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A generalisation of Ising-type models with symmetries of the interactions, which come from Hopf algebras is constructed. General features of such models and some examples are presented.

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We study the effect of temperature gradient on diffusion of an interstitial impurity in simple cubic lattice with the use of Langevin equation. Jump rate and diffusion coefficient as a function of temperature gradient at various temperatures are calculated.

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The Poisson structures on two-dimensional Galilei Group, classified in author’s previous paper are quantized. The dual quantum Galilei Lie algebras are found.

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We prove that the super star product on a Poisson Lie supergroup leads to the structure of quantum superalgebra (triangular Hopf superalgebra) on the super quantized enveloping algebra of the corresponding Lie superalgebra and that equivalent super star products generate isomorphic quantum superalgebras.

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It is a nontrivial problem to formulate a Poincaré invariant quantum theory, that describes the binding of two particles in a confining potential. Four attempts at such theories are discussed and subsequently used to calculate the spectrum of two particles, which are bound in an harmonic oscillator potential or in a linear potential. These theories are described by the following equations

1. The so called “Relativistic Schrödinger equation”.
2. The Klein–Gordon equation.
3. The Dirac equation.
4. RQM (Relativistic Quantum Mechanics), the author’s private theory, which is of the “quasiparticle” type.

For each of these theories the Regge trajectories are calculated, both for the linear and for the harmonic potential. Since in RQM the interaction potential is the carrier, not only of energy, but also of momentum and hence of angular momentum, the Regge slopes differ from their usual values. Along the way it is shown how confining potentials can be handled in a theory which is formulated in the momentum representation, in spite of the fact that their Fourier transforms do not exist. For other quasiparticle theories the spectrum of the relativistic harmonic oscillator has not been calculated.

abstract

Electromagnetic field in a neighbourhood of an arbitrarily moving (electric or magnetic) dipole particle is described up to \(r^1\)-terms, where \(r\) is the distance from the particle.

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In this paper a scenario admitting the participation of the right-handed vector \( V_{\rm R}\) and axial \(A_{\rm R}\) couplings with the conservation of the left-handed standard \((V, A)_{\rm L}\) couplings is considered. The research is based on the muon capture by proton. We consider muon capture at the level of the Fermi theory, whose Hamiltonian describes the four-fermion point (contact) interaction. Neutrinos are assumed to be massive and to be Dirac fermions. We propose neutrino observables, it means transverse components of the neutrino polarization, both \( T\)-odd and \( T\)-even. That would be a test verifying the participation of the \((V, A)_{\rm R}\) couplings in muon capture. The measurements of nuclear observables and of longitudinal neutrino polarization do not offer such possibilities because of the suppressing of interferences between the \((V, A)_{\rm L}\) and \((V, A)_{\rm R}\) couplings caused by the neutrino mass. Using the current data from \(\mu \)-decay and inverse \(\mu \)-decay, the magnitude of effects coming from the transverse components of the neutrino polarization can be determined. Our considerations are model-independent. We give the lower bound of \(305\; {\rm GeV}\) on the mass of the right-handed gauge boson. This limit is compatible with the current bounds on the mass of the \(W_{\rm R}\) received from the weak interaction processes at low energy.

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The perturbative QCD predictions for the small \(x\) behaviour of the nucleon spin structure functions is discussed. The role of the resummation of the \(\ln ^2 1/x\) terms is emphasized. Predictions for the nonsinglet structure function \(g_1\) in case of a flat as well as a dynamical input are given.

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We discuss the meaning of anomalous vector boson self couplings. Implications of present experimental constraints for future colliders are discussed. Results for triple vector boson production at the LHC are given.

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Multiple production of Higgs particles is essential to study Higgs self-couplings at future high-energy colliders. In this paper we calculated the resonance contributions to the production of three lightest neutral supersymmetric Higgs bosons in gluon fusion at LHC. The cross sections due to trilinear Higgs couplings is sizeable but the measurement of the quartic coupling \(\lambda _{hhhH(h)}\) seems to be impossible.

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A four-neutrino effective texture is described, where a sterile neutrino mixes nearly maximally with the electron neutrino and so, it is responsible for the deficit of solar \(\nu _e \)’s (according to the large-angle MSW solution or vacuum solution, of which the latter is selected a posteriori). But, while maximal mixing of muon neutrino with tauon neutrino causes the deficit of atmospheric \(\nu _\mu \)’s, the original magnitude of LSND effect is reduced by as much as four orders, becoming unobservable.

