On the projected spectra from a deformed correlated intrinsic state

It is argued that the residual interaction being relatively of long range, should produce Random Phase Approximation (RPA) type of correlations in the Hartree-Fock (HF) intrinsic state. A model is described to take these correlations inti account in the intrinsic state. A comparison of the projected spectra from this state with the exact shell model diagonalization for a model problem bears out this point. An application of the model is distinguishing two almost degenerate HF solutions for the 2s-1d shell nuclei is mentioned.     

TFD extension of a self-consistent RPA to finite temperatures

The self-consistent RPA (SCRPA) developed by Schuck and coauthors is extended to finite temperatures. The corresponding equations are derived by using the formalism of thermofield dynamics. The intrinsic energy of a system is calculated as the expectation value of the Hamiltonian with respect to a T-dependent thermal vacuum state for a thermal-phonon operator. A nonvanishing number of thermal quasiparticles in the vacuum state are assumed. By virtue of the assumption, the thermal Hartree-Fock (HF) equations appear to be coupled to the equations of motion for phonon variables. The thermal occupation numbers are also calculated in a consistent way with the energies of the HF quasiparticles. The approximation is applied to the two-level Lipkin model. Advantages of the thermal SCRPA (TSCRPA) are most obvious at temperatures near the phase-transition point. In the TSCRPA, the phase transition occurs at lower T than in other approximations. Moreover, within the TSCRPA, a statistical behavior of the Lipkin model is described with an appropriate accuracy at any T even if the HF transformation parameter is kept fixed at a value corresponding to the “spherical” phase of the HF field.     

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.     

A finite sum representation of the angular momentum projection operator

Exact finite sum representations of the angular momentum projection operator in the following two cases are derived: i) when the intrinsic state is axially symmetric but the azimuthal quantum numberK is not equal to zero, ii) when the intrinsic state does not have axial symmetry. Advantages of such representations over projection via exact numerical quadrature are discussed.     

Local and interfacial magnetic properties of inhomogeneous finite linear chains

The Hubbard Model has been used to study the local and interfacial magnetic properties of finite inhomogeneous cluster systems. These are generally of the type, NMMMMMN, where N and M, respectively, refer to non-magnetic and magnetic atoms, of a 7-site finite chain. The applicability of the Hartree–Fock (HF) approximation is gauged via direct comparison of the ground state magnetization results derived from exact diagonalization methods. The underlying HF and exact mechanisms are compared as a function of the model parameters, with particular attention being paid to the local and interfacial (N/M interface) magnetic properties. Regimes, which exhibit favourable comparison between HF and exact results are found. Detailed inspection of the HF prediction is made and general trends established as a function of system size and model parameters.     

Study of doubly evens d-shell nuclei in the Multi-Configuration-Hartree-Fock model

A theory in the spirit of the Hartree-Fock (HF) model is formulated which takes into account general types of correlation effects. This theory, dubbed as Multi-Configuration Hartree-Fock (MCHF) model, makes use of a multideterminantal trial wave function. In the present work the intrinsic ground state wave functions obtained in this theory have been studied. Doubly evenN=Z andN=Z + 2 nuclei in thesd-shell have been treated and the results have been compared against the HF-predictions. While the HF-approximation is found to be quite good forN=Z nuclei, correlations are found to play a strikingly significant role in theN=Z +2 nuclei.     

Beta-vibrations inO(6)-nuclei: A pair mode?

We investigate excitations of an intrinsic state allowing for quadrupole and pair deformations, in theSO (8)S, D-pair model, using the exact Schwinger boson realization and RPA. The 0⁺ head of the quasi-beta band in0 (6) nuclei which is generally interpreted as a shape vibration turns out to be a double pairing vibration. This has experimentally observable consequences for pair transfer strengths. It suggests also the interesting question whether pairing and beta vibrations are generally not independent, or would coexist in less schematic models. AnSU (8) boson model would allow for such more general situations which are briefly discussed.     

