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L. Wilets

Publications and source records attributed to L. Wilets.

18 recordsLinked to original sources
arXiv2005

Coordinates, modes and maps for the density functional

Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary perturbation by an external field can be inverted to generate a mapping between density and potential. Information is obtained for derivatives of the Hohenberg-Kohn functional in density space. A truncation of such an information in subspaces spanned by a few modes is possible. Numerical examples illustrate these algorithms.

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arXiv1999

Effect of Screening on Thermonuclear Fusion in Stellar and Laboratory Plasmas

The fusion enhancement factor due to screening in the solar plasma is calculated. We use the finite temperature Green's function method and a self consistent mean field approximation. We reduce this to one center problems, because in the collision of two fusing ions, the turning point where tunneling may occur lies far inside the screening radius. The numerical results given by this method indicate that screening may be slightly weaker than that obtained in the most recent previous calculations.

astro-ph↗
arXiv1997

Ghost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems

Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pion-nucleon scattering using "dressed" nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A+ is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear-sigma model and study the interplay of low-energy theorems for pion-nucleon scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A+ value is badly described. As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved. In order to fix the two cutoff parameters, we use the A+ value for the chiral limit (m_pion -> 0) and the experimental value of the isoscalar scattering length. Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold.

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arXiv1996

New approach to $^4$He charge distribution

We present a study of the $^4$He charge distribution based on realistic nucleonic wave functions and incorporation of the nucleon's quark substructure. The central depression of the proton point density seen in modern four-body calculations is too small by itself to lead to a correct description of the charge distribution. We utilize six-quark structures calculated in the Chromodielectric Model for N-N interactions, and we find a swelling of the proton charge distribution as the internucleon distance decreases. These charge distributions are combined with the $^4$He wave function using the Independent Pair Approximation and two-body distributions generated from Green's Function Monte Carlo calculations. We obtain a reasonably good fit to the experimental charge distribution without including meson exchange currents.

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arXiv1996

Ghost poles and chiral symmetry in $πN$ scattering

We solve the Schwinger-Dyson equation for the nucleon propagator in the vacuum using $π$, $σ$, and $ω$ mesons. For bare interaction vertices (Hartree-Fock approximation) we obtain a pair of complex-conjugated poles (ghost poles) and for vertices dressed by phenomenological form-factors these ghosts disappeared. We use these two different approaches to evaluate the scattering lengths and the phase shifts for the $πN$ scattering at threshold. Our results show that only when the form factors are present is possible to obtain a good agreement with the low-energy observables.

hep-ph↗
arXiv1996

The Chromo-Dielectric Soliton Model: Quark Self Energy and Hadron Bags

The chromo-dielectric soliton model (CDM) is Lorentz- and chirally-invariant. It has been demonstrated to exhibit dynamical chiral symmetry breaking and spatial confinement in the locally uniform approximation. We here study the full nonlocal quark self energy in a color-dielectric medium modeled by a two parameter Fermi function. Here color confinement is manifest. The self energy thus obtained is used to calculate quark wave functions in the medium which, in turn, are used to calculate the nucleon and pion masses in the one gluon exchange approximation. The nucleon mass is fixed to its empirical value using scaling arguments; the pion mass (for massless current quarks) turns out to be small but non-zero, depending on the model parameters.

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arXiv1996

The "Hole" In He

The measurement and analysis of electron scattering from He-3 and He-4 by Sick and collaborators reported 20 years ago remains a matter of current interest. By unfolding the measured free-proton charge distribution, they deduced a depression in the central point nucleon density, which is not found in few-body calculations based on realistic potentials. We find that using wave functions from such calculations we can obtain good fits to the He charge distributions under the assumption that the proton charge size expands toward the center of the nucleus. The relationship to 6-quark Chromo-Dielectric Model calculations, is discussed. The expansion is larger than than the predictions of mean field bag calculations by others or our CDM calculations in the independent pair approximation. There is interest here in the search for a "smoking gun" signal of quark substructure.

