Showing papers on "Random phase approximation published in 1975"

Effect of Spin Fluctuations on the Specific Heat of Weakly and Nearly Ferromagnetic Metals

Abstract: The specific heat due to the effect of spin fluctuations in itinerant ferromagnets is calculated by using the renormalized spin fluctuation theory of Moriya and Kawabata. The calculation continuously covers all the interesting temperature ranges, both below and above the Curie temperature. The specific heat is shown to be generally enhanced in weakly and nearly ferromagnetic metals. This is particularly so at low temperatures and the effect decreases as temperature goes up far more rapidly than the previous results based on the random phase approximation which generally over-estimates the spin fluctuation effect. An anomaly around the Curie temperature turns out to be rather small.

Dipole properties of atoms and molecules in the random phase approximation

Abstract: A random phase approximation (RPA) calculation and a direct sum over states is used to calculate second−order optical properties and van der Waals coefficients. A basis set expansion technique is used and no continuumlike functions are included in the basis. However, unlike other methods we do not force the basis functions to satisfy any sum−rule constraints but rather the formalism (RPA) is such that the Thomas−Reiche−Kuhn sum rule is satisfied exactly. Central attention is paid to the dynamic polarizability from which most of the other properties are derived. Application is made to helium and molecular hydrogen. In addition to the polarizability and van der Waals coefficients, results are given for the molecular anisotropy of H2, Rayleigh scattering cross sections, and Verdet constants as a function of frequency. Agreement with experiment and other theories is good. Other energy weighted sum rules are calculated and compare very well with previous estimates. The practicality of our method suggests its applications to larger molecular systems and other properties.

Dielectric response of the charged Bose gas in the random-phase approximation

Abstract: A closed form for the dielectric function of a charged Bose gas is found in the random-phase approximation. This dielectric constant is used to explore the quasiparticle energy spectrum (i.e., the allowed modes of oscillation of the gas), the damping of these quasiparticles, and the long-ranged form of the electrostatic potential around a test charge in the gas. We do this around the three temperature regions of interest; namely, $T=0$, $T=\ensuremath{\infty}$, and $T={T}_{c}$, where ${T}_{c}$ is the transition temperature of the gas.

Local environment and magnetic properties in transitional binary alloys. I. (theory)

Abstract: A theory is presented for the study of the local environment effects on the magnetic properties in transitional binary alloys; the local environment effects are taken into account for the calculation of the one electron properties by an extension of the cpa and the electron-electron interactions are taken into account in the random phase approximation.

Theory of paramagnetic singlet-doublet excitations in double-hexagonal close-packed praseodymium

Abstract: The magnetic excitation spectrum of the singlet-doublet magnet double-hexagonal close-packed praseodymium, which has been measured by means of inelastic neutron scattering, is analyzed using a diagrammatic high-density expansion technique. The lowest-order random-phase-approximation diagrams give a detailed description of the wave-vector and temperature dependence of the four modes in terms of a Hamiltonian including isotropic Heisenberg interatomic exchange interactions and anisotropic, dipolarlike exchange interactions. In general, the modes are linearly or elliptically polarized. The leading contributions to the line shapes of the excitations are obtained by extending the $\frac{1}{Z}$ expansion of the generalized susceptibility propagators one order beyond the random-phase approximation. This damping corresponds to spin-wave scattering on single-site fluctuations. The propagators are calculated self-consistently by including internally renormalized Green's functions. The theoretical spectral functions are in detailed agreement with experiment.

Photoionization cross sections for atomic chlorine using an open-shell random-phase approximation

Abstract: The use of the Random Phase Approximation with Exchange (RPAE) for calculating partial and total photoionization cross sections and photoelectron angular distributions for open shell atoms is examined for atomic chlorine. Whereas the RPAE corrections in argon (Z=18) are large, it is found that those in chlorine (Z=17) are much smaller due to geometric factors. Hartree-Fock calculations with and without core relaxation are also presented. Sizable deviations from the close coupling results of Conneely are also found.

