Showing papers on "Random phase approximation published in 2001"

Complexation between oppositely charged polyelectrolytes: beyond the Random Phase Approximation

Abstract: We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of Coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectrolyte mixture that includes both complexation and incompatibility.

Binary Gaussian core model: fluid-fluid phase separation and interfacial properties.

Abstract: Using a mean-field equation of state we calculate the density-concentration phase diagrams for a binary mixture of repulsive Gaussian core particles over a range of size ratios. A simple mean-field density functional (DFT) approach, equivalent to the random phase approximation, is used to calculate the surface tension and density profiles of the interface between the demixed fluid phases of the binary mixture. For certain coexisting states oscillations are found in the density profiles on both sides of the interface, i.e., approaching both bulk phases. The form of the oscillations is determined by the asymptotic decay of the bulk total pairwise correlations, and the onset of oscillations in the interfacial density profiles depends on the location of the crossover line (Fisher-Widom line) in the bulk phase diagram where the asymptotic decay changes from monotonic to damped oscillatory. For certain particle size ratios we find another crossover line that separates a region of the phase diagram where the longest-range decay of the pairwise correlations is damped oscillatory from a region where the longest-range decay is damped oscillatory but with a different wavelength. We argue that many of the predictions of the simple DFT approach should remain valid in more refined treatments.

Comparison of the electron effective mass of the n-type ZnO in the wurtzite structure measured by cyclotron resonance and calculated from first principle theory

Abstract: The electron effective mass of n-type ZnO obtained recently by the cyclotron resonance is compared with the quasiparticle mass predicted by the GW approximation which takes into account the dynamical screening effects within the random phase approximation. The bare electron effective mass has been determined to be about 0.23 m 0 ( B ∥ c -axis) by cyclotron resonance experiments excluding electron–phonon coupling. On the other hand, the calculated quasiparticle mass has been obtained as about 0.24 m 0 . We have found that the dynamical screening effect enhances the mass obtained by the conventional local density approximation by about 17% and the predicted quasiparticle mass is in good agreement with the experiment.

Complexation between oppositely charged polyelectrolytes: beyond the Random Phase Approximation

Abstract: We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectrolyte mixture that includes both complexation and incompatibility.

Unblocking of the Gamow-Teller Strength in Stellar Electron Capture on Neutron-Rich Germanium Isotopes

Abstract: We propose a new model to calculate stellar electron capture rates for neutron-rich nuclei. These nuclei are encountered in the core collapse of a massive star. Using the shell model Monte Carlo approach, we first calculate the finite temperature occupation numbers in the parent nucleus. We then use these occupation numbers as a starting point for calculations using the random phase approximation (RPA). Using the RPA approach, we calculate electron capture rates including both allowed and forbidden transitions. Such a hybrid model is particularly useful for nuclei with proton numbers $Zl40$ and neutron numbers $Ng40,$ where allowed Gamow-Teller transitions are only possible due to configuration mixing by the residual interaction and by thermal unblocking of $\mathrm{pf}$-shell single-particle states. Using the even germanium isotopes ${}^{68\ensuremath{-}76}\mathrm{Ge}$ as examples, we demonstrate that the configuration mixing is strong enough to unblock the Gamow-Teller transitions at all temperatures relevant to core-collapse supernovae.

Excitonic effects on the silicon plasmon resonance.

Abstract: We present an ab initio calculation of the electron energy loss spectrum of silicon including local-field, self-energy, and excitonic effects. When self-energy corrections are added to the standard random phase approximation (RPA) the line shape of the plasmon resonance worsens. The electron-hole interaction cancels this correction and improves the result both compared to the RPA and to the self-energy one, yielding very good agreement between theory and experiment provided that the mixing of interband transitions of both positive and negative frequencies is included.

Time-dependent Gutzwiller approximation for the Hubbard model.

Abstract: 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.

Phase diagram of a symmetric binary fluid in a porous matrix.

