Random-phase approximation and its extension for the O(2) anharmonic oscillator

We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations arround the static solution in the time-dependent Hartree-Bogoliubov equation. We draw the parallel between the two approaches.Received: 8 July 2003, Published online: 5 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 24.10.Cn Many-body theory     

Charge-changing transitions in an extended Lipkin-type model

Charge-changing transitions are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and, in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculation is obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the proton-neutron residual interaction, besides the proton-proton and neutron-neutron residual interactions, is taken into account in the model Hamiltonian. Received: 4 May 1998     

Shapes and β-decay in proton rich Ge,Se, Kr and Sr isotopes

We study ground states and β-decay properties of the proton rich isotope chains Ge, Se, Kr, and Sr. We use a deformed selfconsistent HF+RPA approach with density-dependent effective interactions of Skyrme type. We find that most of the isotopes present two HF minima corresponding to two different shapes. In addition to static quadrupole moments and other ground state band properties, we present results for Gamow Teller strength distributions, as well as for half-lives and summed strengths. The role of deformation is particularly emphasized.     

Competing phases in the cuprates: Charge vs spin order

We have investigated magnetic and charge instabilities of the cuprates within the Gutzwiller approximation RPA (GA+RPA). Interestingly, in GA the dressed Hubbard U is not a single parameter, but has different forms in the spin and charge responses, with distinct doping dependencies. While there are a number of competing magnetic instabilities for hole-doped cuprates, we fail to find any purely electronic charge density waves. The dominant magnetic instabilities are associated with ‘double nesting’, and the phase diagrams are material dependent, with LSCO differing from other cuprates.     

Extended RPA with ground-state correlations

We propose a time-independent method for finding a correlated ground state of an extended time-dependent Hartree-Fock theory, known as the time-dependent density matrix theory (TDDM). The correlated ground state is used to formulate the small amplitude limit of TDDM (STDDM) which is a version of extended RPA theories with ground-state correlations. To demonstrate the feasibility of the method, we calculate the ground state of ²² O and study the first 2 ⁺ state and its two-phonon states using STDDM.Received: 7 November 2003, Published online: 10 August 2004PACS: 21.10.Re Collective levels - 21.60.Jz Hartree-Fock and random-phase approximations - 27.30. + t      

Generalized random phase approximation and gauge theories

Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach to the Random Phase Approximation (RPA) well-known from nuclear physics and recently also employed in pion physics to general bosonic theories with a standard kinetic term. We focus especially on conservation laws, and how they are translated from the full to the approximated theories, demonstrate that the operator approach has the same spectrum as the RPA derived from the time-dependent variational principle, and give—for Yang-Mills theory—a discussion of the moment of inertia connected to the energy contribution of the zero modes to the RPA ground state energy. We also indicate a line of thought that might be useful to improve the results of the Random Phase Approximation.     

Skyrme Forces and Their Applications in Low Energy Nuclear Physics

This paper reviews the present status of Skyrme forces and their applications in the field of low energy nuclear physics as an effective nucleon-nucleon interaction. Their applications in the following five domains are presented:1). Hartree-Fock (HF), selfconsistent semiclassical (SCSC) calculations and nuclear ground state properties;2). random phase approximation (RPA), sum rule approach and properties of nuclear giant resonances;3). calculations of microscopic nucleon-nucleus optical potentials and related quantities;4). calculations of nucleus-nucleus optical potentials and fusion barriers;5). multifragmentation, liquid-gas phase transition and instability of hot/compressed nuclei.     

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.     

From sum rules to RPA: 3. Optical dipole response in metal clusters

The properties of plasmon resonances in metal clusters are computed within the random phase approximation (RPA), starting from the Kohn-Sham ground state within the jellium model. The paper aims at a systematic survey of the general trends with varying parameters such as electron number, angular momentum, Wigner-Seitz radius etc. To this end we exploit the flexibility of a particular RPA scheme which allows to switch easily between different levels of approximation.     

Structure of unstable nuclei near proton drip line

Gamov-Teller (GT) states in nuclei near the proton drip line are studied by using a microscopic Hartree-Fock (H-F) + Tamm-Dancoff approximation (TDA) (or random phase approximation (RPA)). The calculations predict that giant Gamow-Teller (GT) β-decays are possible for N=Z nuclei heavier than ₂₈⁵⁶Ni₂₈, carrying most of the sum rule strength. The amplitude of isospin T=1 admixed to the T=0 ground state in N=Z nuclei is also discussed in relation with Fermi β-decay sum rule. Finally, the shapes of unstable nuclei near the proton drip line are studied by using the finite-range droplet model (FRDM).     