An equations of motion approach for open shell systems

Abstract: A straightforward scheme is developed for extending the equations of motion formalism to systems with simple open shell ground states. Equations for open shell random phase approximation (RPA) are given for the cases of one electron outside of a closed shell in a nondegenerate molecular orbital and for the triplet ground state with two electrons outside of a closed shell in degenerate molecular orbitals. Applications to other open shells and extension of the open shell EOM to higher orders are both straightforward. Results for the open shell RPA for lithium atom and oxygen molecule are given.

Magnetoplasma Oscillation of a Layered Electron Gas

Abstract: The plasma dispersion of a layered electron gas in a magnetic field is calculated in the random phase approximation for the Voigt configuration. We found that the plasmon gradually changes its character from the two-dimensional to the three-dimensional ones as the spacing between the planes of the layer decreases.

Surface-electronic-structure information from bulk plasmon photoexcitation in free-electron metal films

Abstract: Bulk-plasmon-photoexcitation (BPPE) phenomena (particularly the shapes of resonance peaks associated with standing-plasma-wave excitation) in thin free-electron-metal films are shown to be sensitive to surface electronic structure. A formalism is developed which permits the microscopic evaluation of corrections to the classical theory of the optical properties of a jellium solid, through first order in the wave vector of an incident electromagnetic wave. This formalism permits the evaluation of effects due to BPPE in both the ordinarty optical as well as in the photoemissive properties of thin films, and moreover, allows one to determine their dependence on the forms of the one-electron surface potential barriers V(z) at the two film surfaces. Theoretical results based on the random phase approximation (RPA) to a jellium film's dielectric response are compared to the photoyield data of Anderegg et al. taken on potassium films. The experimental BPPE resonance features are found to be considerably narrower than the theory predicts--for all the forms of V(z) that were tried--casting some doubt on the RPA's ability to describe surface dielectric phenomena quantitatively. The asymmetry of Anderegg et al.'s films, i.e., the fact that their upper and lower film surfaces were inequivalent, is shown to require a partial reinterpretation ofmore » their data; in particular, their films were probably only about half as thick as they supposed.Moreover, the argument that leads to this conclusion also provides a simple explanation for the alternation of BPPE resonance peak strengths which appears to be a fairly systematic feature of their data. Directions for further experimental and theoretical work on BPPE phenomena are suggested. (auth)« less

Spin susceptibilities in the theory of itinerant-electron antiferromagnetism. I

Abstract: The spin-density-wave state in the itinerant-electron model of antiferromagnetism is analysed. In the so-called commensurate case it is shown that a simple rotation of the quantization axis disposes of the complications due to the pairing of opposite spins and exposes the really important pairing of electrons in different subbands arising from the reduced translational symmetry. A method is given for obtaining explicit closed expressions for the full transverse and longitudinal magnetic spin susceptibility without making any approximation for the form factors. This method is illustrated by a detailed calculation of the transverse susceptibility in the Hubbard one-band model in the random phase approximation.

Analysis of the random phase approximation for atomic 'open-shell' systems

Abstract: The polarization propagator is analysed in the random phase approximation for atoms with two electrons in an open shell and a core of completely filled shells. The connection between optimization of the energy and the requirement that the so-called B and C matrices should be Hermitian is discussed. Particle-hole symmetry in RPA for open shell systems is examined, and it is shown how RPA formulae for the configurations (nl)1, (nl) 4l+1, and (nl)4l+2 can be derived from the results for (nl)2. The calculation of oscillator strengths from the residues of the propagator is described. Numerical results for silicon I are presented. Finally the applicability of the method is discussed.

Excitation of surface plasmons in metal particles by fast electrons and x rays

Abstract: The cross sections for excitation of surface plasmons by fast electrons and x rays are calculated within the random phase approximation for a spherical metal particle. The results are compared with those obtained within the hydrodynamic model of a free electron gas.