Abstract: The phase behavior of a binary symmetric fluid in thermal equilibrium with a porous matrix has been studied with the optimized random phase approximation and grand canonical Monte Carlo simulations. Depending on the matrix properties and the matrix-fluid and fluid-fluid interactions we find three types of phase diagram characterized by a tricritical point, a tricritical point with a triple point, or a critical end point. Small changes in the properties of the matrix or in the interactions are demonstrated to lead to drastic modifications of the phase diagram of the fluid, in qualitative agreement with observations in experimental studies. We show, in particular, that the change between the different types of phase diagram is triggered not only by the fluid-fluid interactions (internal parameters) but also by the properties of the matrix and of the matrix-fluid potentials (external parameters).

Pygmy dipole resonances in the relativistic random phase approximation

Abstract: The isovector dipole response in ${}^{208}\mathrm{Pb}$ is described in the framework of a fully self-consistent relativistic random phase approximation. The NL3 parameter set for the effective mean-field Lagrangian with nonlinear meson self-interaction terms, used in the present calculations, reproduces ground state properties as well as the excitation energies of giant resonances in nuclei. In addition to the isovector dipole resonance in ${}^{208}\mathrm{Pb},$ the present analysis predicts the occurrence of low-lying $E1$ peaks in the energy region between 7 and 11 MeV. In particular, a collective state has been identified whose dynamics correspond to that of a dipole pygmy resonance: the vibration of the excess neutrons against the inert core composed of an equal number of protons and neutrons.

Beta decay in odd A and even even proton rich Kr isotopes

Abstract: $\ensuremath{\beta}$-decay properties of proton-rich odd-$A$ and even-even krypton isotopes are studied in the framework of a deformed self-consistent Hartree-Fock calculation with density-dependent Skyrme forces, including pairing correlations between like nucleons in BCS approximation. Residual spin-isospin interactions are consistently included in the particle-hole and particle-particle channels and treated in the quasiparticle random phase approximation. The similarities and differences in the treatment of even-even and odd-$A$ nuclei are stressed. Comparison to available experimental information is shown for Gamow-Teller strength distributions, summed strengths, and half-lives. The dependence of these observables on deformation is particularly emphasized in a search for signatures of the shape of the parent nucleus.

Dynamic structure factor of a superfluid Fermi gas

Abstract: We describe the excitation spectrum of a two-component neutral Fermi gas with attractive interactions in the superfluid phase at finite temperature by deriving a suitable Random-Phase approximation in the collisionless regime with the technique of functional derivatives. The obtained spectrum for the homogeneous gas at small wavevectors contains the Bogoliubov-Anderson phonon and is essentially different from the spectrum predicted by the static Bogoliubov theory, which instead shows an unphysically large response. We adapt the results for the homogeneous system to obtain the dynamic structure factor of a harmonically confined superfluid and we identify in the spectrum a unique feature of the superfluid phase.

Pairing correlations in high-K bands

Abstract: The transition of a nucleus from the superfluid to normal state at high angular momentum is an interesting problem that is studied by means of modern g-detector arrays. Contrary to the analogous transition in solids, in the finite nuclear system there is no sharp phase change but an extended transition region within which pairing effects disappear. The most rapid attenuation of pair correlations is caused by quasiparticle excitations, i.e., breaking of pairs. This case is realized in deformed nuclei when a large fraction of the angular momentum is generated along the symmetry axis of the nucleus. These states may appear as high-K isomers near the yrast line. Hence, the experimental data on high-K isomers and the rotational structures built on those states contain valuable information about the pair correlations and how they are influenced by the rotation. The theoretical analysis of high-K band structures presented in this paper is based on the tilted axis cranking ~TAC! model @1#, which is a mean field approach for describing both the rotation and pair correlations in the framework of the Hartree-Fock-Bogoliubov ~HFB! theory. In fact, the TAC model has already been applied to the high-K multiquasiparticle bands in 178,179 W @2#. There, only the effects of static pair field have been considered. The central aim of our present investigation is studying the role of dynamical pair correlations. For this purpose we apply the random phase approximation ~RPA! to the pairing interaction, which includes the fluctuations of the pair field. The fluctuations are particularly important when the static pair field has collapsed. Their relevance is suggested by the results of Refs. @2,3# for 178,179 W as well as in the earlier investigations of the pair correlations of other high-K band head states @4#. The combination of the HFB theory with RPA does not provide a reliable description in the region where the pairing gap disappears @5#. There the particle number projection method ~PNP! works better @3,6#. Therefore, both the RPA and PNP methods are considered and compared with each other.