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arXiv1995

The Nucleon-Nucleon Interaction in the Chromo-Dielectric Soliton Model: Dynamics

The present work is an extension of a previous study of the nucleon-nucleon interaction based on the chromo-dielectric soliton model. The former approach was static, leading to an adiabatic potential. Here we perform a dynamical study in the framework of the Generator Coordinate Method. In practice, we derive an approximate Hill-Wheeler differential equation and obtain a local nucleon-nucleon potential as a function of a mean generator coordinate. This coordinate is related to an effective separation distance between the two nucleons by a Fujiwara transformation. This latter relationship is especially useful in studying the quark substructure of light nuclei. We investigate the explicit contribution of the one-gluon exchange part of the six-quark Hamiltonian to the nucleon-nucleon potential, and we find that the dynamics are responsible for a significant part of the short-range N-N repulsion.

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arXiv1995

QUARK MODEL DESCRIPTION OF THE N-N SYSTEM: MOMENTUM DISTRIBUTIONS, STRUCTURE FUNCTIONS AND THE EMC EFFECT

We employ a relativistic quark bag picture, the chromo-dielectric soliton model, to discuss the quarks' symmetry structure and momentum distribution in the $N$-$N$ system. Six-quark clusters are constructed in a constrained mean-field calculation. The corresponding Hamiltonian contains not only an effective interaction between the quarks and a scalar field, which is assumed to parameterize all non-perturbative effects due to the non-linearity of QCD, but also quark-quark interactions mediated through one-gluon-exchange. We also evaluate the quark light-cone distribution functions, characterizing inclusive deep-inelastic lepton scattering, for the nucleon as well as for the six-quark structures. We find a competition between a softening of the quarks' momenta through the increase of the confinement volume, and a hardening via the admixture of higher symmetry configurations due to the color-electrostatic one-gluon-exchange. These findings suggest an unexpected absence of many-nucleon, multi-quark effects, even though six-quark structures should represent a non-negligible part of the nuclear ground state.

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arXiv1994

Collapse of Flux Tubes

The dynamics of an idealized, infinite, MIT-type flux tube is followed in time as the interior evolves from a pure gluon field to a $\overline q \ q$ plasma. We work in color U(1). $\overline q\ q$ pair formation is evaluated according to the Schwinger mechanism using the results of Brink and Pavel. The motion of the quarks toward the tube endcaps is calculated by a Boltzmann equation including collisions. The tube undergoes damped radial oscillations until the electric field settles down to zero. The electric field stabilizes the tube against pinch instabilities; when the field vanishes, the tube disintegrates into mesons. There is only one free parameter in the problem, namely the initial flux tube radius, to which the results are very sensitive. Among various quantities calculated is the mean energy of the emitted pions.

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arXiv1994

The Nucleon-Nucleon Potential in the Chromo-Dielectric Soliton Model: Statics

We study the N-N interaction in the framework of the chromo-dielectric soliton model. Here, the long-range parts of the nonabelian gluon self-interactions are assumed to give rise to a color-dielectric function which is parameterized in terms of an effective scalar background field. The six-quark system is confined in a deformed mean field through an effective non-linear interaction between the quarks and the scalar field. The CDM is covariant, respects chiral invariance, leads to absolute color confinement and is free of the spurious long range Van der Waals forces which trouble non-relativistic investigations employing a confining potential. Six-quark molecular-type configurations are generated as a function of deformation and their energies are evaluated in a coupled channel analysis. By using molecular states instead of cluster model wave functions, all important six-quark configurations are properly taken into account. The corresponding Hamiltonian includes the effective interaction between the quarks and the scalar background field and quark-quark interactions generated through one gluon exchange treated in Coulomb gauge. When evaluating the gluonic propagators, the inhomogeneity and deformation of the dielectric medium are taken into account. Results for the adiabatic nucleon-nucleon potential are presented, and the various contributions are discussed. Finally, an outlook is given on how, in the next stage of our investigation, the dynamical effects will be incorporated by employing the generator coordinate method.

