Showing papers on "Random phase approximation published in 1997"

Neutron-proton correlations in an exactly solvable model

Abstract: We examine isovector and isoscalar neutron-proton correlations in an exactly solvable model based on the algebra SO(8). We look particularly closely at Gamow-Teller strength and double β decay, both to isolate the effects of the two kinds of pairing and to test two approximation schemes: the renormalized neutron-proton quasiparticle random phase approximation (QRPA) and generalized BCS theory. When isoscalar pairing correlations become strong enough a phase transition occurs and the dependence of the Gamow-Teller β+ strength on isospin changes in a dramatic and unfamiliar way, actually increasing as neutrons are added to an N=Z core. Renormalization eliminates the well-known instabilities that plague the QRPA as the phase transition is approached, but only by unnaturally suppressing the isoscalar correlations. Generalized BCS theory, on the other hand, reproduces the Gamow-Teller strength more accurately in the isoscalar phase than in the usual isovector phase, even though its predictions for energies are equally good everywhere. It also mixes T=0 and T=1 pairing, but only on the isoscalar side of the phase transition.

Compressibility of nuclear matter and breathing mode of finite nuclei in relativistic random phase approximation

Abstract: Isoscalar monopole modes in finite nuclei are studied in the framework of relativistic models currently used in ground state calculations. Response functions in the random phase approximation are calculated with nonlinear models for the first time. It is found that some effective Lagrangians having a bulk compression modulus in the range 280{endash}350 MeV can predict correctly breathing mode energies in medium and heavy nuclei. It is pointed out that the parametrization NL1 (K{sub {infinity}}=211MeV) leads to an anomalous behavior of the monopole response. {copyright} {ital 1997} {ital The American Physical Society}

Ab initio calculations of the polarizability and the hyperpolarizability of C60

Abstract: The linear polarizability, α, and the second hyperpolarizability, γ, of C60 in gas phase have been computed by ab initio cubic response theory in the random phase approximation and with an efficien ...

Optical functions of semiconductors beyond density-functional theory and random-phase approximation

Abstract: Friedrich-Schiller-Universita ¨t, Institut fur Festko¨rpertheorie and Theoretische Optik, Max-Wien-Platz 1, 07743 Jena, Germany~Received 17 May 1996; revised manuscript received 23 August 1996!The linear optical response of semiconductors has been studied beyond the density-functional theory withabinitio pseudopotentials and the random-phase approximation. Effects of the macroscopic local fields and themicroscopic exchange-correlation interaction are included in the description of the optical spectra. Quasipar-ticle corrections to the single-particle energies have been added in the polarization function. Numerical calcu-lations are performed for the group-IV materials Si, SiC, and diamond as model substances. In the static limitand in the low-frequency region, corrections due to the local fields reduce the dielectric function, whereasinclusion of the exchange-correlation interaction enhance the oscillator strengths. In the high-energy regionthese effect have a more complex character, and the signs of the relevant corrections change in dependence onthe photon energy. The effects considered strongly modify the plasmon resonance in the energy-loss function.The results obtained are discussed in comparison with theoretical and experimental data available.@S0163-1829~97!05907-9#I. INTRODUCTION

Vibrations and soliton dynamics of positively charged polyacetylene chains

Abstract: Ab initio molecular dynamics simulation is performed on a small polyacetylene chain with a positive soliton defect. The dynamics is initialized by an external electric field. The collective motion of the carbon and hydrogen atoms are compared to some low frequency vibrational modes of positively charged polyacetylene chains of varying lengths having the characteristics of the soliton displacement. The soliton effective mass estimated using a variety of schemes is found to be about 10 electron masses. The static linear polarizability of singly charged polyacetylene chains of varying lengths is computed and compared with that of undoped chains. The electronic contributions to the polarizability are computed at the level of the coupled Hartree–Fock or the random phase approximation, and the vibrational contributions are estimated by invoking the double harmonic oscillator approximation. The soliton defect causes some enhancement of the electronic term, which covers 10–15 carbon–carbon double bonds, and it ge...

Theory of Spin Fluctuation-Induced Superconductivity Based on a d- p Model

Abstract: Spin fluctuation-induced superconductivity is studied on a two-dimensional d - p model by using a strong coupling theory, and is applied to interpret high- T c cuprates. A self-consistent renormalization scheme is employed within the so-called fluctuation exchange (FLEX) approximation or the renormalized random phase approximation (RRPA). Using the band parameter values which approximately reproduce the observed Fermi surface and the d - and p -hole numbers estimated from NMR experiments, we get reasonable values for T c in an optimum and overdoped concentration range. The dynamical susceptibility, the nuclear spin-lattice relaxation rate and the one electron spectral density are well compared with the existing experimental results.

