Quenching of the mass operator associated with collective states in many-body systems

Giant resonances are understood as superposition of particle-hole excitations. The empirical systematics indicates that the associated spreading widths are considerably smaller than the sum of typical widths of single-particle and single-hole states, and that the centroid energy is in good agreement with the RPA predictions. These results imply a destructive interference between the different contributions to the mass operator associated with collective vibrations. We study the properties of the mechanism responsible for this quenching by inspecting contributions to the mass operator in the semiclassical limit of large single-particle angular momenta.     

The Heisenberg equation for phonon operators and soliton solutions in nonlinear lattices

The Heisenberg equation for phonon operators in nonlinear lattices is derived establishing the interaction Hamiltonian included higher powers of particle-hole pairs in nonlinear lattices. A phonon operator consists of a particle-hole pair in the harmonic potential approximation in the two band model; it represents an up or down transition of atoms between two levels. Applying the boson transformation method to the Heisenberg equation for phonon operators, we obtain the classical dynamical equation and a linear equation with the self-consistent potential created by the extended objects in nonlinear lattices. The boson transformation leads to soliton solutions in the long wavelength limit. The linear equation can be used to obtain scattering states, bound states and translational modes for phonons.     

Negative-parity spectra for mass-18 nuclei in the dynamic-interaction propagator approach

The energy spectra and two-particle strengths of negative-parity states in mass-18 nuclei are calculated by using a Green-function formulation which includes energy-dependent two-particle interactions. The energy dependence is induced by the dynamic exchange of the octupole phonon which appears at 6.13 MeV in ¹⁶O. This state is described within a normal static particle-hole RPA. The two-body interaction parameters are chosen to provide the correct phonon energy and reasonable negative parity mass-17 and positive-parity mass-18 spectra. The negative-parity states are then calculated in a parameter-free way. In order to avoid redundant solutions or ghosts, the fermion lines must be dressed in a way consistent with the phonon exchange.     

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.     

Generalised quartet model for particle-hole excitations across major shells

The schematic quartet model of Arima et al. is generalised to include any number of particle-hole excitations. The assumption of constancy of particle-hole matrix elements with mass number is examined in the deformed-oscillator model and shown to be poor in certain cases. A revised picture for particle-hole excitations shows smoother trends than with the schematic model. Comparison with the Zamick model yields greater insight into the structure of two-particle excited states.     

A quantum field theory of lattice dynamics at finite temperature

A quantum field theoretical treatment of three-dimensional cubic crystals at finite temperature is presented from the view-point of the spontaneous breakdown of the spatial translational invariance using thermo field theory. The effective interaction Hamiltonian is constructed by taking into account the dynamical map of the molecular density operator which is obtained from the Ward-Takahashi relations. The acoustic phonons are expected to be the excitation of particle-hole pairs. The conventional secular equation for the lattice vibrations is obtained by neglecting some quantum effects in the Bethe-Salpeter equation for the molecular density fluctuations. The phonon spectra, the phonon propagators and the dynamical map of the molecular density operator are calculated at finite temperature.     

A quantum field theory of lattice dynamics and melting in fcc crystals

Phonons in crystals are constructed by particle-hole excitations of ion cores. The Ward-Takahashi relations play an essential role in constructing the lattice dynamics and determining the melting temperature. The phonon dispersion and the melting temperature in fcc crystals are presented. In principle, our theory covers metallic, covalent and molecular crystals.     

A generalized RPA theory of the nuclear response function

A new method of calculating the response function is proposed. The new method gives the response which is explicitly a generalization of the RPA response in a perturbative sense.When we calculate the transition amplitude of a one-body operator from the ground state to a particle-hole (p-h) state, the new response function provides all the second-order effects in addition to the first-order ones which can be obtained in the RPA theory. The new response function is obtained by the following procedure. Firstly, we consider the second RPA theory which is a generalization of the usual RPA theory. It is found that the second RPA misses some of the second-order effects. Secondly, we formulate a modified second RPA equation from the equation of motion of the operators, and then derive the p-h response function from it. It is found that the newly derived p-h response function is obtained by adding new terms to the self-energy of the p-h response function derived from the second RPA theory. Lastly, we introducd vertex functions which take into account the transitions from a particle (hole) state to a particle (hole) state. Note that the p-h response function deals with only the transition amplitudes from a particle (hole) state to a hole (particle) state.     

Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained.This new scheme is applied to ⁵⁶Ni (⁵⁶Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2⁺ eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.     

Self-screening of the particle-hole interaction and core polarization of the effective two-particle interaction

The diagrams of the Tamm-Dancoff and random-phase approximations (TDA and RPA) have been summed to calculate the core polarization of the effective interaction between two nucleons in the 1s0d and Ip0f shells. The large core-polarization corrections obtained in the TDA and particularly the RPA are strongly reduced when the self-screening corrections to the particle-hole and ground-state correlation vertices are included. The screening corrections serve to suppress the collectivity of the core phonons and in particular stabilize the isoscalar monopole phonon in ⁴⁰Ca against collapse. When screening is included the TDA and RPA give core-polarization corrections which are similar in magnitude and in many cases lead to good agreement with experiment. Because of neglected effects and other uncertainties the qualitative rather than the quantitative features of the results are stressed.     

Minimal excitation states of electrons in one-dimensional wires

A strategy is proposed to excite particles from a Fermi sea in a noise-free fashion by electromagnetic pulses with realistic parameters. We show that by using quantized pulses of simple form one can suppress the particle-hole pairs which are created by a generic excitation. The resulting many-body states are characterized by one or several particles excited above the Fermi surface accompanied by no disturbance below it. These excitations carry charge which is integer for noninteracting electron gas and fractional for Luttinger liquid. The operator algebra describing these excitations is derived, and a method of their detection which relies on noise measurement is proposed.     

Spin-density response function in a 2D electron system under a magnetic field

We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.     

Particle-hole bound states of dipolar molecules in an optical lattice

We investigate the particle-hole pair excitations of dipolar molecules in an optical lattice, which can be described with an extended Bose-Hubbard model. For strong enough dipole-dipole interaction, the particle-hole pair excitations can form bound states in one and two dimensions. With decreasing dipole-dipole interaction, the energies of the bound states increase and merge into the particle-hole continuous spectrum gradually. The existence regions, the energy spectra and the wave functions of the bound states are carefully studied and the symmetries of the bound states are analyzed with group theory. For a given dipole-dipole interaction, the number of bound states varies in momentum space and a number distribution of the bound states is illustrated. We also discuss how to observe these bound states in future experiments.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Zero-temperature superfluid extension of rpa description for wall dissipation

The quasi-particle RPA is used to study the effects of nuclear superfluidity upon wall dissipation at zero-temperature. Since no gas of quasi-particle excitations exists in this temperature limit, nuclear dissipation proceeds through the breaking of nucleonic Cooper pairs out of the superfluidic condensate due to the very motion of the wall. There is a sudden onset of this process to values larger than the wall-formula value for phonon energies ⩾2 × the gap parameter.     

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.     

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.     

Conserving RPA and the response of 48Ca

The connection between the single-particle self-energy and the corresponding conserving particle-hole (ph) interaction, discussed long ago by Kadanoff and Baym, is employed to study the response of ⁴⁸Ca. Second order self-energy contributions are taken into account in the construction of the energy dependent ph interaction. From this perspective it is possible to make contact with other approaches which also aim to incorporate the coupling to 2p2h excitations within the RPA framework. The method is used to study both the discrete low-energy states as well as the giant resonances in both ⁴⁸Ca and ⁴⁸Sc using a realistic G matrix interaction based on meson exchange. The calculated strength distribution compares favorably with experiment but the strength below 15 MeV is still somewhat too large as compared to experiment for all types of excitations. The quenching of magnetic and Gamow-Teller strength due to 2p2h admixture amounts to about 30%.