A classical mechanics technique for quantum linear response

Abstract: It is shown that the lowest random phase approximation (RPA) excitation energies of a quantum many-fermion system can be obtained by minimizing an effective classical energy functional. The idea is based on an analogy between the RPA and classical Hamiltonian equations of motion. Generalized Lanczos recursion allows the minimum to be found very efficiently. The technique is used to find the electronic excitation spectrum of the C60 molecule.

Distribution of the Gamow-Teller strength in (^90)Nb and (^208)Bi

Abstract: The (He-3,t) charge-exchange reaction has been studied at E(He-3)=450 MeV and angles near 0 degrees on targets of Zr-90 and Pb-208. Fragmentation of the Gamow-Teller (GT) strength into separate components of the particle-hole type has been observed. The distribution of the GT strength in Nb-90 and in Bi-208 has been calculated within the continuum quasiparticle random phase approximation and continuum-random-phase approximation approaches, respectively. These components, especially in Pb-208, could be related with the direct, core polarization, and back-spin-flip Gamow-Teller strength.

Spin and Charge Excitations in Incommensurate Spin Density Waves

Abstract: Dynamical longitudinal spin susceptibility χ z z ( q ,ω) and charge density susceptibility χ n n ( q ,ω) are evaluated within random phase approximation for incommensurate spin density waves, or stripes, in two dimensional Hubbard model. Taking into account all possible higher harmonics of the fundamental component of the order parameter,we calculate these quantities for the full ranges of the momentum and energy, and analyze collective modes related to the motion of the stripe line. The anisotropy of the dispersion cone comes from the moving pattern of the stripes, i.e., the compression mode or the meandering mode. In the metallic stripe, there are also nesting excitations of the parallel sheet of the Fermi surfaces. We also discuss the excitation of the silent position in the insulating stripe.

Dynamical properties and plasmon dispersion of a weakly degenerate correlated one-component plasma.

Abstract: Classical Molecular Dynamics simulations for a one-component plasma are presented. Quantum effects are included in the form of the Kelbg potential. Results for the dynamical structure factor are compared with the Vlasov and random phase approximation theories. The influence of the coupling parameter Gamma, degeneracy parameter rho Lambda(3), and the form of the pair interaction on the optical plasmon dispersion is investigated. An improved analytical approximation for the dispersion of Langmuir waves is presented.

Improved treatment of ground-state correlations: Modified random phase approximation

Abstract: A method is proposed to improve the treatment of the ground-state correlations in a finite Fermi system compared with the standard random phase approximation (RPA) or earlier suggested renormalized RPA. The correlations lead to nonzero quasiparticle occupancies in the ground state. The method employs modified quasiparticles obtained by a canonical transformation of usual quasiparticles explicitly involving the quasiparticle occupation numbers. A set of equations is derived, which allows one to determine these occupation numbers along with the RPA modes. The formalism is illustrated with the Lipkin-Meshkov-Glick model, and a model for superconducting pairing at a finite temperature. With the new approach, the ground-state correlations are significantly reduced, the energy of the first excited state becomes closer to the exact solution around the region where the RPA collapses, and the superconducting gap monotonously decreases instead of the sharp phase transition. We discuss the effective equivalence of the interaction effects and variation of temperature for the ground-state correlations.

Static local-field corrected dielectric and thermodynamic functions

Abstract: We calculate thermodynamic functions using a finite temperature Vashishta-Singwi type formula for the static local-field correction G(q). Comparisons with RPA and closed-form parametrizations are given.