Potential Barrier Effect and Discrete Structure between 40 and 120 angstrom in the Rb I Absorption Spectrum

Abstract: Investigation of the Rb I absorption spectrum between 40 and 120 angstrom has revealed a broad absorption maximum in the 3d photoionization continuum, as well as discrete features associated with the excitation of a 3d-subshell electron. The discrete structure is identified, Hartree-Fock calculations of the transition energies are given and the absorption maximum is discussed in relation to similar spectra and to recent random phase approximation with exchange (r.p.a.e.) and independent particle model calculations.

Electronic and magnetic properties of dilute transition clusters in noble (or transition) metals

Abstract: Using a realistic band structure for the host (noble or transition metal), we present a detailed study of the electronic and magnetic properties of transitional impurity clusters without interactions between the clusters. For the calculation of the one-electron properties, the Hartree-Fock environment effects are self-consistently taken into account by Friedel's rule. The impurity potentials and densities of states are very sensitive to the impurity-impurity interactions inside the clusters. For the calculation of the magnetic properties, the electron-electron interactions are taken into account in the random phase approximation, which allows one to obtain simple expressions for the specific heat and the low-temperature-dependent resistivity. These properties are expressed in terms of three characteristic temperatures T f(1), T f(2) + , and T f(2) − corresponding to three different modes of spin fluctuations for the considered model. We present numerical results from the study of the local magnetic susceptibility, which depends on local environments via several combined effects. Our conclusions on “nearly magnetic” copper-based alloys are in good agreement with the experimental data. In particular, our calculations confirm that a magnetic moment appears on a nickel atom when it is surrounded by approximately eight nearest-neighboring Ni atoms.

Renormalization of magnetic excitations in praseodymium

Abstract: The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev and the ratio between the exchange interaction and d is very close to unity. However, zero-point motion prevents the system from ordering.

Calculation of the collective mass-parameter including RPA corrections

Abstract: A derivation of the vibrational mass-parameterB is given which makes the consistency with RPA calculations explicit. The expected enhancement by the residual particle-hole and particle-particle interaction is demonstrated by solving the quasiparticle-RPA for deformed nuclei in the rare earth region.

Random-phase-approximation calculations on triplet spectra of conjugated molecules

Abstract: Random-phase approximations (RPA) have been applied to the calculation of the triplet π-π* transition spectra of 18 conjugated molecules in the framework of Pariser-Parr-Pople approximations. It is found that the normal RPA (n-RPA) shows the triplet instability for most molecules in the Nishimoto-Mataga approximation of electron-repulsion integrals. However, it is shown that this instability can be circumvented by the use of the renormalized RPA (r-RPA) in which the correlated ground states are calculated by the second-order perturbation theory. It is also shown that even in the n-RPA the suitable parametrization of electron-repulsion integrals removes this instability. It is ascertained that such an increasing order of energies as ω(n-RPA)<ω(Tamm-Dancoff approximation)<ω(r-RPA) holds for most of energy levels.

Magnetic excitations in rare earth Al2 compounds

Abstract: In the rare earth intermetallic compounds, the crystal field is often comparable to the exchange interaction between the magnetic ions. The magnetic excitations (excitons) in such systems are transitions between single‐ion atomic levels, propagating through the lattice via the exchange interaction. This article reviews recent experimental and theoretical work on rare earth Al2 compounds. The excitons in NdAl2 and TbAl2 have been studied by inelastic neutron scattering. The dispersion relations are analysed within the random phase approximation using a Hamiltonian including 4th and 6th order crystal field terms and an isotropic exchange interaction. The spectrum of NdAl2 at 5 K comprises both transverse and longitudinal modes, corresponding to transitions between the ground state and excited mean‐field states. The bulk magnetic properties of NdAl2 can be understood quantitatively using the crystal field parameters derived from the analysis of the exciton spectrum. At 4 K the magnetic excitations in TbAl2 are spin waves. At temperatures above 35 K the neutorn scattering measurements show a double peak structure. This splitting of the spin wave branch is the reuslt of an interaction between the spin‐waves and excitations associated with higher‐lying mean‐field states, a magnon‐exciton interaction.

