, and isoscalar quadrupole response of ${}^{208}\mathrm{Pb},$ are performed in the fully self-consistent RRPA framework based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.
62 citations
TL;DR: An ab initio zeroth-order regular approximation (ZORA) theory for relativistic calculation of the nuclear magnetic shielding tensors is presented at the Hartree-Fock level.
Abstract: An ab initio zeroth-order regular approximation (ZORA) theory for relativistic calculation of the nuclear magnetic shielding tensors is presented at the Hartree–Fock level. The nuclear magnetic shieldings tensors of hydrogen halides, HX (X=F, Cl, Br, and I), are calculated, and the results are compared to experimental values and other calculated results obtained using the Douglas–Kroll–Hess (DKH) transformation, the four-component random phase approximation (RPA), and the Dirac–Fock (DF) approaches. It is shown that the ZORA method underestimates the relativistic effects on the magnetic shieldings as compared to the four-component RPA results. However, as to the proton chemical shifts, the ZORA results are closer to the experimental proton shifts than those of the DKH and 4-RPA approaches.
58 citations
TL;DR: Fully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin-spin couplings and nuclear magnetic shieldings for the group-15 and -16 hydrides are presented in this article.
Abstract: Fully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin–spin couplings 1J(X-H) and 2J(H-H) and nuclear magnetic shieldings σ(X) and σ(H) for the group-15 and -16 hydrides are presented. Relativistic calculations were performed with Dirac–Fock wave functions and the random phase approximation method. Results are compared to its nonrelativistic counterpart. Paramagnetic and diamagnetic contributions to the nuclear magnetic shielding constants are also reported. We found very large relativistic corrections to both properties in the sixth-row hydrides (BiH3 and PoH2). Our calculations of the relativistic corrections to the isotropic part of σ at the heavy nucleus X show that it is roughly proportional to Z3.2 in both series of molecules. Paramagnetic term σp is more sensitive to the effects of relativity than the diamagnetic one σd, even though both have a behavior proportional to third power of the nuclear charge Z.
53 citations
TL;DR: A new and explicitly many-body aspect of the "leveraging" of thespin-orbit interaction is demonstrated, spin-orbit activated interchannel coupling, which can significantly alter the photoionization cross section of a spin- orbit doublet.
Abstract: A new and explicitly many-body aspect of the "leveraging" of the spin-orbit interaction is demonstrated, spin-orbit activated interchannel coupling, which can significantly alter the photoionization cross section of a spin-orbit doublet. As an example, it is demonstrated via a modified version of the spin-polarized random phase approximation with exchange, that a recently observed unexplained structure in the Xe 3d(5/2) photoionization cross section [A. Kivimaki et al., Phys. Rev. A 63, 012716 (2000)] is entirely due to this effect. Similar features are predicted for Cs 3d(5/2) and Ba 3d(5/2).
50 citations
TL;DR: In this article, the angular distributions of photoelectrons from the 2σg shell of a fixed-in-space N2 molecule have been measured for left and right-elliptically polarized, as well as for linearly polarized, light.
Abstract: Angular distributions of photoelectrons (ADPs) from the 2σg shell of a fixed-in-space N2 molecule have been measured for left- and right-elliptically polarized, as well as for linearly polarized, light. From these data a set of dipole matrix elements and phase shift differences characterizing the process has been determined taking into account the acceptance angles of both electron and ion detectors, i.e. the complete experiment has been performed. Good agreement between the experimental and the relevant theoretical values calculated in the random phase approximation is obtained. Based on the results of the complete experiment, three-dimensional ADPs and ions are predicted for different light polarizations.
41 citations
TL;DR: In this paper, single-particle resonant states in the continuum were determined by solving scattering states of the Dirac equation with proper asymptotic conditions in the relativistic mean field theory.
Abstract: Single-particle resonant states in the continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions in the relativistic mean field theory (RMF). The regular and irregular solutions of the Dirac equation at a large radius where the nuclear potentials vanish are relativistic Coulomb wave functions that are calculated numerically. Energies, widths, and wave functions of single-particle resonance states in the continuum for Sn-120 are studied in the RMF with the parameter set of NL3. The isoscalar giant octupole resonance of Sn-120 is investigated in a fully consistent relativistic random phase approximation. Comparing the results including full continuum states and only those single-particle resonances we find that the contributions from those resonant states dominate in the nuclear giant resonant processes.
TL;DR: In this article, self-consistent factorization of two-body residual interaction is proposed for arbitrary density and current-dependent energy functionals, and a separable RPA (SRPA) method is constructed.