OCCUPATION RENORMALIZED HARTREE-FOCK APPROXIMATION IN LIPKIN MODEL

The occupation renormalized Hartree-Fock single particle potential is extended to include the 'particle' state occupation. The exac solution of the occupation renormalized Hartree-Fock approximation and that of the Hartree-Fock approximation are calculated in Lipkin Model. It turns out that the RHF solution is more close to the exact one than the HF solution. The effect of occupation probability depends on the strength of the interaction of the two body term.     

Investigation of native-oxide growth on HF-treated Si(111) surfaces by measuring the surface-state distribution

The evaluation of the surface state distribution of differently HF-treated Si(111) surfaces during the native-oxide growth in air is investigated by the large-signal field-modulated photovoltage technique. The surface state distribution consisting of intrinsic and extrinsic Si dangling bond defects is directly related to the state of oxidation of the Si surface. It is shown that the kind of HF treatment strongly influences the concentration of extrinsic defects with a lower state of oxidation. Special HF preparations for H termination of the Si(111) surface result in a nearly intrinsic surface state distribution. During the oxidation process three typical phases can be distinguished each characterized by specific defect structures. It was found that native-oxide growth is highly sensitive to the concentration of extrinsic defects directly after HF treatment.     

Perfect fluid spheres in general relativity

Spherically symmetric perfect fluid distributions in general relativity have been investigated under the assumptions of (i) uniform expansion or contraction and (ii) the validity of an equation of state of the formp=p(ρ) with nonuniform density. An exact solution which is equivalent to a solution found earlier by Wyman is obtained and it is shown that the solution isunique. The boundary conditions at the interface of fluid distribution and the exterior vacuum are discussed and as a consequence the following theorem is established:Uniform expansion or contraction of a perfect fluid sphere obeying an equation of state with nonuniform density is not admitted by the field equations. It is further shown that the Wyman metric is not suitable on physical grounds to represent a cosmological solution.     

Field-theoretical treatment of approximations to radiative transitions in atoms

Starting with a field-theoretical many-body definition of eigenvalues and radiative transition matrix elements for atomic systems, a systematic approach is taken to approximations of the exact results. The guiding principle is the maintenance of gauge invariance (GI) in radiative transition S matrix elements. At the level of the one Coulomb exchange approximation in both the one-electron and the electron-hole propagator kernels, one obtains the well-known Hartree-Fock (HF) and random phase approximations (RPA). A detailed discussion and comparison of various approaches to RPA is made, in the case of both N and N ? 1 electron shielding (the regular HF and HF with frozen relaxed core—FRC). In the former case, a new and considerably simpler form of the RPA equations are obtained than heretofore proposed equivalent forms. Finally, a different approximation than the usual HF and RPA, involving higher-order correlations, is developed to illustrate how such approximations can be systematically generated.     

Discrete breathers in nonlinear Schrödinger hypercubic lattices with arbitrary power nonlinearity

We study two specific features of onsite breathers in Nonlinear Schrödinger systems on d-dimensional cubic lattices with arbitrary power nonlinearity (i.e., arbitrary nonlinear exponent, n): their wavefunctions and energies close to the anti-continuum limit-small hopping limit-and their excitation thresholds. Exact results are systematically compared to the predictions of the so-called exponential ansatz (EA) and to the solution of the single nonlinear impurity model (SNI), where all nonlinearities of the lattice but the central one, where the breather is located, have been removed. In 1D, the exponential ansatz is more accurate than the SNI solution close to the anti-continuum limit, while the opposite result holds in higher dimensions. The excitation thresholds predicted by the SNI solution are in excellent agreement with the exact results but cannot be obtained analytically except in 1D. An EA approach to the SNI problem provides an approximate analytical solution that is asymptotically exact as n tends to infinity. But the EA result degrades as the dimension, d, increases. This is in contrast to the exact SNI solution which improves as n and/or d increase. Finally, in our investigation of the SNI problem we also prove a conjecture by Bustamante and Molina [C.A. Bustamante, M.I. Molina, Phys. Rev. B 62 (23) (2000) 15287] that the limiting value of the bound state energy is universal when n tends to infinity.     

