Showing papers on "Random phase approximation published in 1979"

Multichannel relativistic random-phase approximation for the photoionization of atoms

Abstract: A multichannel relativistic random-phase approximation (RRPA) for the photoionization of atoms is presented. The RRPA equations are obtained by generalizing the nonrelativistic time-dependent Hartree-Fock equations using the Dirac-Breit Hamiltonian to describe the atomic electrons. The angular decomposition of the RRPA equations to a set of coupled equations for the radial wave functions is given, and the radiative-transition operators are developed for arbitrary electric and magnetic multipoles. Formulas are obtained for the total photoionization cross sections and angular distributions, including all multipoles. The method of constructing multichannel solutions from the RRPA radial wave functions is described and various ways of choosing approximate potentials for the photoelectron are given.

New theory of the spin-peierls transition with special relevance to the experiments on TTFCuBDT

Abstract: A new theory of the spin-Peierls transition in spin-1/2 Heisenberg chains is developed in which the phonons are treated in a mean field, random phase approximation as in previous work, but in which the relevant response functions of the spins are calculated using the procedure of Luther and Peschel. 7 This gives a much better approximation than the Hartree treatment used before, taking realistically into account the one-dimensional nature and showing the important differences from an XY model.The leading divergences of the spin response should be given exactly by our calculation. We find a new linear dependence of the transition temperature of the spin-phonon coupling constant and an enhancement of the transition temperature and also of the phonon softening above this temperature. Predictions of some other signatures of the transition, such as the specific heat jump to normal specific heat ratio, are not much changed from earlier work, however. New exact results are found at zero temperature.

Characteristics of the consistent ground state of the random phase approximation

Abstract: Detailed considerations of the ground-state vector derived for the random phase approximation obtained earlier in a generator coordinate representation employing the unitary group parameter space reveal a particular correlated pair structure. The results of explicit calculations of ground-state averages are discussed.

Hypervirial relations as constraints in calculations of electronic excitation properties: the random phase approximation in configuration interaction language

Abstract: Off-diagonal hypervirial relations (for example, the equivalence of the dipole length and dipole velocity forms of the electronic transition moment for exact wavefunctions) are imposed upon two approximate configuration interaction (CI) representations of the ground and excited states of interest in an atomic or molecular system It is shown that, if the ground state is approximated by the exact Hartree-Fock function correlated by double excitations and the excited state is represented by mono-excited CI, the hypervirial constraint on the transition moments leads directly to the random phase approximation (RPA) equations No second-quantized formulation or assumed excitation operator is invoked The same constraint, applied to an uncorrelated ground state, leads to non-variational mono-excited CI schemes, which are related to Hartree-Fock instability conditions The methods are illustrated by 5–31/G computations of the chiroptical properties, in dipole length, velocity and acceleration forms, of two low-l

Excitation operators and the extended random phase approximation: II. Applications

Abstract: The random phase approximation (RPA) and its extensions are tested by applying them to the π electron system of a series of linear polyenes in the PPP approximation, for which exact solutions are available. The importance of electron correlation is varied by altering the form of the electronic repulsion matrix elements in the PPP model. Emphasis is placed on a comparison between recently suggested refinements in the RPA and the more standard RPA scheme. The elements of the modifications of the RPA are illustrated by the simple example of ethylene. Calculations for longer polyenes (butadiene, hexatriene, and octatetraene) demonstrate that certain improvements in the RPA are essential if reliable results are to be obtained for highly correlated excited states. The results provide support for use of the extended RPA method in molecular excited state calculations.

Exact removal of spurious states in RPA calculations

Abstract: An exact, yet simple elimination of spurious states for actual (non-ideal) RPA calculations is presented. The new method restores translational and Galilean symmetry for arbitrary Hamiltonians and arbitrarily truncated ph spaces.

Random‐phase circular dichroism calculations of the σ/3s←n transition in chiral alcohols

Abstract: The circular dichroism of the long wavelength electronic transition in 10 chiral alcohols is calculated in the random‐phase approximation using time‐dependent Hartree theory. This long wavelength transition (1850–2000 A) which is associated with the hydroxyl group is assumed to be largely localized on the oxygen atom and to originate in nonbonding density of the ground state, namely in an oxygen 2p orbital. The upper state is mixed, having both intravalence σ and Rydberg 3s character. The σ*/3s←n electric‐dipole transition moment (μe) is perpendicularly polarized with respect to the COH plane, while the associated magnetic‐dipole transition moment (μm) is polarized in plane. The circular dichroism is calculated as a function of hydroxyl rotation about the CO bond by coupling the zeroth‐order σ*/3s←n transition moments to the backbone CC and CH bond density of states via a polarizability approximation. These values are then Boltzmann averaged over an empirical rotational potential, and the resulting circul...

