Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime

The problem of scattering of neutral fermions in two-dimensional spacetime is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein's paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given. (C) 2003 Elsevier B.V. B.V. All rights reserved.

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.

Bounded solutions of neutral fermions with a screened Coulomb potential

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength. (c) 2005 Elsevier B.V. All rights reserved.

Trapping neutral fermions with kink-like potentials

The intrinsically relativistic problem of neutral fermions subject to kink-like potentials (similar to tanh gamma x) is investigated and the exact bound-state solutions are found. Apart from the lonely hump solutions for E = +/- mc(2), the problem is mapped into the exactly solvable Sturm-Liouville problem with a modified Poschl-Teller potential. An apparent paradox concerning the uncertainty principle is solved by resorting to the concepts of effective mass and effective Compton wavelength. (c) 2005 Elsevier 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.

Sobre o limiar para a produção de pares e localização de partículas sem spin

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Missing solution in a Cornell potential

Missing bound-state solutions for fermions in the background of a Cornell potential consisting of a mixed scalar-vector-pseudoscalar coupling is examined. Charge-conjugation operation, degeneracy and localization are discussed. © 2013 Elsevier Inc.

Estados ligados em mecânica quântica relativística

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of a mixed vector-scalar kink-like potential for spinless particles in two-dimensional space time

The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink- like potentials (similar to tanh gamma x) is investigated. The problem is mapped into the exactly solvable Sturm - Liouville problem with the Rosen - Morse potential and exact bounded solutions for particles and antiparticles are found. The behavior of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.

Jeans instability criterion modified by external tidal field

The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an external field such as the tidal field due to a neighbour. Here, we do a linear perturbation analysis for a system in an external field and obtain a generalized dispersion relation that depends on the wavenumber, the sound speed and also the magnitude of the tidal field. A typical, disruptive tidal field is shown to make the system more stable against perturbations, and results in a higher effective Jeans wavelength. The minimum mass that can become unstable is then higher (super-Jeans) than the usual Jeans mass. Conversely, in a compressive tidal field, perturbations can grow even when the mass is lower (sub-Jeans). This approach involving the inclusion of tidal field opens up a new way of looking at instabilities in gravitating systems. The treatment is general and the simple analytical form of the modified Jeans criterion obtained makes it easily accessible.

LINEAR ACCELERATION EMISSION IN PULSAR MAGNETOSPHERES

Linear acceleration emission occurs when a charged particle is accelerated parallel to its velocity. We evaluate the spectral and angular distribution of this radiation for several special cases, including constant acceleration (hyperbolic motion) of finite duration. Based on these results, we find the following general properties of the emission from an electron in a linear accelerator that can be characterized by an electric field E acting over a distance L: (1) the spectrum extends to a cutoff frequency (h) over bar omega(c)/mc(2) approximate to L(E/E(Schw))(2)/(lambda) over bar (C), where E(Schw) = 1.3 x 10(18) V m(-1) is the Schwinger critical field and (lambda) over bar (C) = (h) over bar /mc = 3.86 x 10(-13) m is the Compton wavelength of the electron, (2) the total energy emitted by a particle traversing the accelerator is 4/3 alpha(f)(h) over bar omega(c) in accordance with the standard Larmor formula where alpha(f) is the fine-structure constant, and (3) the low frequency spectrum is flat for hyperbolic trajectories, but in general depends on the details of the accelerator. We also show that linear acceleration emission complements curvature radiation in the strongly magnetized pair formation regions in pulsar magnetospheres. It dominates when the length L of the accelerator is less than the formation length rho/gamma of curvature photons, where rho is the radius of curvature of the magnetic field lines and gamma the Lorentz factor of the emitting particle. In standard static models of pair creating regions linear acceleration emission is negligible, but it is important in more realistic dynamical models in which the accelerating field fluctuates on a short length scale.

Sobre interações escalares e vetoriais na teoria de Duffin-Kemmer-Petiau

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Determinação de conservantes e contaminantes em alimentos e bebidas por Eletroforese capilar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

The long wavelength limit of hard thermal loop effective actions

We derive a closed form expression for the long wavelength limit of the effective action for hard thermal loops in an external gravitational field. It is a function of the metric, independent of time derivatives. It is compared and contrasted with the static limit, and with the corresponding limits in an external Yang-Mills field. (C) 2009 Elsevier B.V. All rights reserved.