Abstract: Self-consistent factorization of two-body residual interaction is proposed for arbitrary densityand current-dependent energy functionals. Following this procedure, a separable RPA (SRPA) method is constructed. SRPA considerably simplifies the calculations and demonstrates quick convergence to exact results. The method is tested for SkI3 and SkM* forces.
TL;DR: In this paper, a finite rank separable approximation for particle-hole random phase approximation (RPA) calculations with Skyrme interactions is extended to take into account the pairing, and the results obtained within their approach are very close to those that were calculated within quasiparticle RPA (QRPA), with the full Skyreme interaction.
Abstract: A finite rank separable approximation for particle-hole random phase approximation (RPA) calculations with Skyrme interactions is extended to take into account the pairing. As an illustration of the method energies and transition probabilities for the quadrupole and octupole excitations in some O, Ar, Sn, and Pb isotopes are calculated. The values obtained within our approach are very close to those that were calculated within quasiparticle RPA (QRPA) with the full Skyrme interaction. They are in reasonable agreement with experimental data.
TL;DR: In this paper, the mass enhancement of LiV 2 O 4 was investigated with consideration to orbital degeneracy as well as a geometrically frustrated lattice structure, and various types of instability upon increasing electron interaction, V, were examined at zero temperature by calculating generalized susceptibilities based on the random phase approximation.
Abstract: In order to investigate a large mass enhancement of LiV 2 O 4 , I studied a realistic model Hamiltonian with consideration to orbital degeneracy as well as a geometrically frustrated lattice structure. Various types of instability upon increasing electron interaction, V , are examined at zero temperature by calculating generalized susceptibilities based on the random phase approximation. The most prominent instability is a spin density wave order accompanied by orbital polarization with a wave vector close to (π,-π,π), and the critical interaction strength is of the same order as the estimate for the V atom. However, the wave vector dependence of spin fluctuations is rather weak, and other spin polarizations with different wave vectors are enhanced at the same time. The enhancement is not only in the spin sector; it is interesting that the fluctuations of orbital angular momentum are also enhanced around k =0. This indicates the importance of orbital fluctuations in this system.
TL;DR: In this paper, the dipole-coupling-induced quartic in-plane anisotropy of a square ferromagnetic Heisenberg monolayer is calculated.
Abstract: In this study we calculate the dipole-coupling-induced quartic in-plane anisotropy of a square ferromagnetic Heisenberg monolayer. This anisotropy increases with an increasing temperature, reaching its maximum value closeto the Curie temperature of the system. At T=0 the system is isotropic, besides a small remaining anisotropy due to the zero-point motion of quantum mechanical spins. The reason for the dipole-coupling-induced anisotropy is the disturbance of the square spin lattice due to thermal fluctuations ("order-by-disorder" effect). For usual ferromagnets its strength is small as compared to other anisotropic contributions, and decreases by application of an external magnetic field. The results are obtained from a Heisenberg Hamiltonian by application of a mean field approach for a spin cluster, as well as from a many-body Green's function theory within the Tyablikov decoupling (the random phase approximation).
TL;DR: Using the random phase approximation, it is shown that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations.
Abstract: Using the random phase approximation, we show that a crossed-chains model of spin- $1/2$ Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a ``sliding Luttinger liquid.'' In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.
TL;DR: In this article, the Coulomb drag between two low density, closely spaced, two-dimensional electron systems was measured and the experimentally measured drag exceeds that calculated in the random phase approximation by a significant, and density dependent, factor.
TL;DR: In this paper, the ground state electronic properties and the optical/UV response function of linear carbon chains C N, using ab-initio methods based on local density and on time-dependent local density approximations (LDA and TDLDA), were analyzed.
TL;DR: In this paper, the strength functions of quadrupole modes in the unstable oxygen isotopes 22 O and 24 O were calculated using an extended version of the time-dependent Hartree-Fock theory known as the timedependent density-matrix theory (TDDM).
TL;DR: In this article, the Hartree-Fock + RPA binding energy is calculated in full 0-hbar-omega shell-model spaces and compared to exact diagonalization.
Abstract: The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We find that in general HF+RPA gives a very good approximation to the ``exact'' ground state energy. In those cases where RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wavefunction.
TL;DR: In this article, the dynamics of the interLandau-level excitations of a 2DEG in large magnetic fields using coherent time-resolved nonlinear spectroscopy were investigated.
