Harmonic approximation to small amplitude nuclear vibrations

We present a microscopic treatment of many body correlations for small amplitude nuclear vibrations in the harmonic approximation. Although this approximation will be valid only within discussed limits, it leads to a very simple generalized form of the usual RPA matrix equation     

Effects of the Dirac sea on the Coulomb sum value for electron scattering

Polarization effects of the Dirac sea on the Coulomb sum values for electron scattering are investigated within the framework of the random-phase approximation (RPA) in the relativistic σ-ω model. Divergence due to NN̄ excitations in the correlation functions is renormalized using a method of dimensional regularization. Particle-hole correlations reduce the sum values of the relativistic Hartree approximation by 15≈20%, while effects of the Dirac sea reduce them further by about 10≈20%. The quenching phenomena of the Coulomb sum values observed in medium heavy nuclei are rather well explained in the renormalized relativistic RPA.     

Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.     

Soft mode at an incommensurate structural phase transition

We show within the RPA approximation that a soft mode is associated with an incommensurate structural phase transition in a simple microscopic model of two level ions interacting with the phonons of a crystal.     

Phase Separation of Penetrable Core Mixtures

A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the random phase approximation (RPA) and the hypernetted chain (HNC) integral equation. The analytical RPA predictions are in semi-quantitative agreement with the numerical solutions of the HNC approximation, which itself is very accurate for gaussian core systems. A fluid-fluid phase separation is predicted to occur for a broad range of potential parameters. The pair structure exhibits a nontrivial clustering behaviour of the minority component. Similiar conclusions hold for the related model of parabolic core mixtures, which is frequently used in dissipative particle dynamics (DPD) simulations.     

Lineshape theory of the plasmon-phonon sidebands of a semiconductor plasma gain spectrum

The gain spectrum of an electron-hole plasma in direct-gap semiconductors due to plasmon-phonon-assited radiative transitions is calculated for various plasma densities at zero temperature. The screened Coulomb interaction is treated within a damped plasmon-phonon-pole approximation. The validity of this approximation is checked in the simpler case without phonon participation by comparing it with the dynamical random-phase approximation (RPA). For CdS the calculated spectra are in good qualitative agreement with the spectra experimentally observed by Saito.     

Consistent second-order approximate solution of the n-fermion problem

A simplified approximation method for the n-fermion problem is developed and tested within the exactly solvable model of Lipkin, Meshkov and Glick. Results are compared with the exact solutions and those of another approximation, which we have discussed in a previous paper, and those of the RPA.     

Effect of thermal ground state correlations on the statistical properties of the Lipkin model

The renormalized random phase approximation for hot finite Fermi systems is evaluated with the use of the thermo field dynamics formalism. This approximation treats vibrations of a hot finite Fermi system as harmonic ones but takes into account the Pauli principle in a more proper way than the usual thermal RPA, thus incorporating a new type of correlations in a thermal ground state. To demonstrate advantages of the approximation and to analyze a range of its validity, it is applied to the exactly solvable Lipkin model. A comparison is made with the exact grand canonical ensemble calculations, results of the thermal Hartree – Fock approximation and the thermal random phase approximation. The intrinsic energy of the system, the heat capacity, the average value of the quasispin operator z-projection and the particle number variance are calculated as functions of temperature. On the whole, the thermal renormalized RPA appears to be a better approximation than the other two. Its advantage is especially evident in the vicinity of the phase transition point. It is found that within TRRPA the phase transition occurs at lower temperature than in THFA and TRPA. Received: 4 January 1999 / Revised version: 10 March 1999     

Collective excitations and a backbending phenomenon in <Superscript>156</Superscript>Dy

We propose a self-consistent practical method to study collective excitations in rotating nuclei within the cranking + random phase approximation approach. It consists in solving the cranking Hartree-Bogolyubov equations for the modified Nilsson potential + monopole pairing forces. Further, the mean field results are used to construct collective vibrations treated in the random phase approximation (RPA). Special attention is paid to fulfill all conservation laws in the RPA to separate spurious and physical solutions. We demonstrate that the backbending in ¹⁵⁶Dy can be explained as a result of the disappearance of collective γ vibrations of the positive signature in the rotating frame.     