Calculation, with the inclusion of vibrational corrections, of the dc-electric-field-induced second-harmonic-generation hyperpolarizability of methane

Abstract: Calculations of γ(−2ω;ω,ω,0) for CH4 are reported for a number of frequencies (ω) This mean frequency-dependent second hyperpolarizability governs the nonlinear optical process: dc-electric-field-induced second-harmonic generation Two levels of calculation have been carried out: one is based on the random phase approximation and the other on the multiconfigurational random phase approximation using a complete active space self-consistent-field wavefunction This is the first calculation of γ(−2ω;ω,ω,0) that has been made for CH4 using electron-correlated wavefunctions Included in the calculations are corrections for vibrational effects of which the zero-point vibrational-averaging correction is both dominant and significant (13–18% of the electronic values) Comparison with experiment shows that not all the electron correlation is captured by our treatment The dispersion properties are also discussed

Single- and double-beta decay Fermi transitions in an exactly solvable model

Abstract: An exactly solvable model suitable for the description of single- and double-beta decay processes of the Fermi type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single-j shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the Hamiltonian in the quasiparticle basis ~qp! and with the results of both the standard quasiparticle random phase approximation ~QRPA! and the renormalized one ~RQRPA!. The role of the scattering term of the quasiparticle Hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented. @S0556-2813~97!03507-3# PACS number~s!: 21.60.Fw, 21.60.Jz, 23.40.Hc

Linear density response in the random-phase approximation for confined Bose vapours at finite temperature

Abstract: A linear response framework is set up for the evaluation of collective excitations in a confined vapour of interacting Bose atoms at finite temperature. Focusing on the currently relevant case of contact interactions between the atoms, the theory is developed within a random-phase approximation with exchange. This approach is naturally introduced in a two-fluid description by expressing the density response of both the condensate and the non-condensate in terms of the response of a Hartree - Fock reference gas to the self-consistent Hartree - Fock potentials. Such an approximate account of correlations (i) preserves an interplay between the condensate and the non-condensate through off-diagonal components of the response, which instead vanish in the Hartree - Fock - Bogoliubov approximation; and (ii) yields a common resonant structure for the four partial response functions. The theory reduces to the temperature-dependent Hartree - Fock - Bogoliubov - Popov approximation for the fluctuations of the condensate when its coupling with the density fluctuations of the non-condensate is neglected. Analytic results are presented which are amenable to numerical calculations and to inclusion of damping rates.

Spin waves in quasi-periodic magnetic superlattices

Abstract: A microscopic theory is employed to investigate the spin-wave spectra in structures that exhibit what has been called deterministic disorder. A class of models that has attracted particular attention in this context are the quasi-periodic magnetic multilayers, which are artificial crystals fabricated from the juxtaposition of two (or more) materials obeying a quasi-periodic arrangement of substitutional character forming a Cantor set. These quasi-periodicity can be of the type so-called substitutional sequences, and can be characterized by the nture of their Fourier spectrum, which may be dense pure point (Fibonacci sequences) or singular continuous (Thue-Morse and double-period sequences). The calculations are carried out for the exchange dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation (RPA). We consider that the magnetic material has a ferromagnetic order, and a transfer matrix treatment is applied to simplify the algebra, which can be otherwise quite involved. Comparisons with the spectra found in periodic and complete random structures are also done, with more interesting features to understand the physical properties of these structures.

Application of free energy expansions to mesoscopic dynamics of copolymer melts using a Gaussian chain molecular model

Abstract: The present paper deals with some mathematical aspects of generalized time-dependent Ginzburg–Landau theories for the numerical simulation of mesoscale phase separation kinetics of copolymer melts. We shortly discuss the underlying theory and introduce an expansion of the external potential, to be used in the dynamics algorithm, which is similar to free-energy expansions. This expansion is valid for both compressible and incompressible multicomponent copolymer melts using a Gaussian chain model. The expansion is similar to the well-known random phase approximation (RPA) but differs in some important aspects. Also, the application of RPA like free energy expansions to dynamics is new. Our derivation leads to simple expressions for the vertex coefficients, which enables us to numerically calculate their full wave vector dependence, without assuming an ordered morphology. We find that our fourth-order vertex is negative for some wave vectors which has important consequences for the simulation of mesoscopic d...

