Assumption Of Weak Coupling Research Articles

Density functional theory for a model of nonuniform liquid metal in partially ionized states

The problem of the electronic, ionic and atomic density profiles in a nonuniform liquid metal which can locally exist in partially ionized states is examined using the density functional formalism. Ions and electrons are allowed to bind into atoms through a «reaction» governed by the mass action law. Formally exact equations for the density profiles are given in terms of the inverse response matrix of the nonuniform system, which consists of two terms: the first corresponding to to a mixture of ions, electrons and structureless atoms and the other to the atomic internal degrees of freedom. Approximate schemes are proposed for both contributions, stressing, in partieular, i) how ionization of the atoms arises with increasing density and the relation with Mott’s criterion for the metal-insulator transition, and ii) the usefulness of a weak-coupling assumption for interspecies correlations. This formalism used together with properly parametrized trial functions for the density profiles should be particularly useful for studying the liquid-vapour interface of alkali metals.

The heavy-ion potential and its increasing transparency at intermediate energies

Starting from the Reid soft-core potential and the collision of two nuclear matters we solve the Bethe-Goldstone equation for the complex reaction matrix. The local density approximation including a finite range correction enables us to calculate the volume part of the optical potential between two heavy ions up to 100 MeV per nucleon. The surface contributions are calculated from the second-order Feshbach expression including low- and high-lying collective states. The data for 16O- 16O are nicely reproduced including the reduction of the reaction cross section above 20 to 30 MeV per nucleon. The maximum of the reaction cross section at 10–20 MeV per nucleon is essentially due to the surface contributions. The description of the 12C- 12C data is not so satisfactory due to the assumption of weak coupling and the neglect of some rotational excitations

Cosmological baryon production versus intermediate mass scales?

We analyze the conditions for a late cosmological matter-antimatter asymmetry production at some intermediate energy scale ∼10 6 GeV. We envisage a new class of models where the compatibility between enough βB production and decoupling of subsequent B violating interactions at T ∼ 10 6GeV is automatically achieved through the assumption of weak coupling between B nonconserving particles and ordinary matter. Possible consequences for nucleon stability are analyzed. The mechanism could be interesting for dynamical schemes (technicolor, composite models) where B production seems very difficult to be obtained before T ∼ Λ H. Furthermore a late origin of matter-antimatter asymmetry could be essential in the resolution of some cosmological puzzles, such as the excess of monopole density.

Classical dynamics of triatomic systems: Energized harmonic molecules

The dynamical assumptions underlying the Slater and RRK classical-mechanical theories of unimolecular reaction rates are investigated. The predictions of these theories for several nonlinear, triatomic, harmonically bonded molecular models are compared with the results obtained from the integration of the classical equations of motion. The accuracy of the small-vibration and weak-coupling assumptions are found to break down at energies above about one-quarter of a bond dissociation energy. Nonetheless, the small-vibration approximation predicts reaction frequencies in good agreement with the exact results for the models. The effects of rotation on intramolecular energy exchange are examined and found to be significant.

Analysis of the Dupree-Weinstock theory of turbulent plasma in a magnetic field

The Dupree-Weinstock model which describes the plasma turbulence is analysed with an applied strong magnetic field. The conservation of energy and the validity of the weak coupling assumption are investigated. The theory is applied to the particular case of an ion acoustic turbulence.

Connected kernel methods in nuclear reactions: (III). Effective interactions

The recently derived connected kernel equation (CKE) for N-body scattering operators is applied to direct nuclear reactions. A spectral representation is derived for the kernel of the CKE in order to obtain manageable approximations. This allows the kernel to be split into orders corresponding to the propagation of different numbers of bound clusters. By formally solving one part of the kernel at a time, the CKE is written as a hierarchy of nested equations in increasingly many variables. The first equation of this hierarchy is a set of coupled channel Lippmann-Schwinger equations coupling together all two-cluster channels. These equations reduce to the usual coupled channel equations for inelastic scattering and to the coupled channel Born approximation for rearrangement reactions when weak coupling assumptions are made. The second equation of the hierarchy is a two-variable integral equation for the effective interactions appearing in the coupled channel equations. The driving terms and kernel of this integral equation are obtained from the third equation of the hierarchy which is a three-variable integral equation and so forth. The use of the spectral expansion results in a renormalized theory in the sense that the bound state and reaction problems are separated. This permits the inclusion of nuclear models in the theory in a straightforward manner. The hierarchy is applied to a particular example, that of nucleon-nucleus scattering. For this case the hierarchy is truncated at the level allowing no more than three clusters in the continuum. By suppressing exchange and keeping only one-particle transfer and single-nucléon knockout channels, a set of equations for the optical potentials and transfer operators is obtained. These equations provide a three-body treatment of the single scattering approximation to the optical potential. Iteration of the equations yields the usual single scattering approximation in first order including three-body off-shell effects. After suppression of Fermi motion and off-shell effects, the standard impulse approximation is recovered. Modifications of the method for other cases are discussed and other possible applications suggested.