Abstract: We present an investigation of the dynamics of the inter-Landau-level (LL) excitations of a two-dimensional electron gas (2DEG) in large magnetic fields using coherent time-resolved nonlinear spectroscopy. The results are compared directly with measurements on undoped quantum wells. We observe time-dependent Coulomb coupling between the LL's induced by the 2DEG that induces a large transfer of oscillator strength to the lowest LL. The time dependence of the nonlinear response reveals non-Markovian and memory effects of the photoexcited system that cannot be understood in terms of the random phase approximation. We introduce a theoretical approach that treats the interactions of the magnetoexcitons with the 2DEG excitations and qualitatively accounts for the most salient experimental results in terms of shake-up of the 2DEG.
TL;DR: In this article, the optical properties of single-walled boron nitride nanotubes have been studied theoretically and the dielectric functions calculated from the gradient approximation and the random-phase approximation are consistent with each other.
Abstract: Optical properties of single-walled boron nitride nanotubes have been studied theoretically. The dielectric functions calculated from the gradient approximation and the random-phase approximation are consistent with each other. The imaginary and the real parts of the dielectric function, respectively, exihibit the special peaks and dips. The strong e-h absorption peaks at ω < 4 γ 0 comes from the π band and the others from the π + a bands (γ 0 is the nearest-neighbor interaction of 2p z orbitals). Such single-particle excitations also induce the peak structures in the reflectance spectrum. On the other hand, the loss function shows the prominent π- and π + σ-plasmon peaks. The π and π + a plasmons (collective excitations) reveal themselves in the reflectance spectrum as strong and abrupt edges. The optical properties are affected by the polarization direction and the nanotube radius, but not the chiral angle. The calculated results could be experimentally checked with optical spectroscopies or EELS.
TL;DR: In this article, a random-phase approximation study of collective excitations in a Bose-Fermi mixed degenerate gas of alkali-metal atoms was performed by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas Fermi equations.
Abstract: We perform a random-phase approximation study of collective excitations in a Bose-Fermi mixed degenerate gas of alkali-metal atoms at $T=0.$ The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of Bose and Fermi multipole (L) operators with $L=0,1,2,3.$ Transition densities and dynamical structure factors are calculated for collective excitations. A comparison with the sum rule prediction for the collective frequency is given. The time dependent behavior of the system after an external impulse is studied.
TL;DR: In this paper, the authors present a review of the approximation methods relevant to describe many-fermion systems at finite temperature, including the random phase approximation (RPA) method.
Abstract: The purpose of the present paper is to review the approximation methods relevant to describe many-fermion systems at finite temperature. In Sections 1.2 and 1.3 we review the grand canonical formalism for independent fermions and discuss its applicability to the case of finite nuclei for which fluctuations arising from the small number of particles involved are expected to be sizeable. In Section 1.4 we present a derivation of the mean-field equations based on the variational method. In Section 2 we discuss perturbation expansions of partition functions. We consider a particularly important subseries containing the so called ring diagrams whose summation leads to the random phase approximation (RPA). In Section 3 an application to the physics of giant resonances in hot nuclei is described.
TL;DR: In this article, the Coulomb drag between two low density, closely spaced, two-dimensional electron systems was measured and the experimentally measured drag exceeds that calculated in the random phase approximation by a significant, and density dependent, factor.
Abstract: Measurements and calculations of Coulomb drag between two low density, closely spaced, two-dimensional electron systems are reported. The experimentally measured drag exceeds that calculated in the random phase approximation by a significant, and density dependent, factor. Studies of the dependence of the measured drag on the difference in density between the two layers clearly demonstrate that previously ignored q=2k_F scattering processes can be very important to the drag at low densities and small layer separations.
TL;DR: Partial and total photoionization cross sections of the K shell of the N 2 molecule are calculated using the generalization of the random-phase approximation that has been applied earlier to the valence shells of N 2 as discussed by the authors.
Abstract: Partial and total photoionization cross sections of the K shell of the N 2 molecule are calculated using the generalization of the random-phase approximation that has been applied earlier to the valence shells of N 2 [Phys. Rev. A 61, 032704 (2000)]. At zero order the relaxed core Hartree-Fock approximation is used. It is demonstrated that due to strong intershell correlations the σ* shape resonance reveals itself not only in the 1σ g →∈σ u channel as it takes place in all single-particle approximations, but also in the 1 σ u →∈σ g channel. The influence of vibrational motion on the cross sections is taken into account. Good agreement with the most recent experimental data for different partial cross sections is achieved.
