Correlation effects in the one-dimensional Bose gas

We discuss interaction effects for the one-dimensional Bose gas with a repulsive delta-function interaction potential. We use the random-phase approximation and a finite local-field correction. Analytical results are given for the local-field correction, the pair-correlation function and the ground-state energy. The groundstate energy is found to be in much better agreement with the exact result than the ground-state energy calculated within the Bogoliubov approximation, where local-field corrections are neglected.     

Orbital polarization in itinerant magnets

We propose a parameter-free scheme of calculation of the orbital polarization (OP) in metals, which starts with the strong-coupling limit for the screened Coulomb interactions in the random-phase approximation (RPA). For itinerant magnets, RPA can be further improved by restoring the spin polarization of the local-spin-density approximation through the local-field corrections. The OP is then computed as the self-energy correction in the static GW method, which systematically improves the orbital magnetization and the magnetic anisotropy energies in transition-metal and actinide compounds.     

Dynamical correlations in the one-dimensional electron gas with short-range interactions

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj?lander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction . There is a corresponding local-field factor for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of and , and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations. Received 11 December 1998 and Received in final form 25 April 1999     

Effect of residual interactions on nuclear level densities

We calculate the contribution of residual interactions to nuclear level densities in the framework of the random-phase approximation. We first investigate the case of the schematic model for which analytical formulae can be worked out. More realistic calculations are performed numerically for ⁴⁰Ca and ⁵⁶Ni using oscillator wave functions and a zero-range interaction. In ⁵⁶Ni it is found that residual interactions increase level densities significantly in the random-phase approximation, while small corrections are found in ⁴⁰Ca. A comparison with the results of second-order perturbation theory is presented.     

Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Longitudinal dielectric behavior of a harmonically bound two-dimensional electron gas in a uniform magnetic field

We have employed random-phase approximation to determine the inverse dielectric function for a harmonically confined two-dimensional electron gas in a magnetic field. We examine the plasmon dispersion relation and show the results for the variation of plasmon frequency with the magnetic field strength and confinement energy.     

Electrical conductivity and thermopower of metallic helium

The pair effective interionic interaction, electrical resistance, and thermopower of liquid metallic helium have been calculated over wide temperature and density ranges using the perturbation theory for the potential of electron-ion interaction. For conduction electrons, the random-phase approximation has been used taking into account the exchange interaction and correlations in the local-field approximation. The nuclear subsystem has been described by the hard-sphere model. The sphere diameter is the only parameter of the theory. The diameter and the system density at which helium is transformed from the singly ionized to doubly ionized state have been estimated based on an analysis of the pair effective interaction between helium nuclei. The case of doubly ionized helium atoms has been considered. The numerical calculations have been performed taking into account the perturbation theory in terms up to the third order. In all cases, the role of the third-order correction is significant. In the case of metallic helium, the values of the electrical resistance and its temperature dependence are characteristic of divalent simple liquid metals, as well as the dependences of the thermopower on the density and temperature.     

Exchange and correlation effects in a semiconductor quantum-well wire

The exchange and correlation effects of a quasi-one-dimensional electron gas are investigated by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs rectangular quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The plasmon dispersion relation and structure factor are calculated as a function of electron density and thickness of the wire. Results for the total energy per electron including kinetic, exchange and correlation energies and electron effective mass are presented. The Hartree-Fock and the random-phase approximation (RPA) results are also presented for comparison. We have found that exchange and correlation effects are more evident in wires of reduced dimensions.     

Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.     

Dynamical exchange effects in a two-dimensional many-polaron gas

We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism. At weak electron-phonon coupling, we find that dynamical exchange effects lead to substantial corrections to the random-phase approximation results for the ground state energy, the effective mass, and the optical conductivity of the polaron system. Furthermore, we show that the reduction of the spectral weight of the optical absorption spectrum at frequencies above the longitudinal optical phonon frequency, due to many-body effects, is overestimated by the random-phase approximation.Received: 24 December 2003, Published online: 9 April 2004PACS: 71.45.Gm Exchange, correlation, dielectric and magnetic response functions, plasmons - 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) - 71.38.Fp Large or Fröhlich polarons     

Local-field corrections to the static dielectric function of semiconductors: A model study

We present results for the macroscopic static dielectric function at small wave vector q for semiconductors, including the local-field corrections (LFCs). We have used the Penn model for our study. Our calculations demonstrate that LFCs depend on the parameters characterizing a semiconductor. Our calculations are in agreement with the calculations based on more detailed band structures.     