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Using the known experimental data for the hyperon semileptonic decay constants, we calculate integrated polarized quark densities \(\Delta q_{\mit \Lambda }\) and \(\Delta {\mit \Sigma }_{\mit \Lambda }\) for the hyperon \({\mit \Lambda }\) with flavor SU(3) symmetry breaking taken into account. Symmetry breaking is implemented with the help of the chiral quark-soliton model in such a way that the dynamical parameters in the model are fixed by the experimental data for six hyperon semileptonic decay constants. This parametrization allows us to reproduce the first moment of the \(g_1^{{ p}}(x)\) of the proton. For the \({\mit \Lambda }\) we obtain: \(\Delta u_{{\mit \Lambda }}=\Delta d_{{\mit \Lambda }} \approx 0\) and \(\Delta s_{{\mit \Lambda }}\) of the order of 1. Unfortunately large experimental uncertainties of the \({\mit \Xi }^-\) decays propagate in our analysis, in particular, in the case of \(\Delta {\mit \Sigma }_{{\mit \Lambda }}\) and \(\Delta s_{{\mit \Lambda }}\), where they amount in the end to the errors of more than 50%. Only if the errors for these decays are reduced, accurate theoretical predictions for \(\Delta {\mit \Sigma }_{{\mit \Lambda }}\) and \(\Delta s_{{\mit \Lambda }}\) will be possible.

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The Heavy Ion (HI) interaction potential between spherical and deformed nuclei is improved by calculating its exchange part using finite range nucleon–nucleon (NN) force. We considered U\(^{238}\) as a target nucleus and seven projectile nuclei to show the dependence of the HI potential on both the energy and orientation of the deformed target nucleus. The effect of finite range NN force has been found to produce significant changes in the HI potential. The variation of the barrier height \(V_{\rm B}\), its thickness and its position \(R_{\rm B}\) due to the use of finite range NN force are significant. Such variation enhance the fusion cross-section at energy values just below the Coulomb barrier by a factor increasing with the mass number of projectile nucleus.

abstract

The Elastic Model of two free parameters \(m, d\) given by Scalia has been used for wider energy regions to fit the available experimental data for potential barriers and cross sections. In order to generalize Scalia’s formula in both sub- and above-barrier regions, we calculated \(m\,,d \) for pairs rather than those given by Scalia and compared the calculated cross sections with the experimental data. This makes a generalization of the Elastic Model in describing fusion process. On the other hand, Scalia’s range of interacting systems was \(24\leq A\leq 194\) where \(A\) is the compound nucleus mass number. Our extension of that model includes an example of the pairs of \(A\) larger than his final limit aiming to make it as a general formula for any type of reactants: light, intermediate or heavy systems. A significant point is the comparison of Elastic Model calculations with the well known methods studying complete fusion and compound nucleus formation, namely with the resultants of using Proximity potential with either Sharp or Smooth cut-off approximations.

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The target-like fragment excitation energy in \(^{40}\)Ar (9.5 MeV/nucleon) +\(^{159}\)Tb reaction has been obtained by applying a neutron evaporation calculation to data resulting from coincidence measurements of projectile-like fragments and neutrons. The comparison between the data and results of statistical evaporation simulations with different assumptions of the excitation energy sharing between the reaction partners confirms an equal temperature hypothesis in describing of fragment heating.

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The neutron–proton pairing correlations have been analysed in comparison with like-nucleon correlations by means of the elementary method based on the group theory treatment. Analytical formulae allow to compare the contribution of the neutron–proton interaction only, which is in several cases the main ingredient of the total pairing interaction. The obtained formulae have also been applied to the binding energy (the congruence energy).

abstract

The transverse mass and rapidity spectra of participant protons and negative pions in central C+C and C+Ta collisions at 4.2\(A\) GeV/\(c\), have been interpreted, in the full phase space, on the basis of thermal model with assumption that several fireballs in relative motion are formed, and that each fireball represents a mixture of ideal relativistic gases of protons, pions and \({\mit \Delta }\) resonances in thermal equilibrium. For adequate description of the particle spectra, the stopping and symmetry/asymmetry of the colliding system require three fireballs (two fragmentation and one central) in the case of C+C and two fireballs (fragmentation and central) in the case of C+Ta. By using the classical regime, we find that regardless of the colliding system, the freeze-out temperature of the fragmentation (central) fireballs is in the range 65–75 MeV (170–180 MeV), while the average relative velocity of the fragmentation fireball(s), with respect to the central one, is (0.55–0.60)\(c\). Also, we find that (20–30)% of protons and (50–60)% of negative pions originate from \({\mit \Delta }\) resonance decays.

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The rearrangement contribution to the real part of the single particle potential of a \({\mit \Sigma }\) hyperon in nuclear matter, \(U_{\mit \Sigma }\), is investigated. The isospin and spin dependent parts of \(U_{\mit \Sigma }\) are considered. Results obtained for four models of the Nijmegen baryon–baryon interaction are presented and discussed.