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

The scattering of a fermion in the background of a sign potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling under the Sturm-Liouville perspective. When the vector coupling and the scalar coupling have different magnitudes, an isolated solution shows that the fermion under a strong potential can be trapped in a highly localized region without manifestation of Klein's paradox. It is also shown that the lonely bound-state solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries.Comment: 4 figure

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time.Comment: 5 figures. arXiv admin note: substantial text overlap with arXiv:1310.847

Polarimetry of Li-rich giants

Protoplanetary nebulae typically present non-spherical envelopes. The origin of such geometry is still controversial. There are indications that it may be carried over from an earlier phase of stellar evolution, such as the AGB phase. But how early in the star's evolution does the non-spherical envelope appear? Li-rich giants show dusty circumstellar envelopes that can help answer that question. We study a sample of fourteen Li-rich giants using optical polarimetry in order to detect non-spherical envelopes around them. We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in V band. Foreground polarization was estimated using the field stars in each CCD frame. After foreground polarization was removed, seven objects presented low intrinsic polarization (0.19 - 0.34)% and two (V859 Aql and GCSS 557) showed high intrinsic polarization values (0.87 - 1.16)%. This intrinsic polarization suggests that Li-rich giants present a non-spherical distribution of circumstellar dust. The intrinsic polarization level is probably related to the viewing angle of the envelope, with higher levels indicating objects viewed closer to edge-on. The correlation of the observed polarization with optical color excess gives additional support to the circumstellar origin of the intrinsic polarization in Li-rich giants. The intrinsic polarization correlates even better with the IRAS 25 microns far infrared emission. Analysis of spectral energy distributions for the sample show dust temperatures for the envelopes tend to be between 190 and 260 K. We suggest that dust scattering is indeed responsible for the optical intrinsic polarization in Li-rich giants. Our findings indicate that non-spherical envelopes may appear as early as the red giant phase of stellar evolution.Comment: to be published in A&A, 15 pages, 10 figures. Fig. 3 is available in ftp://astroweb.iag.usp.br/pub/antonio/4270/4270.fig3.pd

The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach

We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three-vortices system on the symmetric ellipsoid is non-integrable.Comment: 14 pages, 1 figur