Collective excitations in semiconductor superlattices

Collective excitations in semiconductor superlattices are studied beyond tbe random-phase approximation (RPA). The Singwi, Tosi, Land and Sjölander (STLS) theory, which accounts for exchange and short-range correlations effects through an effective potential depending on the structurc factor, is generalized to the layered electron system described by the model of Visscher and Falicov. The exact numerical solution of the STLS self-consistent equations provides information about intraplane and interplane correlations. The plasmon dispersion curves are evaluated for some typical values of the coupling constant r_s of the electron system and the distance between the planes for GaAs/AlGaAs semiconductor superlattices. For comparison, the RPA and the Hubbard approximation are also considered.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Theory of elementary excitations and the metal-insulator transition of semiconductor surfaces

The microscopic theory of density and spin response of surface systems and its application to elementary excitations is discussed. Particular emphasis is placed on semiconductor surfaces, for which the often-used jellium approximation is not valid. The discussion is based on a solution of Maxwell's equations or, formally, of the Bethe-Salpeter equation for the two-particle Green's function of the surface system. This solution is achieved in a local wave function representation and takes density fluctuations on a microscopic scale (surface profile and local-field effects parallel to the surface) into account. Many-body effects of random-phase (RPA) and electron-hole type are included. The resulting spin and density response functions present a practical scheme for a microscopic calculation of surface elementary excitations in conducting as well as non-conducting solids. As examples, the conditions for the appearance of an electronic (charge- and spin-density) instability at the surface and the coupling of the resulting charge-density wave to the lattice are studied in detail.Results of quantitative calculations of the charge- and spin-density-response function of the Si(111) surface establish the importance of including both excitonic (electron-hole) and (RPA) local-field many-body interactions. In particular, they lead to an instability of the ideal paramagnetic surface with respect to spin-density waves (SDW) with wavelength corresponding to the observed (2 × 1) and (7 × 7) superstructures. Another example deals with an a-priori calculation of the phonons and the electron-phonon interaction of the same surface system. Various results of the theory such as phonon softening due to the coupling of the charge-density fluctuations to the lattice are summarized and general aspects of the importance of many-body effects for the a-priori determination of surface structures via elementary excitations are discussed.     

Equation of state of metallic helium

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.     

Many-electron effects in atomic processes

The major role of the collectivization of electrons in atoms and quasiatomic formations is demonstrated. The random-phase approximation with exchange, which permits allowance for these effects, is discussed in detail. The need to extend the scope of this approximation when some processes are considered, which is achieved by combining it with perturbation theory, is noted. The role of the collective effects is illustrated by the results of recently performed calculations of the photoionization cross sections of atomic iodine and its positive and negative ions, the single-electron ionization of Xe⁺, resonance-enhanced photon emission in collisions of electrons with atoms and quasiatomic formations, the nondipole corrections to the angular distribution of photoelectrons, and the probabilities of two-electron transitions in which all the energy is released in the form of a single photon. Zh. Tekh. Fiz. 69, 31–35 (September 1999)     

Anisotropy and interplane interactions in the dielectric response of graphite

We determined the anisotropic dielectric response of graphite by means of time-dependent density-functional theory and high-resolution valence electron energy-loss spectroscopy. The calculated loss function was in very good agreement with the experiment for a wide range of momentum-transfer orientations with respect to the graphitic basal planes, provided that local-field effects were included in the response. The calculations also showed strong effects of the interlayer Coulomb interaction on the total pi+sigma plasmon. This finding must be taken into account for the explanation of recent loss spectra of carbon nanotube materials.