SOME GENERAL EFFECTS OF STRONG HIGH-FREQUENCY EXCITATION: STIFFENING, BIASING AND SMOOTHENING

Mechanical high-frequency (HF) excitation provides a working principle behind many industrial and natural applications and phenomena. This paper concerns three particular effects of HF excitation, that may change the apparent characteristics of mechanical systems: (1) stiffening, by which the apparent linear stiffness associated with an equilibrium is changed, along with derived quantities such as stability and natural frequencies; (2) biasing by which the system is biased towards a particular state, static or dynamic, which does not exist or is unstable in the absence of the HF excitation; and (3) smoothening, referring to a tendency for discontinuities to be effectively “smeared out” by HF excitation. Illustrating first these effects for a few specific systems, analytical results are provided that quantify them for a quite general class of mechanical systems. This class covers systems that can be modelled by a finite number of second order ordinary differential equations, generally non-linear, with periodically oscillating excitation terms of high frequency and small amplitude. The results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems, for calculating effects for specific systems using well-defined formulas, and for possibly designing systems that display prescribed characteristics in the presence of HF excitation.     

Pairing vibrational and isospin rotational states in a particle number and isospin projected generator coordinate method

Pairing vibrational and isospin rotational states are described in different approximations based on particle number and isospin projected, proton-proton, neutron-neutron and proton-neutron pairing wave functions and on the generator coordinate method (GCM). The investigations are performed in models for which an exact group theoretical solution exists. It turns out that a particle number and isospin projection is essential to yield a good approximation to the ground state or isospin yrast state energies. For strong pairing correlations (pairing force constant equal to the single-particle level distance) isospin cranking (-ωT_x) yields with particle number projected pairing wave function also good agreement with the exact energies. GCM wave functions generated by particle number and isospin projected BCS functions with different amounts of pairing correlations yield for the lowest T = 0 and T = 2 states energies which are practically indistinguishable from the exact solutions. But even the second and third lowest energies of charge-symmetric states are still very reliable. Thus we conclude that also in realistic cases isospin rotational and pairing vibrational states may be described in the framework of the GCM method with isospin and particle number projected generating wave functions.     

An application of the theory of Bi-determinantal intrinsic states to28Si

For some 4n nuclei in the 2s?1d shell, Hartree-Fock (HF) theory with most two-body interactions predicts nearly degenerate prolate and oblate Intrinsic states. The spectrum ofJ ^π states obtained from these Intrinsic states by projection is too compressed in relation to the observed levels. For such systems with a two-fold degeneracy of HF solutions, a Bi-Determinantal Intrinsic state (BDIS) is the more apt variational state. The equations of the theory of BDIS, which were first derived by B. Bremond, are here simplified and cast in a form suitable for numerical solution. The transformation operators introduced by Bremond are given a suitable representation, compatible with the symmetries of these 4n nuclei, and an independent definition is then given of self-consistent (SC) Hamiltonians. These equations are then iteratively solved in a tripyl-SC way, by the method of diagonalizing the SC Hamiltonions, for the problematic nucleus²⁸Si. By angular momentum projection from this BDIS, the low-lying spectrum is obtained. The discrepancy between this projected spectrum and the observed levels suggests that²⁸Si is not describable by a BDIS. The present results are in reasonable agreement with those of other Multi-Determinantal Theories for this nucleus.     

Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact results allows us to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution can be identified with the classical charge distribution.Received: 24 October 2003, Published online: 6 January 2004PACS: 73.20.Qt Electron solids - 73.21.-b Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems     

Time-dependent Gutzwiller approximation for the Hubbard model

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.