Investigation of the effective interaction by means of a modified shell model

The effective InteractionU for a shell model with hamiltonianH _m is investigated by means of a “mixed” model with hamiltonianH _m . For this model the Bornv. Neumann expansion of the effective interaction? reduces to its first two terms. Within the finite dimensional function space ? _n used in the shell model calculation the operatorsU and? are exactly equivalent. This is used to show that an energy independent approximation forU- if it is possible at all-is necessarily equal to the residual interaction, i.e. to the difference between nucleon-nucleon interaction and shell model interaction.     

An eikonal line-integral model and factorization in QCD

We study an approximation to perturbative QCD in which all quarks (active and spectator) move along eikonal lines. These eikonal lines are described by matrix operatorsU defined by time-ordered and path-ordered integrals. All known examples of Bloch-Nordsieck cancellations follow simply from the unitary properties ofU. In particular, when the eikonal lines are space-like, the time-ordering can be omitted and the unitarity ofU is evident. In this model, it is possible to examine rather explicitly the soft and very-soft gluons whose effects must cancel if factorization is hold (to leading twist). We can show such cancellation if there is a smooth continuation from space-like eikonal lines to time-like ones. We give some examples relevant to this conjecture, but we are unable to prove it in general.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.     

Quantum group invariant integrable n-state models with periodic boundary conditions

Using the methods of topological quantum field theory we construct aU _q [sl(n)] invariant integrable transfer matrix for the case ofq being a root of unity. It corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. its interior. By means of the nested Bethe ansatz method we analyse conformai properties and discuss the representational content of the Bethe ansatz solutions.     

A remark on a theorem of Powers and Sakai

Given an abelian locally compact groupG and aC*-algebra with unit,U, the set of those continuous representations ofG by automorphisms ofU which fulfill a spectrum condition is closed.     

Kondo lattice state within the slave boson approach: spin-split masses and effective interaction among heavy quasiparticles

We provide a brief overview of our Hamiltonian approach to the the Kondo-lattice state at both finite Coulomb interaction U and nonzero applied magnetic field. In the mean-field approximation we introduce the spindependent effective masses, as well as calculate the effective Kondo (hybridization) temperature as a function of U. The effective interaction coming from the slave-boson exchange is shown to contain both the local (intraband) pairing and the Kondo (interband) interaction.     

Formation of heavy quasiparticles and singlet superconductivity in the periodic Anderson model

The periodic Anderson model is investigated by the method of equations of motion for the symmetric case. The narrowing of the central peak in the density of states with an increase of Coulomb correlation energyU is derived and the resulting enhancement of the effective mass is scaled by the hybridization strength asV ^–4. An intersite pairing is allowed forf electrons and a Green function for the superconducting state is calculated. One can conclude that the conduction electron mediatedf-f interaction, which manifests itself as an effective pairing mechanism, supports singlet superconductivity off electrons.Supported by Polish Academy of Sciences, CPBP, 01.12     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

Investigation of the50Cr(n, α)47Ti reaction atE n =14.1 MeV

The energy and angular distribution of theα-particles from the⁵⁰Cr(n, α) reaction for 14.1 MeV incident neutron energy was measured by means of a multitelescope system. The results are compared with calculations based on the statistical model of nuclear reactions including precompound processes. This comparison indicates that there is somewhat more emission of high energyα-particles than predicted from the conventional precompound model suggesting direct excitation of the lowest excited states of⁴⁷Ti. No indication is found for a reduction of the effective moment of inertia below the rigid body value. From the shape of theα-spectrum in the backward hemisphere and the known total number of levels below (U=3 MeV the level density parameters of⁴⁷Ti were determined asa=5.4±0.3 MeV^?1 andΔ=?1.9±0.2 MeV in the framework of the back-shifted Fermi-Gas model.     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

ESR- und ENDOR-Untersuchungen vonU 2-Zentren in CsCl- und CsBr-Kristallen

We report on ESR and ENDOR investigations ofU ₂ centers in CsCl and CsBr. The results of the measurements are explained by a center model, where the interstitial hydrogen atom is situated between two anions and surrounded by four Cs ions.     

The effective potential and the bound states for a class of two dimensional gauge theories

The effective potential is calculated for a two dimensionalU(N) gauge theory with scalar quarks to leading order in the 1/N expansion. If there is noφ ⁴ interaction present, the potential is unbounded from below. If theφ ⁴ interaction is present, the potential is bounded from below and there is an unbroken and a spontaneously broken symmetry phase. The bound state spectrum of the unbroken phase is very similar to that of anU(N) gauge theory without theφ ⁴ term.     

Nontrivial class of composite U(σ+μ) vector solitons

A mixed problem for the compact U(m) vector nonlinear Schrödinger model with an arbitrary sign of coupling constant is exactly solved. It is shown that a new class of solutions—composite U(σ+μ) vector solitons with inelastic interaction (changing shape without energy loss) at σ>1 and strictly elastic interaction at σ=1— exists for m≥3. These solitons are color structures consisting of σ bright and μ dark solitons (σ+μ=m) and capable of existing in both self-focusing and defocusing media. The N-soliton formula universal for attraction and repulsion is derived by the Hirota method.     

Necessity of intermediate mass scales in grand unified theories with spontaneously brokenCP invariance

It is demonstrated that the spontaneous breakdown ofCP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context ofSU(2)_L×SU(2)_R×U(1) _B?L model embedded in grand unified theories.     

Self-trapping of interacting electrons in crystalline nonlinear chains

Considering the nonlinearity arising from the interaction between electrons and latticevibrations, an effective electronic model with a self-interaction cubic term is employedto study the interplay between electron-electron and electron-phonon interactions. Basedon numerical solutions of the time-dependent nonlinear Schroedinger equation for aninitially localized two-electron singlet state, we show that the magnitude of theelectron-phonon coupling χ necessary to promote the self-trapping of theelectronic wave packet decreases as a function of the electron-electron interactionU. We show that such dependence is directly linked to the narrowing ofthe band of bounded two-electron states as U increases. We obtain thetransition line in the χ × U parameter space separatingthe phases of self-trapped and delocalized electronic wave packets. The present resultsindicates that nonlinear contributions plays a relevant role in the electronic wave packetdynamics, particularly in the regime of strongly correlated electrons.     

Reentrant phase transition in granular superconductors

The conditions for the appearance of a reentrant superconducting phase in granular materials are studied in mean field approximation applied to periodic models. We assume that the relevant low-lying excitation is the transfer of a Cooper pair from a grain to one of its neighbours, and neglect pair breaking. Both on-grain (U) and nearest neighbour (V) Coulomb interactions are taken into account, and the Coulomb problem is treated in Bethe-Peierls approximation. WhenV/U is not too large, reentrance is predicted ifV/U>(4+3z)^?1/2 wherez is the coordination number. This result is different from a recent criterion suggested by ?imánek, which allows reentrance only in the immediate vicinities of certain discrete values ofV/U. For strong enoughV/U, the models treated here show a transition to an ionic-salt-like charge-ordered state. Reentrant superconductivity is shown to occur also on an ionic background. In actual systems, close-packing effects partially frustrate the ionic ordering and enhance the reentrant feature.