Many-body treatment of electron inelastic scattering on metal clusters

Abstract: In this paper we suggest the many-body treatment for the inelastic scattering of fast electrons on metal clusters. The accurate many-body theory for this process is necessary because electrons in the cluster experience collective excitations during the collision. We perform our calculation in the random phase approximation with exchange using the wavefunctions of the Hartree-Fock jellium model and also in the plasmon resonance approximation. The latter approach is appropriate to treat collective excitations in clusters. We analyse the differential and total inelastic scattering cross sections and elucidate the relative importance of collective electron excitations and single-electron transitions in the formation of the inelastic scattering cross section on metal clusters. We perform this calculation for the magic sodium clusters Na20 ,N a 40 ,N a 58 and Na92. Theoretical results are also compared with the experimental data available for electron collisions with the Na8 ,N a 20 and Na40 clusters. We report some discrepancy between theoretical and experimental results.

The effect of spin fluctuations on thermal properties in strongly correlated fermion systems

Abstract: The effect of spin fluctuations on the thermal properties of strongly correlated itinerant fermion systems is discussed based on the self-consistent renormalized (SCR) spin fluctuation model. Specific heat and magnetic susceptibility in the normal phase of liquid-3He and heavy electron compounds at finite temperatures are well described by the unified SCR picture including the mode-mode coupling of spin fluctuations beyond the random phase approximation (RPA).

Charge Fluctuations in One-Dimensional Quarter-Filled Spin Density Wave States with Dimerization

Abstract: The charge fluctuation of the SDW (spin density wave) state has been examined for a system which consists of one-dimensional quarter-filled band with repulsive interactions of both on-site and nearest-neighbor site ( U and V ) and the dimerization energy ( t d ). The commensurability energy in the ground state is studied within the mean-field theory and the collective mode representing the charge fluctuation is calculated in terms of the random phase approximation. It is found that the gap of the excitation spectrum, ω g , induced by the commensurability energy vanishes at a critical value of V corresponding to the onset of the coexistence of 2 k F -SDW and 4 k F -CDW (charge density wave) where k F denotes the Fermi wave number. The spectral weight indicates the enhancement of the charge fluctuation in the presence of the energy V which competes with energies t d and U .

Quasiparticle random-phase approximation and {beta}-decay physics: Higher-order approximations in a boson formalism

Abstract: The quasiparticle random-phase approximation (QRPA) is reviewed and higher-order approximations are discussed with reference to {beta}-decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the first-order boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi {beta} operators: exact and approximate transition amplitudes are discussed together with the Ikeda sum rule. The range of applicabilty of the QRPA formalism is analyzed. {copyright} {ital 1997} {ital The American Physical Society}

Double beta decay of 92 Mo: Comparison of the shell model and the quasiparticle random-phase approximation

Abstract: The two-neutrino double beta decay of 92Mo to the ground state and excited states of 92Zr is analyzed using the shell-model approach and the quasiparticle random-phase approximation (QRPA). Two different valence spaces and three different Gamow-Teller operators are used in the shell-model analysis. The resulting double beta matrix elements and half-lives are compared with the corresponding QRPA results.

The hyperpolarizability of trans-butadiene: A critical test case for quantum chemical models

Abstract: The conspicuous fact that the low-order method - the random phase approximation - has served as the best approach to obtain accurate one-photon spectra of the trans-polyenes is scrutinized by perfo ...

Photoabsorption in hot, dense plasmas : the average atom, the spherical cell model, and the random phase approximation

Abstract: This work is a continuation of our earlier work on the finite temperature random phase approximation (FTRPA) for inhomogeneous, finite electron systems. In the earlier work we obtained the fundamental FTRPA eigenvalue equation for the spectral amplitudes of the linear response function via the use of the Matsubara Green's function technique arrived at earlier by des Cloizeaux via the density matrix technique. In this work we show that the normalization requirement for the FTRPA spectral amplitudes obtainable via the Matsubara Green's function technique is the same as the one obtained by des Cloizeaux. Thus, the two techniques in every respect give identical equations and formulas for the FTRPA. We also derive the fundamental equations for the actual linear responses of finite temperature inhomogeneous finite electron systems to specific external perturbations in the FTRPA. This side steps the problem of normalization by the use of an inhomogeneous integro–differential equation.

