Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.

A dynamical gluon mass solution in Mandelstam's approximation

We discuss the pure gauge Schwinger-Dyson equation for the gluon propagator in the Landau gauge within an approximation proposed by Mandelstam many years ago. We show that a dynamical gluon mass arises as a solution. This solution is obtained numerically in the full range of momenta that we have considered without the introduction of any ansatz or asymptotic expression in the infrared region. The vertex function that we use follows a prescription formulated by Cornwall to determine the existence of a dynamical gluon mass in the light cone gauge. The renormalization procedure differs from the one proposed by Mandelstam and allows for the possibility of a dynamical gluon mass. Some of the properties of this solution, such as its dependence on A(QCD) and its perturbative scaling behavior are also discussed.

Ps-He scattering using the three-state positronium close-coupling approximation

A three-state target elastic positronium close-coupling approximation (CCA) is employed to investigate Ps-He scattering in the energy range 0-200 eV with and without electron exchange. Low-lying phase shifts below the first excitation threshold and the total integrated cross sections using both the models are reported. Estimation of integrated excitation cross sections for Ps(1s --> 2s) and Ps(1s --> 2p) using CCA are presented for the first time. The present total cross sections are in good agreement with the measured data in the incident Ps energy range 20-30 eV.

Weak-field approximation of effective gravitational theory with local Galilean invariance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ON NUCLEON-NUCLEUS SCATTERING AND THE RELATIVISTIC EIKONAL APPROXIMATION

We introduce a generalization of the relativistic eikonal amplitude originally developed to describe elastic scattering between structureless particles. The coherent and incoherent proton-nucleus scattering processes are analysed and closed-form expressions for elastic and inelastic amplitudes are derived. In particular, for the incoherent case, an energy-conserving version of Glauber's theory is obtained.

Positronium-alkali-ion scattering in the close-coupling approximation

We present results for low- and medium-energy elastic and capture cross sections for positronium-atom-alkali-ion scattering using the coupled static close-coupling approximation.

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

ON THE INDEPENDENT-PARTICLE APPROXIMATION OF GAUGE-THEORIES - A SIMPLE EXAMPLE

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1 + 1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

Ps-H scattering using the three-state positronium close-coupling approximation

Positronium scattering off a hydrogen target has been studied employing a three-state positronium model close-coupling approximation (CCA) with and without electron exchange. Elastic, excitation and quenching cross sections are reported at low and medium energies. The effect of electron exchange is found to be significant at low energies. The ratio of quenching to the total cross section (the conversion ratio) approaches the value of 0.25 with increase of energy, as expected.

Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

Integrable approximation to the overlap of resonances

We study the interaction of resonances with the same order in families of integrable Hamiltonian systems. This can occur when the unperturbed Hamiltonian is at least cubic in the actions. An integrable perturbation coupling the action-angle variables leads to the disappearance of an island through the coalescence of stable and unstable periodic orbits and originates a complex orbit plus an isolated cubic resonance. The chaotic layer that appears when a general term is added to the Hamiltonian survives even after the disappearance of the unstable periodic orbit. © 1992.

Interaction potential between vortex lines for uniaxial superconductors in the London approximation

Two distinct expressions of the interaction potential between arbitrarily oriented curved vortex lines with respect to the crystal c axis are derived within the London approximation. One of these expressions is used to compute the eigenvalues of the elasticity matrix. We examine the elastic properties of the vortex chain lattice, recently proposed, concerning shearing deformation.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark-pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data. © 2000 Elsevier Science B.V.