Exercises B pdf

Exercises and solutions in PDF

NUCLEAR INTERACTIONS: THE CHIRAL PICTURE

Chiral expansions of the two-pion exchange components of both two- and three-nucleon forces are reviewed and a discussion is made of the predicted pattern of hierarchies. The strength of the scalar-isoscalar central potential is found to be too large and to defy expectations from the symmetry. The causes of this effect can be understood by studying the nucleon scalar form factor.

Supersymmetric 3-3-1 model with right-handed neutrinos

We consider the supersymmetric extension of the 3-3-1 model with right-handed neutrinos. We study the mass spectra in the scalar and pseudoscalar sectors, and for a given set of the input parameters, we find that the lightest scalar in the model has a mass of 130 GeV and the lightest pseudoscalar has mass of 5 GeV. However, this pseudoscalar decouples from the Z(0) at high energy scales since it is almost a singlet under SU(2)(L)circle timesU(1)(Y).

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.

Warm asymmetric matter in the quark-meson coupling model

In this work we study the warm equation of state of asymmetric nuclear matter in the quark-meson coupling model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar, vector, and isovector mesons. Mechanical and chemical instabilities are discussed as a function of density and isospin asymmetry. The binodal section, essential in the study of the liquid-gas phase transition is also constructed and discussed. The main results for the equation of state are compared with two common parametrizations used in the nonlinear Walecka model and the differences are outlined.

A new algorithm for the relationship between vision and ametropia

Refraction simulators used for undergraduate training at Aston University did not realistically reflect variations in the relationship between vision and ametropia. This was because they used an algorithm, taken from the research literature, that strictly only applied to myopes or older hyperopes and did not factor in age and pupil diameter. The aim of this study was to generate new algorithms that overcame these limitations. Clinical data were collected from the healthy right eyes of 873 white subjects aged between 20 and 70 years. Vision and refractive error were recorded along with age and pupil diameter. Re-examination of 34 subjects enabled the calculation of coefficients of repeatability. The study population was slightly biased towards females and included many contact lens wearers. Sex and contact lens wear were, therefore, recorded in order to determine whether these might influence the findings. In addition, iris colour and cylinder axis orientation were recorded as these might also be influential. A novel Blur Sensitivity Ratio (BSR) was derived by dividing vision (expressed as minimum angle of resolution) by refractive error (expressed as a scalar vector, U). Alteration of the scalar vector, to account for additional vision reduction due to oblique cylinder axes, was not found to be useful. Decision tree analysis showed that sex, contact lens wear, iris colour and cylinder axis orientation did not influence the BSR. The following algorithms arose from two stepwise multiple linear regressions: BSR (myopes) = 1.13 + (0.24 x pupil diameter) + (0.14 x U) BSR (hyperopes) = (0.11 x pupil diameter) + (0.03 x age) - 0.22 These algorithms together accounted for 84% of the observed variance. They showed that pupil diameter influenced vision in both forms of ametropia. They also showed the age-related decline in the ability to accommodate in order to overcome reduced vision in hyperopia.

The influence on unaided vision of age, pupil diameter and spherocylindrical refractive error

Background - The aim was to derive equations for the relationship between unaided vision and age, pupil diameter, iris colour and sphero-cylindrical refractive error. Methods - Data were collected from 663 healthy right eyes of white subjects aged 20 to 70 years. Subjective sphero-cylindrical refractive errors ranged from -6.8 to +9.4 D (mean spherical equivalent), -1.5 to +1.9 D (orthogonal component, J0) and -0.8 to 1.0 D (oblique component, J45). Cylinder axis orientation was orthogonal in 46 per cent of the eyes and oblique in 18 per cent. Unaided vision (-0.3 to +1.3 logMAR), pupil diameter (2.3 to 7.5 mm) and iris colour (67 per cent light/blue irides) was recorded. The sample included mostly females (60 per cent) and many contact lens wearers (42 per cent) and so the influences of these parameters were also investigated. Results - Decision tree analysis showed that sex, iris colour, contact lens wear and cylinder axis orientation did not influence the relationship between unaided vision and refractive error. New equations for the dependence of the minimum angle of resolution on age and pupil diameter arose from step backwards multiple linear regressions carried out separately on the myopes (2.91.scalar vector +0.51.pupil diameter -3.14 ) and hyperopes (1.55.scalar vector + 0.06.age – 3.45 ). Conclusion - The new equations may be useful in simulators designed for teaching purposes as they accounted for 81 per cent (for myopes) and 53 per cent (for hyperopes) of the variance in measured data. In comparison, previously published equations accounted for not more than 76 per cent (for myopes) and 24 per cent (for hyperopes) of the variance depending on whether they included pupil size. The new equations are, as far as is known to the authors, the first to include age. The age-related decline in accommodation is reflected in the equation for hyperopes.

Relativistic effects of mixed vector-scalar-pseudoscalar potentials for fermions in 1+1 dimensions

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar Poschl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases.

Stationary states of fermions in a sign potential with a mixed vector-scalar coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Studies on Pseudoscalar Meson Bound States and Semileptonic Decays in a Relativistic Potential Model

In this thesis quark-antiquark bound states are considered using a relativistic two-body equation for Dirac particles. The mass spectrum of mesons includes bound states involving two heavy quarks or one heavy and one light quark. In order to analyse these states within a unified formalism, it is desirable to have a two-fermion equation that limits to one body Dirac equation with a static interaction for the light quark when the other particle's mass tends to infinity. A suitable two-body equation has been developed by Mandelzweig and Wallace. This equation is solved in momentum space and is used to describe the complete spectrum of mesons. The potential used in this work contains a short range one-gluon exchange interaction and a long range linear confining and constant potential terms. This model is used to investigate the decay processes of heavy mesons. Semileptonic decays are more tractable since there is no final state interactions between the leptons and hadrons that would otherwise complicate the situation. Studies on B and D meson decays are helpful to understand the nonperturbative strong interactions of heavy mesons, which in turn is useful to extract the details of weak interaction process. Calculation of form factors of these semileptonic decays of pseudo scalar mesons are also presented.

Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2004 Elsevier B.V. All rights reserved.

Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V-v = V-s + constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time

The problem of confinement of fermions in 1 + 1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V(v) + V(s) = constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.

Pseudospin and spin symmetries in 1+1 dimensions: the case of the Coulomb potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)