Effect of tensor correlations on Gamow–Teller states in Zr and Pb

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree–Fock plus Random Phase Approximation (HF + RPA) model. The Gamow–Teller (GT) strength function of ⁹⁰Zr and ²⁰⁸Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA.     

An RPA model for the description of one-nucleon emission processes and application to 16O(γ, N) reactions

A coordinate space RPA formalism is proposed to handle one-nucleon emission processes in a self-consistent way. A method is outlined to solve the RPA equations so obtained for the whole class of rotationally invariant effective interactions, including those having a velocity dependence. The method is used to study ¹⁶O(γ, N) reactions with Skyrme-type effective interactions. The use of the long-wavelength approximation (LWA) when handling reactions of this type at medium energies, is criticized. Different alternative forms for the electric transition operators are used, applying Siegert's theorem or not, and it is shown that at higher momentum transfer, the obtained results are strongly sensitive to it. We emphasize that especially beyond energy regions where the LWA is valid, the use of Siegert's theorem should be carefully examined.     

The breathing mode and the nuclear surface

The role of the nuclear surface in the breathing mode of nuclei is analyzed. We discuss a simple model in which the density varies according to a scaling of the coordinates. We show that this model reproduces accurately the results of microscopic calculations in heavy nuclei, and we use it to estimate the contribution of the surface to the effective compression modulus of semi-infinite nuclear matter. The calculation is performed in the framework of an extended Thomas-Fermi approximation and using several effective interactions. It is shown that the surface energy is maximum with respect to variations of the density around saturation density. The reduction of the effective compression modulus due to the surface turns to be proportional to the bulk compression modulus. The magnitude of the effect is compared with results of RPA calculations. Other contributions to the effective compression modulus of finite nuclei are also discussed.     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Nuclear Spin Transverse Response Function

The spin transverse response functions for ⁴⁰Ca and ¹²C in different approximations have been calculated.By using the coupled RPA equations for polarization propagator including the delta degree of freedom,the influence of the delta on the response function has been investigated.The results show that they are reduced explicitly.Introducing the energy dependent effective nucleon mass,which embodies the manybody ef ects,the satisfactory results are obtained.     

The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

Properties of nuclear matter using the velocity-dependent effective potential ofs-wave interaction

Two forms of a velocity-dependent effective potential are used. The binding energy and the incompressibility of the nuclear matter are calculated. These are found to be in a good agreement with those obtained by others and with the experimental results. The single-particle potential, the effective massM ^* and the nuclear surface energy are also discussed and compared with those obtained by the others.     

Nuclear matter and neutron star properties with the extendedNambu-Jona-Lasinio model

An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.     

Random phase approximation and extensions applied to a bosonic field theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the ϕ⁴ theory in 1 + 1 dimensions. We show that the standard RPA approach leads to an instability which can be removed when going to a superior version, i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many-electron problem to calculate the correlation energy and the RPA effective potential. Received: 18 February 2002 / Accepted: 8 May 2002     

Local forces and the 16O reaction matrix

It is demonstrated that the G-matrix elements obtained from a solution of the Bethe-Goldstone equation for finite nuclei and a given NN interaction can be very well approximated by an effective local interaction. The local approximation is determined from the reaction matrix in nuclear matter using the same realistic NN interaction. The comparison is performed on the level of RPA calculations for the excited states in ¹⁶O. Very good agreement is found between the results for both interactions except for scalar-isoscalar states. It is shown that this is due to the energy dependence of the reaction matrix and can be cured rather easily. A comparison with experiment for isovector states is very satisfactory.     

Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.     

The Random Phase Approximation: Its role in restoring symmetries lacking in the Hartree-Fock approximation

Hartree-Fock wave-functions often lack symmetries possessed by the Hamiltonian. It is often said that the Random Phase Approximation (RPA) restores the missing symmtries. Since the RPA does not readily lead to explicit wave-functions, it is not a trivial matter to verify this assertion. We analyse the situation, and show that, while RPA restores symmetry in some respects, it does not do so completely. Besides the normal RPA, we discuss the generalisation of RPA that describes modes in isobars of the given nucleus. This is needed to enable us to discuss the case of isospin symmetry, which is analysed in detail.     

Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuouslybroken symmetry, this being the main focus of the present article. Correlations beyondstandard RPA are summed up correcting for the quasi-boson approximation in standard RPA.Desirable properties of standard RPA such as fulfillment of energy weighted sum rule andappearance of Goldstone (zero) modes are kept. We show theoretically and, for a modelcase, numerically that, indeed, SCRPA maintains all properties of standard RPA forpractically all situations of spontaneously broken symmetries. A simpler approximate formof SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equationsare first outlined as an eigenvalue problem, but it is also shown how an equivalent manybody Green’s function approach can be formulated.     

Superfluid nuclear matter in BCS theory and beyond

Medium polarization effects are studied for ¹S₀ pairing in nuclear matter within BHF approach. The screening potential is calculated in the RPA limit, suitably renormalized to cure the low density mechanical instability of nuclear matter. The self-energy corrections are consistently included resulting in a strong     

Auto-tuning of a two-degree-of-freedom rotational pendulum absorber

A dynamic vibration absorber is effective in suppressing harmonic excitation by tuning its natural frequency to match the excitation frequency. The rotational pendulum absorber (RPA) has a wide-range of natural frequencies that are continuously tunable by setting a suitable rotational speed. In this paper it is shown how to automatically tune the rotational speed of a two-degree-of-freedom RPA by detecting the phase between the vibration of the primary structure and that of the RPA. For this purpose the speed response of the RPA is introduced in addition to the frequency response. It is seen that if the excitation frequency is above a critical value dependent on the parameters of the RPA, the second vibration mode of the RPA is effective, allowing a relatively low rotational speed for the pendulums. The speed tuning algorithm is tested on a flexible plate that is subject to excitations of around 80 Hz, which do not generate visible oscillations but emit audible noise instead. Experimental results confirm the noise-level reduction effect of the RPA.     

Exchange and correlation effects in a semiconductor quantum-well wire

The exchange and correlation effects of a quasi-one-dimensional electron gas are investigated by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs rectangular quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The plasmon dispersion relation and structure factor are calculated as a function of electron density and thickness of the wire. Results for the total energy per electron including kinetic, exchange and correlation energies and electron effective mass are presented. The Hartree-Fock and the random-phase approximation (RPA) results are also presented for comparison. We have found that exchange and correlation effects are more evident in wires of reduced dimensions.