Restoration of the Ikeda sum rule in self-consistent quasiparticle random-phase approximation

Abstract: The so-called self-consistent quasiparticle random phase approximation, accounting for a better treatment of ground-state correlations, is applied to a schematic Hamiltonian, describing the Fermi beta decay process. The self-consistent procedure coupling the BCS minimum with the quantum fluctuations yields an exact fulfillment of the Ikeda sum rule. The role of the ground-state correlations is analyzed in the case of the double beta decay process. {copyright} {ital 1997} {ital The American Physical Society}

Multipole oscillations in sodium clusters: Separable ansatz in the random-phase-approximation description

Abstract: The modified random-phase-approximation (RPA) method with the self-consistent {ital separable} residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in sodium clusters. The method allows one to study the coupling of different kinds of collective motion. As a particular case, the coupling of surface and volume modes is considered. The SRPA is applied to neutral and singly charged spherical sodium clusters in a wide size region (N{sub e}=8,20,40,58,92,138,196,440,952) and good agreement with experimental data is achieved. This testifies to the applicability of the separable ansatz, which has the essential advantage of avoiding diagonalization of the RPA matrices and thus drastically simplifies the RPA calculations. The latter could be quite urgent for very large and deformed clusters where an extended configuration space and, consequently, high-rank RPA matrices are used. The predictions for E2 and E3 collective excitations are presented. The results obtained with the self-consistent Kohn-Sham and phenomenological Woods-Saxon single-particle schemes are exhibited and different parameters for the Woods-Saxon potential are proposed. {copyright} {ital 1997} {ital The American Physical Society}

1 S 0 pairing correlations in relativistic nuclear matter and the two-nucleon virtual state

Abstract: We use the Gorkov formulation of the Dirac-Hartree-Fock-Bogoliubov approximation to nuclear pairing to study the {sup 1}S{sub 0} nucleon-nucleon correlations in nuclear matter. We find the short-range correlations of the {sup 1}S{sub 0} pairing fields to be almost identical to those of the two-nucleon virtual state. We obtain mutually consistent results for the pairing fields, using several different sets of effective interaction parameters, when we demand that each of these sets places the virtual-state pole at its physical location. {copyright} {ital 1997} {ital The American Physical Society}

Pairing interaction and superconducting transition temperature in the d-p model

Abstract: Effective pairing interaction and superconducting transition temperature T c are investigated on the basis of the simplest d - p model by using the auxiliary particle method together with the 1/ N -expansion theory. The pairing interaction mediated by both charge and spin fluctuations is calculated by considering higher order terms in the 1/ N -expansion within the random phase approximation(RPA) to find that it is attractive only for the d x 2 - y 2 channel. T c is calculated by solving a linearized Eliashberg equation to confirm that it can be finite only for d x 2 - y 2 pairing. Doping dependence of T c seems to be consistent with experiments with a reasonable choice of the parameter for the charge-transfer energy. The highest T c is obtained at a hole-doping rate δ=0.15 and estimated to be ≃100 K. It is also shown that the spin fluctuation plays a dominant role in the system to realize the high- T c superconductivity rather than the charge fluctuation does.

Two neutrino double beta decay: Critical analysis

Abstract: We have performed a critical analysis of different approximation schemes for the calculation of two-neutrino double beta decay (TNDBD) matrix elements. We have shown that within the single-particle approximation of nuclear Hamiltonian the TNDBD matrix element is equal to zero. The (renormalized) quasiboson approximation scheme imply for TNDBD transition operator to be a constant, if one requires the equivalence of initial and final (renormalized) QRPA Hamiltonians. It means that TNDBD is a higher order process in the boson expansion of the nuclear Hamiltonian. We have found that the mismatching of both Hamiltonians is getting worse with increasing strength of particle- particle interaction especially in the case of QRPA Hamiltonians. It is supposed to be one of the reasons of the extreme sensitivity of studied matrix element to the residual interaction appearing in explicit calculations involving the intermediate nucleus. Further, the Operator Expansion Method (OEM) has been reconsidered and new transition operators have been rederived in a consistent way. The validity of the OEM approximation has been discussed in respect to the other approximation schemes. The OEM combined with QRPA or RQRPA ground state wave functions reflects sensitively the instabilities incorporated in the considered ground states. Therefore, the predicting power of the OEM should be studied with help of other ground state wave functions. e.g. shell model ones.

Consistent calculation of the stopping power for slow ions in two-dimensional electron gases

Abstract: Within the framework of quantum scattering theory, we present a consistent calculation of the stopping power for slow protons and antiprotons moving in two-dimensional electron gases. The Friedel sum rule is used to determine the screening constant in the scattering potential. For the stopping power our results are compared with that of the random-phase approximation dielectric theory and that predicted by the linear Thomas-Fermi potential. {copyright} {ital 1997} {ital The American Physical Society}