Dielectric constant of polarizable,nonpolar fluids and suspensions

We study the dielectric constant of a polarizable, nonpolar fluid or suspension of spherical particles by use of a renormalized cluster expansion. The particles may have induced multipole moments of any order. We show that the Clausius-Mossotti formula results from a virtual overlap contribution. The corrections to the Clausius-Mossotti formula are expressed with the aid of a cluster expansion. The integrands of the cluster integrals are expressed in terms of two-body nodal connectors which incorporate all reflections between a pair of particles. We study the two- and three-body cluster integrals in some detail and show how these are related to the dielectric virial expansion and to the first term of the Kirkwood-Yvon expansion.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

Multipole contributions to the effective dielectric constant of suspensions of spheres

We study multipole contributions to the effective dielectric constant of dilute suspensions of uniform spheres. It is shown that for frequencies near the plasma resoance multipole contributions are negligible in comparison with the dipole contributions. Outside resoance multipolar corrections to the Clausius-Mossotti formula are of the same order of magnitude as the dipolar ones. We argue that in resonance the dipole approximation should be valid also for more complicated sphere models.     

Eikonal expansion

An eikonal expansion of the potential scattering T matrix is evaluated, without approximation, through third order in the inverse momentum. Based on the results, their correspondence with the WKB approximation and a new statement of the unitarity constraint, we propose a sequence of four approximations to the exact impact parameter (Fourier-Bessel) representation of the scattering matrix. The sequence consists of the Glauber approximation and three systematic corrections to the Glauber approximation. The corrections are analytic functions of the impact parameter for Yukawa and Gaussian potentials; they vanish for a Coulomb potential.The sequence of eikonal amplitudes is convergent at high energy and is clearly established for small momentum transfer. Validity for all momentum transfer is conjectured based on systematic cancellation, explicitly verified through third order in the expansion, of momentum transfer dependence in the eikonal impact parameter representation. Such cancellation is shown to occur in the explicit construction of the eikonal expansion of the second Born amplitude for a Yukawa potential.Numerical tests of the sequence of eikonal amplitudes show systematic increase of the angular range of validity by comparison with partial wave results for continuous potentials; the theory is not convergent for discontinuous potentials.The WKB phase shift formula is shown to produce a systematic connection with eikonal expansion results. From this we deduce a generating function for the eikonal phase corrections of arbitrary order and also conjecture a sum of the eikonal expansion valid in the limit of high energy and arbitrary potential strength.     

Multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres

We study multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres with identical uniform dielectric constant embedded in a uniform background. The first few moments of the spectral density occurring in the Bergman representation are evaluated exactly to second order in the volume fraction. We present numerical results for a log-normal distribution of sphere radii.     

Theory of cyclotron resonance halfwidth for electrons scattered by impurities and phonons

A general theory of the cyclotron resonance halfwidth for electrons scattered by impurities and phonons is developed on the basis of the proper connected diagram expansion of the current-correlation-function formula for the dynamic conductivity. The theory is applied to the cases of Ge samples at extremely high magnetic fields and different temperatures. The usual form of Matthiessen's rule Γ = Γ₁ + Γ₂ + …, where Γ and Γ_j are the total and component energy-dependent resonance widths, is valid only if the component widths Γ_j computed separately for each cause of scattering depend linearly on the densities of scatterers. The resonance width Γ_I due to the charged impurities at very low electron densities ($\text{\$}\text{?}$10¹² cm^?3) and at very low temperatures is known to vary in proportion to the square-root of the impurity density. Large deviations from the Matthiessen's rule occur in such a case. The theory is in good quantitative agreement with currently available experimental data. In order to test the generalized form of Matthiessen's rule, however, the high-field resonance experiments around 15 K is desirable where both phonon and impurity scatterings contribute in a comparable manner.     

Quantum-statistical conductance theory of nonideal plasmas by use of the force-force correlation function method

Using the formalism of force-force correlation functions developed recently, the Spitzer formula for the conductance is generalized by taking into account the following effects: (1) dynamical screening; (2) ion-ion correlations by the ion structure factor; (3) deviations from Coulomb's interaction law; (4) influence of the Debye-Onsager relaxation effect; (5) quantum effects.It is shown that all these effects decrease the conductance in comparison with the values predicted by the Spitzer theory and lead to a more reasonable agreement with the experimental data in the region μ = e²/r_DkT ? 1 (r_D - Debye radius).Electron-electron interactions are treated by a systematic perturbative expansion of the force-force correlation function with the help of the Matsubara Green's function technique.     

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two-component Fermi gas as a function of the number of particles, angular momentum, and excitation energy. The result includes smooth low-energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy-Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low-lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.     

Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.     

