Showing papers on "Random phase approximation published in 1970"

Nuclear Collective Motion: Models and Theory

Abstract: Phenomenological Models: General Trends and Coupling Schemes The Collective Vibrational Model The Unified Model for Vibrations The Vibrating Potential Model The E1 Photoresonance The Collective Rotational Model The Unified Model for Rotations The Moment of Inertia Microscopic Theories: Hartree?Fock Self-Consistent Field Theory: Spherical Nuclei Hartree?Fock Self-Consistent Field Theory: Deformed Nuclei Pairing-Force Theory The Tamm?Dancoff Approximation or Simple Particle?Hole Theory An Equations-of-Motion Method The Random Phase Approximation or Sophisticated Particle-Hole Theory Time-Dependent Hartree?Fock (TDHF) Theory The Microscopic Foundations of the Unified Vibrational Model Concluding Remarks.

Higher random-phase approximation as an approximation to the equations of motion.

Abstract: Starting from the equations of motion expressed as ground-state expectation values, we have derived a higher-order random-phase approximation (RPA) for excitation frequencies of low-lying states. The matrix elements in the expectation value are obtained up to terms linear in the ground-state correlation coefficients. We represent the ground state as eU|HF〉, where U is a linear combination of two particle-hole operators, and |HF〉 is the Hartree-Fock ground state. We then retain terms only up to those linear in the correlation coefficients in the equation determining the ground state. This equation and that for the excitation energy are then solved self-consistently. We do not make the quasiboson approximation in this procedure, and explicitly discuss the overcounting characteristics of this approximation. The resulting equations have the same form as those of the RPA, but this higher RPA removes many deficiencies of the RPA.

Theory of the High Density Exciton. I

Abstract: The boson creation and annihilation operators of excitons are introduced and the fermion Hamiltonian of high density electrons and holes is expanded in terms of these boson operators. Then a nonlinear integral equation for the high density excitons is derived and it is solved in two ways: 1) by the perturbational method and 2) exactly for a simple model of the Coulomb interaction in the random phase approximation and the effective mass approximation for the two band model of a conduction band and a valence band. As a result, the cutting down effects of both the band edges due to formation of high density excitons are shown to overcome the exchange self-energy of the electrons and the holes composing the high density excitons.

Application of a Higher RPA to a Model π‐Electron System

Abstract: We have applied a proposed higher‐order random phase approximation (RPA) to the simple model system of two π electrons in the double bond of ethylene. The higher‐order RPA removes some difficulties involved in the usual RPA, but retains the form of the RPA equations. To derive the higher RPA we retain all terms linear in the ground state correlation coefficients in the equations of motion for the excitation energy and in the equation determining the ground state. These equations are solved self‐consistently and are simpler to handle than a configuration interaction solution in a realistic example. We do not use the quasiboson approximation.

Surface excitations in the random phase approximation

Abstract: Density fluctuations in inhomogeneous systems are treated in the RPA using the Kadanoff–Baym Green's function method. In our analysis, the Wigner distribution function plays an important role. Well...

Impurity screening near a metal surface

Abstract: The linear response of a metal to an embedded charge impurity near the surface is treated within the random phase approximation. The surface is assumed to be perfectly reflecting, which allows the boundary value problem to be solved by symmetric continuation of the metal. The resulting integral equation for the symmetrized charge density is solved numerically in momentum space. When quantum-mechanical interference effects are neglected (quasi-classical limit) an analytic solution is obtained. Graphs are presented for the potential and the normal field at the surface in the quantum-mechanical and quasi-classical case. These graphs display the Friedel oscillations as a function of the radial co-ordinate on the surface and of the distance of the impurity from the surface. In the quasi-classical case, asymptotic expressions which describe these oscillations are obtained. The results for the Fermi-Thomas approximation are also given for comparison. In every case the impurity charge is completely screened, in the sense that the average of the normal field at the surface is zero.

Nuclear Rotation and Boson Expansions. I

Abstract: The Beliaev-Zelevinsky method, which represents fermion-pair operators by infinite expansions in exact bosons, is applied to the problem of nuclear rotation. In the harmonic order, which is essentially the random-phase approximation (RPA), the rotation, viewed as infinitesimal, is decoupled from the collective vibrations. The higher orders, however, give rise to various band-mixing terms, which may be interpreted as rotation-vibration and higher-order Coriolis interactions, as well as to vibrational anharmonicities and renormalization of the moment of inertia. A systematic approach is given for extracting these higher-order corrections for the idealized case of a two-dimensional system of interacting particles. Both the Hamiltonian and transition operators are treated. The self-consistent-field approximation is then formulated in the boson picture and applied to the cranking model. The advantage of this formulation is that it allows one to establish the correctness of the higher-order cranking model, which is shown to provide the ground-state-band rotational energies with an error of the order of the small boson-expansion parameter (or the square of this parameter, depending on its definition). The usefulness of the cranking model for obtaining the angular momentum dependence of transition operators is also demonstrated. The Appendix illustrates some of the ideas by way of application to a system of particles interacting through a two-dimensional analog of the quadrupole-quadrupole force.