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.     

Schematicity and ground state correlations in the lead isotopes

The relationship between collectivity and ground state correlations is analyzed for the single closed shell lead isotopes. The effects of the schematic approximation are discussed, within the framework of both the quasiparticle Random Phase Approximation and the quasiparticle Tamm-Dancoff approach. The consistency of the RPA is investigated.     

Influence of isolated para-hydrogen molecules in solid ortho-hydrogen on the libron density of states

A Green function theory is used to calculate the influence of isolated para-hydrogen defects in solid hydrogen on the libron density of states. Librons are treated within the harmonic approximation (RPA).Extract from D 26     

On the microscopic description of nuclei at high spins

The behaviour of nuclei at high angular momenta is studied within the framework of many-body Greenfunctions. A theory is developed which can be applied to interacting Fermi-systems in strong external fields. In a qualitative calculation, using the semiclassical approximation, it is shown that at high angular momenta the groundstate band can nearly coincide with the first vibrational band, which corresponds to a breakdown of the usual RPA approximation. We also obtain the socalled “backbending” effect.     

Quantum correlations in rotating nuclei

Using the Hamiltonian that consists of the separable quadrupole + pairing forces and the cranking term, we analyze the correlations associated with shape, orientation, and particle-number fluctuations in rotating nuclei. Quantum fluctuations around mean field solutions are treated in the random phase approximation (RPA), with special emphasis on the restoration of rotational symmetry and particle number conservation. The mean field calculations have been made within the self-consistent cranking model. The effect of the RPA correlation energy for the moment of inertia is studied with the integral representation method proposed.     

Anisotropy of plasmon dispersion in Al: An electron correlation effect

Electron energy-loss spectroscopy of epitaxial Al films shows a small, but well-established anisotropy of the plasmon dispersion. This cannot be explained within the random-phase approximation (RPA). Anisotropic electron exchange correlations, caused by the lattice pseudopotential, account qualitatively for the observed differences of dispersion.     

Competing phases in the cuprates: Charge vs spin order

We have investigated magnetic and charge instabilities of the cuprates within the Gutzwiller approximation RPA (GA+RPA). Interestingly, in GA the dressed Hubbard U is not a single parameter, but has different forms in the spin and charge responses, with distinct doping dependencies. While there are a number of competing magnetic instabilities for hole-doped cuprates, we fail to find any purely electronic charge density waves. The dominant magnetic instabilities are associated with ‘double nesting’, and the phase diagrams are material dependent, with LSCO differing from other cuprates.     

Time-dependent Gutzwiller approximation for the Hubbard model

We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. This new formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement over traditional GA and HF+RPA treatments. Dynamical correlation functions can be computed and are also substantially better than HF+RPA ones and obey well behaved sum rules.     

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.     

聚二苯分子中基态结构的稳定性及各种凝聚相

本文利用统计物理中量子场论方法分析无限长聚二苯分子(Polyacenacene)基态结构的稳定性问题。在无规周相近似(RPA)范围内得到各种有序相:电荷密度波(CDW)、自旋密度波(SDW)及超导相存在的可能性,指出发生这些相变的条件。从而从理论上表明,聚二苯分子在适当条件下有可能成为一种有希望的高温超导体。     

Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuouslybroken symmetry, this being the main focus of the present article. Correlations beyondstandard RPA are summed up correcting for the quasi-boson approximation in standard RPA.Desirable properties of standard RPA such as fulfillment of energy weighted sum rule andappearance of Goldstone (zero) modes are kept. We show theoretically and, for a modelcase, numerically that, indeed, SCRPA maintains all properties of standard RPA forpractically all situations of spontaneously broken symmetries. A simpler approximate formof SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equationsare first outlined as an eigenvalue problem, but it is also shown how an equivalent manybody Green’s function approach can be formulated.