铍原子基态交换-相关能的多体理论计算

到目前为止,几乎所有的关于原子基态的多体计算都是以Hartree-Fock(HF)模型为零级近似。本文将零级哈密顿量取为Hartree-Fock-Slater(HFS)型的,在双激发(两体)近似下,对Be原子基态交换-相关能进行了多体理论计算,得到了与实验及别的作者以HF模型为零级近似所作多体计算相符合的结果。计算表明,以HFS模型为零级近似,对闭合壳层原子基态亦可成功地进行多体计算。 关键词：     

Imaginary Eigenvalue Solution in RPA and Phase Transition

The phase transition (PT) of a many-particle system with a close-shell configuration,the stability of the Hartree-Fock(HF) solution and the random phase approximation (RPA) are studied by means of a generalized three-level solvable model.The question whether the occurrence of an imaginery eigenvalue solution in RPA (OISA) may be considered as a signature of PT is explored in some detail,It is found that there is no close relation between OISA and PT.Generally,OISA shows that RPA becomes poor.     

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2 ⁺ states in ²⁴O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2 ⁺ states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory.Received: 26 May 2003, Revised: 30 October 2003, Published online: 26 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Re Collective levels     

CORRELATION EFFECTS ON THE GROUNDSTATES OF THREE-ELECTRON QUANTUM DOTS IN A STRONG MAGNETIC FIELD

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Evaluation of entanglement measures in spin systems with the random phase approximation

We discuss a general formalism based on the mean field plus random phase approximation (RPA) for the evaluation of entanglement measures in the ground state of spin systems. The method provides a tractable scheme for determining the entanglement entropy as well as the negativity of finite subsystems, which becomes analytic in the case of systems with translational invariance, in one or D dimensions. The approach improves as the spin increases, and also as the interaction range or connectivity increases. Illustrative results for different types of entanglement entropies (single site, block and comb) in the ground state of a small spin lattice with ferromagnetic type XY couplings in a transverse field are shown and compared with the exact numerical result. Effects arising from symmetry breaking at the mean field level are also discussed.     

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.     

The photodetachment spectrum of OHF−: the influence of vibration at a transition state

New ab initio potential energy functions for collinear OHF^? and OHF have been used with time-dependent wavepacket studies in a simulation of the photodetachment spectrum of the OHF^? anion. Franck—Condon excitation of OHF^? lies within the transition state region for the bimolecular reaction F + OH ? O + HF on the lowest triplet surface. The branching ratios for fragmentation of the excited OHF are such that the peaks in this spectrum may each be correlated with dissociation to a single vibrational state of the O + HF(v) or OH(v) + F products. The possible influence of vibrational excitation of the anion has been explored also. This is predicted to lead to marked changes in the spectra. Experimental observations of such spectra could be used in refinement of the potential as could an experiment in which the electron kinetic energy is detected in coincidence with the vibrational states of the molecular products or with the kinetic energy of the atomic products. The calculations revealed a number of metastable resonances on the OHF surface, although these are all at higher energies than are relevant to the photodetachment spectrum from the ground state anion.     

聚二苯分子中基态结构的稳定性及各种凝聚相

本文利用统计物理中量子场论方法分析无限长聚二苯分子(Polyacenacene)基态结构的稳定性问题。在无规周相近似(RPA)范围内得到各种有序相:电荷密度波(CDW)、自旋密度波(SDW)及超导相存在的可能性,指出发生这些相变的条件。从而从理论上表明,聚二苯分子在适当条件下有可能成为一种有希望的高温超导体。     

Effect of ground state correlations on the imaginary part of the optical-model potential

The effect of the ground state correlations on the imaginary part of the nucleon-nucleus optical-model potential is qualitatively discussed within the random phase approximation (RPA). We also investigate the effect of terms of order higher than two in the microscopic nucleon-nucleus interaction. A rough estimate of both effects is given for the case K³⁹+p.     

Schematicity and ground state correlations in the lead isotopes

The relationship between collectivity and ground state correlations is analyzed for the single closed shell lead isotopes. The effects of the schematic approximation are discussed, within the framework of both the quasiparticle Random Phase Approximation and the quasiparticle Tamm-Dancoff approach. The consistency of the RPA is investigated.