The xenon 4d5/2/4d3/2 photoelectron intensity ratio in the region of the Cooper minimum

Abstract: The photoelectron intensity ratio of the xenon 4d spin-orbit components has been studied at four photon energies between 132 and 192 eV and at a photon-photoelectron angle of 90 degrees . The 4d5/2/4d3/2 ratios obtained are: 1.34+or-0.04 at 132.50 eV, 1.33+or-0.07 at 151.65 Ev, 1.22+or-0.15 at 171.69 eV and 1.65+or-0.15 at 192.53 eV. Data are compared with relativistic single-particle calculations (Dirac-Slater and Dirac-Fock) and multi-body predictions (relativistic random phase approximation, RRPA). The RRPA results agree satisfactorily with the experimental values.

Molecular statistical description of nematics in terms of the random-phase approximation

Abstract: A calculation of the Maier-Saupe model is given in terms of the random-phase approximation. The influence of the range of the intermolecular potential is analyzed. Notably, attention is paid to short-range-order effects in the isotropic phase. It appears that light-scattering data can be understood using a short-range potential.

Two-channel relativistic random-phase approximation applied to the photoionisation of helium- and beryllium-like ions?

Abstract: Atomic photoionisation cross sections including both relativistic and correlation effects for the helium and beryllium isoelectronic sequences are calculated in two-channel relativistic random-phase approximation (RRPA). By studying the relativistic E1 transition along the sequence, the coupling between the low-energy photoelectron and the core electron (electrons) is found to deviate from relativistic jj coupling even for high Z elements. The deviation of the sum of dipole oscillator strength from the non-relativistic Thomas-Reiche-Kuhn rule is also investigated.

Calculation of giant monopole resonances in the adiabatic time-dependent Hartree-Fock theory

Abstract: Giant monopole resonances in doubly magic nuclei are investigated by the adiabatic time-dependent Hartree-Fock method. The collective paths are constructed using constrained Hartree-Fock techniques with various Skyrme interactions. The calculation of the mass parameter is reduced to the solution of a finite set of linear equations which contain the usual cranking expression as an approximation. The resulting masses and energies allow the extraction of various energy moments of the random phase approximation monopole strength distribution. Predictions of the resonance widths are also presented.

Self-consistent theory of Coulomb isospin mixing in nuclei

Abstract: The residual isovector forces in separable form are derived for a given form of shell-model potential The derivation is based on the isotopic invariance of nuclear forces The form and the strength parameters of the interaction are related to the potential by self-consistency relations The Coulomb forces are approximated by an effective single-particle potential The theory of isobaric states is developed using the random-phase approximation The effects of Coulomb isospin mixing are analyzed for nuclear ground states and excited 0/sup +/ states1) Physics Institute, Azerbaidzhan Acd Sci, Baku 2) Institute of Applied Physics, Moldavian Acad Sci, Kishinev 3) University of Sofia, Bulgaria (AIP)

Generalized oscillator strengths for beryllium atom in the random‐phase approximation with exchange

Abstract: The generalized oscillator strengths for the transitions from the ground state to the excited discrete and continuous states of the beryllium atom are calculated in the framework of the random‐phase approximation with exchange for a range of momentum transfer values from 0 to 3 a.u. The results for the 2s→2p transition are compared with calculations of Sinanoglu and Davis and good agreement is obtained. Also the influence of electron correlation is examined for the transitions to the lowest excited states in the discrete and continuous spectrum, as for these transitions the influence is strongest.

Theoretical analysis of plasmon dispersion in simple metals

Abstract: The dielectric response of an electron gas has been investigated with a view to understanding the small momentum behaviour of the plasmon peak in inelastic electron energy loss spectra. It is shown that the lifetime of the plasmon and the width of the incident beam both contribute to the apparent flattening of the plasmon dispersion which has been seen to occur in some metals (magnesium, aluminium, indium) for plasmon wavevectors less than ~O·5 A -1. Expressions, beyond the random phase approximation, are derived for the dispersion coefficients up to fourth order in the plasmon wavevector. Good agreement with experiment is obtained.