Energy equation of state' of high-density plasmas

The equation of state for fully degenerate high-density plasmas is derived using a modified Thomas-Fermi model. Although the classical TF model is adequate to obtain the energy of an atom at very high densities it fails for low densities. A new version of this model for plasmas is presented which addresses this deficiency by including near-nucleus, exchange and correlation corrections. An analytic formula for the equation of stateE(n _i ) is obtained, valid for all densities (n _i <10²⁶ cm^–3). For low densities, Hartree-Fock results are reproduced with less than 1% error, and the classical result is recovered in the high-density limit.     

Modified expression for permeability tensor in partially magnetised ferrites

Green and Sandy's experimental results [IEEE Trans Microwave Theory Tech.MTT-22 641 (1974)] for μ', the permeability tensor element of the partially magnetised ferrites, show systematic discrepancies with the values computed by them from their formula for large values of the normalised average magnetisation. It has been shown that a good agreement is possible if Schlömann's expression for μ'₀ occuring in this formula is replaced by another expression originally given by Sandy provided the average demagnetisation factor N of the domains is taken as a linear function of the magnetisation. This modification is also able to interpret the author's experimental results on Magneto-Microwave Kerr Effect successfully, which are not at all explained by the original Green and Sandy formula.     

Ensemble Dependence of Fluctuations: Canonical Microcanonical Equivalence of Ensembles

We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures and the first order corrections. We are particularly interested in extensive observables, like the total kinetic energy. This result is obtained by proving an Edgeworth expansion for the local central limit theorem for the energy in the canonical measure, and a corresponding local large deviations expansion. As an application we prove a formula due to Lebowitz–Percus–Verlet that express the asymptotic microcanonical variance of the kinetic energy in terms of the heat capacity.     

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula,this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container.The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed.It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy.It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects,such as the nonextensivity of the system,the anisotropy of the pressure,and so on.     

The effective dielectric constant of a dispersion of clustering spheres

If one measures the dielectric constant of a water in oil microemulsion the large increase of this dielectric constant both as function of the temperature as well as a function of the volume fraction of water suggests that the water droplets will bind together in clusters. In order to analyse this suggestion in more detail we derive a systematic expansion of the Clausius-Mossotti function in terms of integrals over products of excess cluster polarizabilities and correlation functions. It is found that the excess polarizability of a cluster of spherical droplets is zero except when the spheres almost touch each other. Crucial for this property is the fact that the water spheres are conducting or if they are not conducting have a dielectric constant much larger than the dielectric constant of oil. The large increase of the dielectric constant is a consequence of the increase of the number of bound clusters. An explicit formula is given for the resulting temperature and volume fraction dependence of the dielectric constant.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Antihydrogen from antiproton-positronium collisions

We survey the progress made towards the production of antihydrogen by antiproton-positronium collisions as of June 1995. The tasks remaining before such an experiment can be attempted are outlined. Some comments are made concerning the effects of the intended closure of the Low Energy Antiproton Ring (LEAR) at the end of 1996. We conclude with a personal account of the development of, in particular, the Aarhus—UCL collaboration and some memories of Bernie Deutch.     

Validity of the semiclassical periodic orbit approximation in the two- and three-disk problems

The high-lying resonances in the quantum mechanical scattering problem of a point particle from two or three equally sized (and spaced) circular hard disks in the two-dimensional plane are predicted quite well by the classical cycle expansion. There are, however, noticeable deviations for the lowest resonances. Therefore, the leading corrections from creeping paths to the cycle expansion in the two-disk scattering problem are constructed. Generalizations to the three-disk problem are indicated. The size of the corrections are estimated. They are shown to be too small to account for the deviations mentioned above. Finally, arguments are given that, for the two- and three-disk problem, the semiclassical predictions of the low-lying resonance poles are bound to fail.     

Rotating wave approximation: systematic expansion and application to coupled spin pairs

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments. Received 2 September 1998     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.     

A relativistic quark model for baryons

The Bethe-Salpeter equation for the relativistic three quark bound state is solved for an instantaneous interaction in the ladder approximation. The particular solution obtained is valid for simple potentials in both the weak and strong binding situations. The general method for calculating matrix elements for the interaction of the bound state with an external electromagnetic field is presented. Particular attention is paid to the emergence of the nonrelativistic quark model interaction as the lowest order approximation in a perturbative expansion in the inverse quark mass. Relativistic corrections to this approximation are investigated, and their importance is seen to depend on the quark mass. For light quarks these corrections can be large, and to reproduce the proton magnetic moment, for instance, a substantial anomalous moment is necessary. The model has several encouraging features. The form factors with a harmonic potential have an asymptotic k^?2 behavior, and the relativistic corrections to the SU(6) results for the form factors are of the correct order of magnitude.