TL;DR: In this paper, the electron transmission through a monatomic nanowire containing N attached quasiperiodically distributed nanoclusters is studied within the ballistic model, where a decimation procedure is performed to renormalize the self-energy of the nanowires sites connected to the clusters and to transform the nanodevice into an effective disordered one-dimensional chain.
Abstract: The electron transmission through a monatomic nanowire containing N attached quasiperiodically distributed nanoclusters is studied within the ballistic model. A decimation procedure is performed to renormalize the self-energy of the nanowire sites connected to the clusters and to transform the nanodevice into an effective disordered one-dimensional chain. The transmittance is determined using the transfer matrix formalism. It allows us to express each elementary reflection/transmission process per cluster in terms of a single parameter which accounts for the self-energy renormalization. It is shown that cluster antiresonances are responsible for the occurrence of a localization-delocalization transition which discriminates between insulating and conducting regimes for the electron transport. These results are interpreted in a general way on the basis of the scaling theory which involves the random phase approximation to characterize the behavior of the probability distribution connected to the transmittance. However, the scaling theory fails for particular values of the electron energy leading to singularities in the average transmittance called tips and dips. These singularities are related to the reminiscence of quantum interferences which the disorder is not sufficient to break.
TL;DR: In this article, the properties of pairing interaction in the shell model framework are considered with the aid of an exact numerical solution utilizing the quasispin symmetry, emphasizing the features which are out of reach for the usual approximate techniques based on BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS plus random-phase approximation theory fails.
Abstract: The properties of the pairing interaction in the shell model framework are considered with the aid of an exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate techniques based on the BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS plus random-phaseapproximation theory fails. Chaotic aspects of the mixing generated by the pairing interaction are studied. The level repulsion and large information entropy of the eigenstates coexist with the absence of thermalization of single-particle motion. The full spectrum of pair vibration on average displays a spin dependence similar to that for a rigid rotor.
01 Mar 2002
TL;DR: In this paper, the authors proposed a new scheme for numerically computing collective-mode spectra for large-size systems, using a reformulation of the Random Phase Approximation.
Abstract: We propose a new scheme for numerically computing collective-mode spectra for large-size systems, using a reformulation of the Random Phase Approximation. In this study, we apply this method to investigate the spectrum and nature of the spin-waves of a (III,Mn)V Diluted Magnetic Semiconductor. We use an impurity band picture to describe the interaction of the charge carriers with the local Mn spins. The spin-wave spectrum is shown to depend sensitively on the positional disorder of the Mn atoms inside the host semiconductor. Both localized and extended spin-wave modes are found. Unusual spin and charge transport is implied.
TL;DR: In this paper, the form factor of extremely weak l-forbidden and isoscalar $M1$ excitations in the self-conjugate nucleus was studied.
Abstract: Magnetic dipole transitions in the self-conjugate nucleus ${}^{32}\mathrm{S}$ up to an excitation energy of 12 MeV have been investigated in inelastic electron scattering at ${\ensuremath{\Theta}}_{e}=180\ifmmode^\circ\else\textdegree\fi{}$ at the superconducting Darmstadt electron linear accelerator (S-DALINAC). Transition strengths have been determined from a plane-wave Born approximation analysis including Coulomb distortion. For the two strongest $M1$ transitions, where a discrepancy of a factor of about 2 was observed in previous ${(e,e}^{\ensuremath{'}})$ experiments, values intermediate between the two extremes are deduced from the present work. The resulting strength distribution is well described by shell-model calculations using the unified $\mathrm{sd}$-shell interaction and an effective $M1$ operator. The shell-model wave functions also provide a reasonable description of the form factors. A quasiparticle random phase approximation calculation is less successful. The present results allow for the first time studies of the form factor of extremely weak l-forbidden and isoscalar $M1$ excitations in ${}^{32}\mathrm{S}.$ The l-forbidden transition allows a sensitive test of tensor corrections to the $M1$ operator. A combined analysis with the isospin-analog Gamow-Teller (GT) transitions in the $A=32$ triplet reveals a situation similar to previous studies in $A=39$ nuclei: microscopic calculations reasonably account for the GT strengths, but fail in the case of $M1$ strengths. A possible explanation may be found in the nonrelativistic treatment of the latter. Some examples of the role of relativistic corrections are discussed. A consistent description of the reduced transition strength and the form factor of the isoscalar $M1$ excitation requires isospin mixing with the close-lying isovector transitions. The extracted Coulomb matrix elements are roughly within the limits set by the approximate constancy of the spreading width derived from the analysis of compound-nucleus reactions.