Current conserving random phase approximation

Abstract: The consequences of the continuity equation for the RPA are exploited, if charge and current densities are given. Simple, yet stringent conditions for the RPA amplitudes and the residual interaction are obtained. Under these conditions the RPA equations are simplified and exactly reduced to a hermitean eigenvalue problem of half the original dimensionality. Transition current matrix elements are then similar to those of an effective current recently proposed for TDA calculations.

A Calculation of the Spin Wave Energy in fcc Fe-Ni Alloys

Abstract: An expression of the exchange stiffness constant of spin waves in disordered ferromagnetic alloys is obtained in the combined approximation of the random phase approximation and the coherent potential approximation. Both the diagonal randomness and the off-diagonal randomness are taken into account. By using the realistic band structures, the exchange stiffness constants in fcc Fe-Ni alloys are calculated numerically. The difference between the observed and calculated values of the exchange stiffness constants in fcc Fe-Ni alloys is attributed to the inter-atomic exchange interaction between d-electrons.

Treatment of the random-phase-approximation including continuum

Abstract: The random-phase approximation has been treated in two steps: (a) First, we solve the so-called nuclear structure problem in which the single particle continuum states are excluded. (b) In the second part, we include the continuum utilizing a reformulated version of the random-phase approximation which uses the outcome of the nuclear structure method as an input. Thus the effect of the continuum is directly estimated. Below threshold the excitation energies are shifted; above threshold they obtain additionally a width. Numerical results are presented for $^{16}\mathrm{O}$ and $^{16}\mathrm{N}$.

Coupled LO phonon-plasmon modes in a magnetized semiconductor

Abstract: The longitudinal optic (LO) phonon susceptibility is evaluated for a semiconductor subjected to a steady magnetic field. Coupling of the lattice vibrations and free electrons is described by a Frohlich interaction, and electron correlation effects are treated within the random phase approximation (RPA). The susceptibility displays resonances, as a function of frequency for a fixed wavevector perpendicular to the applied field, at frequencies that correspond to excitation of coupled LO phonon-plasmon–cyclotron modes. The spectrum and corresponding spectral weights for inelastic neutron scattering are evaluated for a model of n-type GaAs.

Nonlinear generalization of the quasiparticle random phase approximation for description of anharmonic effects in vibrational spectra: Application to the even Ni isotopes

Abstract: The theory of anharmonic nuclear vibrational motion (nonlinear equations-of-motion method) developed in the preceding paper is applied to $^{60,62,64}\mathrm{Ni}$, which exhibit one and two phonon quadrupole collective states. A model Hamiltonian consisting of a modified pairing plus quadrupole interaction is studied first by comparing the results of the nonlinear equations-of-motion method with those of an exact diagonalization. Contrary to popular opinion, the model chosen fails to produce a vibrational spectrum, except in the case of $^{60}\mathrm{Ni}$, and, as a consequence, the nonlinear equations-of-motion method, designed specifically to describe vibrational spectra, accords well with the exact calculations only for this case. A simple method is then described, within the framework of the nonlinear equations-of-motion method, for refining the model Hamiltonian so as to bring it into accord with experiment. In practice, it is found that a simple additional parameter in the Hamiltonian suffices to yield descriptions of the quadrupole states in Ni isotopes comparable in precision to the most up-to-date versions (modified, adjusted, etc.) of the surface delta interaction model.

Treatment of nucleon scattering in the continuum random-phase approximation

Abstract: By using the Lehmann-Symanzik-Zimmer (LSZ) theorem one can obtain a microscopic formulation of the nonrelativistic nuclear-scattering problem which links theS-matrix elements to the so-called «vertex parts» of appropriate Green’s functions. This method leads, for the case of nucleon-nucleus scattering on one-hole nuclei, to a direct relation between the transition amplitude and the linear response function. By utilizing the spectral decomposition of the response function the treatment can be further reduced to the renormalized random-phase (RPA) problem in the continuum with appropriate scattering boundary conditions. In order to obtain a better insight into the problem, the coupled integro-differential system is reformulated in such a manner that the standard nuclear-structure calculations can be used as an input for the complete calculation including continuum. An approximate method is presented which considerably simplifies the continuum calculations. We have applied the method to some scattering processes in the oxygen region and compared them with corresponding experiments.