Paramagnetic Mössbauer spectra of161Dy(Г6 or Г7 and166Er(Г8) in cubic symmetry: Influence of relaxation

Abstract: When hyperfine interactions are non-diagonal with respect to the electronic states, the effective-field approximation does not hold, and the influence of relaxation on paramagnetic Mossbauer spectra can be described by the Clauser and Blume stochastic theory. This theory involves the inversion of matrices whose dimension is:d=(2S+1)2 (2Ie+1)(2Ig+1) and becomes impracticable ifd is large. It is then possible to simplify the method by using the random phase approximation, which eliminates the stochastic indices in the expression of the line shape: only matrices of dimension (2Ie+1)(2Ig+1) have to be inverted at each point of the spectrum. Specific calculations are presented for161Dy and166Er nuclei in a cubic environment.

A time-dependent variation-perturbation method for the calculation of transition properties and its relation to the random phase approximation

Abstract: A time−dependent variation−perturbation (VP) formulation is presented for the simultaneous calculation of the ground state correlation function and the excited state wave function of an atomic or molecular system. The wave functions are chosen for the optimal calculation of transition properties with a relatively small number of molecular integrals. The VP equations so obtained for a singlet system are identical with the equations in the random phase approximation (RPA). On the other hand, if the ground state is a singlet and the excited state a triplet, the VP and RPA equations are different. The latter assumes a ground state correlation function with an open shell component, which is a poor approximation for a closed shell ground state. The orthonormalization condition in the VP scheme is different from that in the RPA. The consequence of this difference is discussed. It is also pointed out that the RPA excitation energy actually contains part of the ground state correlation energy; hence the RPA excita...

Instability of Neutron Star Matter for Pion Condensation

Abstract: The instability of normal neutron star matter is investigated from the viewpoint of collective oscillations which are coupled with condensed pions in neutron matter. It is shown that there is no inconsistency between the instability conditions obtained by· two apparently different approaches, i.e., the mean field method by Sawyer et al. and the Green's function method by Migdal. The double pole condition, which determines the instability threshold in the Green's function method, is interpreted in terms of collective motions. §I. Introduction It is of great interest whether or not the pion condensate appears in superdense nuclear matter in connection with the cooling mechanism of neutron stars/> the understanding of transient superdense states caused by high-energy heavy-ion col­ lisions2> and other related problems. 3) There are two apparently different approach­ es to the problem of pion condensation in neutron star matter. That is, Sawyer and Scalapino4> h;l.Ve worked the problem on the basis of the Hamiltonian in which the condensed n- field has been replaced by the mean field. A series of their work has indicated the possibility that the ground state of neutron star matter would be rearranged at a slightly greater nucleon density than the normal nuclear matter density p0• Then the new ground state has been prepared to be a coherent mixture of protons, neutrons and condensed negtive pions. In a preceding paper, 5>, we have shown that this state can be treated with the coherent-state representation of proton particle-neutron hole. On the other hand, by using the pion Green's function, Migdal6> has obtained the conclusion that neutral pions would be able to appear at the smaller density than Po and charged pions nearly at the same density. It is the purpose of this paper to reproduce the results of the mean field method and the Green's function method by using the method of normal mode which was introduced by Sawada and Fukuda 7> in order to study the stability of the Hartree-F ock state within the rang~ of the random phase approximation (RP A). They have pointed out that there exists an extremely important relation between the instability of the Hartree-Fock state and the solution of the RPA equation which describes some kind of approximate normal mode. When an infinitesimal