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arXiv1993

A Quark Model of Lambdabar-Lambda Production of Pbar-P Interactions

A quark model which includes both scalar and vector contributions to the reaction mechanism (SV quark model) is used in a DWBA calculation of $\bar ΛΛ$ production in $\bar p p$ interractions. Total and differential cross-sections, polarizations, depolarizations, and spin-correlattion coefficients are computed for laboratory momenta from threshold to 1695 MeV/c. The free parameters of the calculation are the scalar and vector strengths, a quark cluster size parameter,and the parameters of the unknown $\bar ΛΛ$ potentials. Good agreement with experiment is found for constructive interference of the scalar and vector terms, and for $\bar ΛΛ$ potentials which differ from those suggested by several authors on the basis of SU(3) arguments. The fit to the data is better than that obtained by other quark models, which use only scalar $or$ vector annihilation terms. The agreement with experiment is also better than that found in meson-exchange models. The recent suggestion[1] that measurement of the depolarization parameter $D_{nn}$ can be used to discriminatebetween meson-exchange and quark models is examined in detail. We conclude that a measurement of $D_{nn}$ will provide a test of which of these models, as presently constructed,is the more appropriate description of strangeness production in the $\bar p p \ rightarrow \bar ΛΛ$ reaction.

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arXiv1993

Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

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arXiv1993

Semi-Classical Description of Antiproton Capture on Atomic Helium

A semi-classical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on Helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular momentum states of incident antiprotons which result in capture via single or double electron ionization, i.e. into [He$^{++}\,\bar p$ or He$^{+}\,\bar p$], and the distribution of energy and angular momentum states following the Auger cascade. These final states are discussed in light of recently reported, anomalously long-lived antiproton states observed in liquid He.

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arXiv1993

Ghost Poles in the Nucleon Propagator: Vertex Corrections and Form Factors

Vertex corrections are taken into account in the Schwinger-Dyson equation for the nucleon propagator in a relativistic field theory of fermions and mesons. The usual Hartree-Fock approximation for the nucleon propagator is known to produce the appearance of complex (ghost) poles which violate basic theorems of quantum field theory. In a theory with vector mesons there are vertex corrections that produce a strongly damped vertex function in the ultraviolet. One set of such corrections is known as the Sudakov form factor in quantum electrodynamics. When the Sudakov form factor generated by massive neutral vector mesons is included in the Hartree-Fock approximation to the Schwinger-Dyson equation for the nucleon propagator, the ghost poles disappear and consistency with basic requirements of quantum field theory is recovered.

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arXiv1993

A Quark Model of Antilambda-Lambda Production in Pbar-P Interactions

A quark model which includes both scalar and vector contributions to the reaction mechanism is used in a DWBA calculation of total and differential cross-sections, polarizations, and spin correlation coefficients for the reaction $\bar p p \rightarrow \bar ΛΛ$ at laboratory momenta from threshold to 1.92 GeV/c. The free parameters of the calculation include the scalar and vector strengths, a quark cluster size parameter, and six parameters in the unknown $\bar ΛΛ$ interaction. Excellent agreement with experiment is found for a constructive interference of scalar and vector terms, and for a $\bar ΛΛ$ potential which differs from that suggested by several authors on the basis of SU(3) arguments. The fit to the data is better than that obtained by other quark models, which use only scalar or vector annihilation terms. The agreement with experiment is as good as that found in meson-exchange models, which use more parameters than the present calculation.

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arXiv1992

Atomic Parity Nonconservation: Electroweak Parameters and Nuclear Structure

There have been suggestions to measure atomic parity nonconservation (PNC) along an isotopic chain, by taking ratios of observables in order to cancel complicated atomic structure effects. Precise atomic PNC measurements could make a significant contribution to tests of the Standard Model at the level of one loop radiative corrections. However, the results also depend upon certain features of nuclear structure, such as the spatial distribution of neutrons in the nucleus. To examine the sensitivity to nuclear structure, we consider the case of Pb isotopes using various recent relativistic and non-relativistic nuclear model calculations. Contributions from nucleon internal weak structure are included, but found to be fairly negligible. The spread among present models in predicted sizes of nuclear structure effects may preclude using Pb isotope ratios to test the Standard Model at better than a one percent level, unless there are adequate independent tests of the nuclear models by various alternative strong and electroweak nuclear probes. On the other hand, sufficiently accurate atomic PNC experiments would provide a unique method to measure neutron distributions in heavy nuclei.

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