Atomic resonance from a many-body point of view. II

Abstract: For pt. I see ibid. vol. 3, no. 4, p. 455 (1970). The author derived the Fano formula with generalized parameters using many-body perturbation theory. In this paper he applies the theory, in the lowest order, to helium. For the 2s2p 1P resonance a rough estimate gives a value for the (dynamical) dipole matrix element within twenty per cent of the experimental value and with a correct sign. For many-electron atomic systems polarization effects become important. The author demonstrates the effects of screening using a random phase approximation for the continuum from a single shell.

Effect of localized spin fluctuations on the superconducting critical temperature of dilute alloys

Abstract: The effects of localized spin fluctuations (LSF) on the properties of dilute superconducting alloys are investigated in both the weak magnetic and strong magnetic limits. In the weak magnetic limit, the inverse lifetime Gamma s of the LSF is long compared with kTc where Tc is the superconducting critical temperature of the alloy. The renormalized random phase approximation is applied to obtain an expression in this limit. The theory accounts for the decrease in Tc with impurity concentration in AlMn. In the strong magnetic limit Gamma s<

The treatment of correlations in the theory of electron impact broadening

Abstract: Quantum Statistical techniques are used to determine the best way to approximate the effects of correlations amongst the perturbers in calculations of electron impact broadening. It is shown that, in this context, the shielding of the interaction can never be described by the static Debye potential, since the physical similarity between the electron-impact broadening process and Landau damping requires that the latter be always included in the calculation. The effects of correlations not included in the Random Phase Approximation are discussed briefly.

Collective excitations from condensed Fermi systems and the Goldstone theorem

Abstract: By means of the two-particle Green function, the collective modes of a condensed Fermi system (i.e. a Fermi system with long-range order present) describable by means of a 2*2 matrix propagator are studied. The random phase approximation is given in terms of diagrams and is applied to a ferromagnetic state. Finally, the Goldstone theorem is shown to be an immediate consequence of the order-parameter equation.

The 2 + and 3 - collective states in the Sn and Zr isotopes using schematic forces

Abstract: The energies and transition probabilities of the low-lying 2+ and 3− states in the Sn and Zr isotopes are calculated by the Random Phase Approximation method The results forδ-force and surface delta interaction are compared The properties of 3− states are practically independent of the residual interaction used while for the 2+ states the adequate agreement with experimental data was obtained usingδ-force only The influence of the interaction in the particle-particle channel proves to be important in the case of 2+ excitations only

Low‐Temperature Expansion for Impure Heisenberg Ferromagnets

Abstract: The thermodynamics of impure Heisenberg magnets have been studied previously within the random phase approximation (RPA) which neglects some important correlations between exchange‐coupled spins. To test the accuracy of the RPA and to allow more detailed comparison with experiment we have extended the rigorous Dyson low‐temperature boson formalism to impure systems. Spin‐wave interactions are treated in Hartree‐Fock approximation (equivalent to Dyson's first Born results for the pure system). We find only very small differences from the RPA impurity magnetization results, but there is substantial variation from RPA predictions of the temperature dependence of local mode energies.

On the structure of the paired states

Abstract: In this paper the quasi-particle structure of the ground state of the pairing Hamiltonian is analysed for the Ni isotopes and 206Pb. The particle-number projected Bardeen-Cooper-Schrieffer states are used for describing the states under consideration. The quasi-particle amplitudes are evaluated in the saddle-point approximation. The amplitudes with the number of quasi-particles a multiple of four are shown to be comparable with the quasi-particle vacuum amplitude. The value of the other quasi-particle amplitudes depends essentially on the system considered. In particular, the two-quasi-particle component can sometimes be comparable with the four-quasi-particle one (206Pb). On the basis of the data obtained it is concluded that the random phase approximation ground-state wave function with small admixture of the quasi-particle components, the components with the odd number of quasi-particle pairs being neglected completely, is rather poor.