Effective electron and hole masses in intrinsic and heavily n-type doped GaN and AlN

Abstract: We have investigated the electronic structure near the band edges in intrinsic and heavily n-type doped GaN and AlN. Both the wurtzite and the zinc-blende polytypes have been considered. The electronic structures of the intrinsic materials were obtained from a full-potential linearized augmented plane wave calculation. We show the importance of performing a fully relativistic calculation. For instance, the hole mass in cubic AlN is a very large and negative quantity if spin-orbit coupling is excluded, whereas the fully relativistic calculation gives a relatively small and positive value. The electron-phonon coupling was taken into account according to the Frohlich Hamiltonian for large polarons, resulting in effective polaron masses. The effects on the effective electron masses due to doping were investigated by using a Green's function formalism within the random phase approximation and with a local-field correction according to Hubbard.

On the phase separation of a binary fluid in a porous medium

Abstract: Our investigations of the phase diagram of a symmetric binary fluid in equilibrium with a porous matrix show that moderate changes in the properties of the matrix or in the matrix-fluid interaction lead to drastic modifications of the phase diagram of the fluid. Thus our results confirm on a qualitative basis recent experimental data. The phase diagrams that we have obtained show a wide variation and can be classified in terms of archetypes of systems of two order parameters. These different types can be characterised in terms of the loci where the λ-line of the demixing transition intersects the first-order liquid-vapour coexistence curve. Results are based on the optimised random phase approximation and on grand-canonical Monte Carlo simulations.

Pion condensation based on a relativistic description of particle-hole and delta-hole excitations

Abstract: The critical density of neutral pion condensation is reinvestigated based on the relativistic framework and compared with nonrelativistic results. The particle-hole and delta-hole polarizations of the pion selfenergy are calculated in the relativistic way by using a new set of Landau–Migdal parameters derived from recent experimental data. It is concluded that the use of relativistic particle-hole and delta-hole excitations for the pion selfenergy increases the critical density, but still leads to condensation for densities from two to three times the normal nuclear matter density within the random phase approximation.

Inhomogeneous random-phase approximation and many-electron trial wave functions

Abstract: The long-range electronic correlations in a uniform electron gas may be deduced from the random-phase approximation (RPA) of Bohm and Pines [Phys. Rev. 92, 609 (1953)]. Here we generalize the RPA to nonuniform systems and use it to derive many-electron Slater-Jastrow trial wave functions for quantum Monte Carlo simulations. The RPA theory fixes the long-range behavior of the inhomogeneous two-body terms in the Jastrow factor and provides an accurate analytic expression for the one-body terms. It also explains the success of Slater-Jastrow trial functions containing determinants of Hartree-Fock or density-functional orbitals, even though these theories do not include Jastrow factors. After adjusting the RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo simulations. In the small inhomogeneous electron gas system we consider, the analytic RPA-based Jastrow factor slightly outperforms the standard numerically optimized form. The inhomogeneous RPA theory therefore enables us to reduce or even avoid the costly numerical optimization process.

Many-electron correlation effects in the generalized oscillator strengths of noble-gas atoms

Abstract: Calculated generalized oscillator strengths for monopole, dipole, and quadrupole discrete and continuous spectrum excitations in Ne, Ar, Kr, and Xe are presented. The results cover the broad range of transferred energy $\ensuremath{\omega}, 0l~\ensuremath{\omega}l120 \mathrm{Ry}$ and momentum $q, 0l~ql2 \mathrm{a}.\mathrm{u}.$ The calculations were performed in the one-particle Hartree-Fock approximation and with account of many-electron correlations. The latter effects are included via the random phase approximation with exchange, proving to be important in all dipole, monopole, and quadrupole channels as well as in all the domains of the transferred energies and momenta considered. Particularly important are the many-electron correlations at high q values, where new additional purely correlational maxima and minima appear. These results, particularly the maxima and minima are expected to stimulate experimental activity in this domain of atomic physics.