The role of the 4p-4h excitations in the microscopic description of56Ni

An effective Hamiltonian for shell model calculations in the middle of the 2p-1f shell is microscopically deduced from the Tabakin nucleon-nucleon potential. Its matrix elements are tabulated. Such a Hamiltonian is applied to the description of56Ni. All configurations up to four particle-hole excitations are considered and a weak-coupling assumption is used to select the relevant shell model states. The weakcoupling assumption turns out to be very effective in reducing the dimensions of the secular matrices. No phenomenological parameter is used. Only a small adjustment of the 1f2/7-2p2/3 gap with respect to its theoretical value is allowed. The adopted value is 2.65 MeV. The inclusion of the 4p-4h configurations is essential to get a reasonable agreement between the theoretical and experimental spectra of56Ni. The ground state turns out to be 61% closed and 36% 2p-2h, while the excited states are almost pure 4p-4h.

Theory of Physisorption: He on Metals

The attractive and repulsive contributions to the physisorption interaction energy are derived from the assumption of weak coupling between an atom and a metal surface. Results for the physical adsorption of He atoms indicate that an accurate determination of the dynamic polarizability is essential in calculations of the attractive interaction energy using a local-dielectric-function formalism. The major contribution to the physisorption interaction is the van der Waals energy, so that the physisorption energy curve is largely temperature independent. The repulsive energy is evaluated via the density-functional method. The equilibrium distances of the atom are a monotonically increasing function of the metallic-electron density. For high electron densities the binding energy increases monotonically. Values for the adsorption energies of He on various metals are in good agreement with available experimental results.

The energy dependence of [formula omitted] for 233U, 235U and 239Pu below 5·0 MeV

Measurements were made of the energy dependence of v p for neutron induced fission of 233U from thermal to 2·0 MeV. An analysis has been made of all existing data below 5 MeV for 233U, 235U and 239Pu It is observed from this analysis that the energy dependence of v v for all three nuclei may be characterized by a two line dependence in which the change of slope occurs at the pairing energy. The nature of the v v(E n) dependence is explained in terms of the double-humped fission barrier, and is consistent with the adiabatic assumption of weak coupling of the collective degrees of freedom at the saddle point to the nuclear degrees of freedom at scission.

Zero sound in anisotropic metals

The Gor'kov-Dzyaloshinskii theory of zero sound in anisotropic metals is generalized, and applied to specific metals. The main generalizations are: (a) sufficient conditions for the existence of zero sound are derived without the assumption of weak coupling; (b) examples are discussed in which these conditions are satisfied even when the propagation vector does not lie along or close to a symmetry axis. A survey of metallic Fermi surfaces indicates that zero sound may be possible in the noble metals along directions close to the [111] direction, and in beryllium and graphite along directions close to the c axis. It may also be possible in the semimetal bismuth (and perhaps antimony and arsenic) along certain nonsymmetry directions. In all these cases sufficient conditions on the Landau F-function are derived for zero sound modes to exist at infrared frequencies (and, in some cases, at radio frequencies.) The conditions can be satisfied in the weak coupling limit, provided F has the appropriate sign. Unfortunately this is beyond reliable theoretical calculation, and the final question of whether the modes exist is best settled by experiment.

Higher order effects in the master equation for coupled systems

The usual derivations of the master equation for coupled systems such as the laser make an assumption of weak coupling both for the coupling of the components to their heat baths and for the internal coupling between the components. It is this second condition that we wish to relax. In the usual derivation of the irreversible part of the master equation the approximation is made that the density operator for the coupled system factorizes into a product of the density operators for the two components. However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid. To illustrate how the irreversible part of the master equation may be derived without making the factorization ansatz we consider the case of two coupled boson fields. Our derivation leads to additional terms in the usual master equation arising from correlations between the heat baths introduced by the coupling. This modified master equation yields the correct stationary solution for the density operator of the coupled system, whereas the usual master equation leads to a stationary solution for the density operator correct for the free components only.

Order—Disorder Phenomena. I. Instability and Hysteresis in an Ising Model Near Its Critical Point

The mechanical behavior of a system near a cooperative order—disorder transition point is discussed in terms of an Ising model for a set of spins located on mass particles which form a compressible lattice. With the assumption of weak coupling between the lattice and spin systems, it is shown that this Ising model is unstable in the immediate vicinity of its critical point and undergoes a first-order transition. In addition, many properties should show hysteresis in the critical region. These general conclusions are illustrated by several two-dimensional examples.

Molecular Excitations in Liquid Helium

CELL theories of liquid helium have been proposed by several investigators1. They distinguish successfully between the statistics of helium-3 and helium-4 but are unable to reconcile the measured energy gap with the distance of the observed nearest neighbour. Co-operative motion of the cells accounts without difficulty for the phonon spectrum, but the assumption of weak coupling between the diatomic rotors and the acoustical vibrations is inadequate. The analysis recorded here is a new attack on the nature of the excitations which account for the normal component.

Non perturbation treatment of scattering in quantum field theory

A sequence of approximations to theS andK operators is obtained by means of a variational method. The form of the approximations is such that discussions on general questions like convergence and renormalization become possible without any weak coupling assumption. The method is particularly suited for the study of two body collision problems: in this case the difficulties in the treatment of the higher order approximations are reduced to the problem of evaluating the perturbationS-matrix elements.