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 boundstate solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries.

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 chiralconjugation 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.

Measurements of di-hadron azimuthal correlations at different centralities for Au+Au collisions at 200 AGeV were reported by the PHENIX Collaboration. The data were presented for different ranges of transverse momentum. In particular, it was observed that the away-side correlation evolves from double-to a single-peak structure when the centrality decreases. In this work, we show that these features naturally appear as due to an interplay between the centrality-dependent smooth background elliptic flow and the one produced by event-by-event fluctuating peripheral tubes. To compare with the PHENIX data, we also carry out numerical simulations by using a hydrodynamical code NeXSPheRIO, and calculate the correlations by both cumulant and the ZYAM method employed by PHENIX Collaboration. It is shown that our results are in reasonable agreement with the data. A brief discussion on the physical content of the present model and its difference from other viewpoint is also presented.

In this work, a hydrodynamic study of the di-hadron azimuthal correlations for the Au+Au collisions at 200 GeV is carried out. The correlations are evaluated using the ZYAM method for the centrality windows as well as the transverse momentum range in accordance with the existing data. Event-plane dependence of the correlation is obtained after the subtraction of contributions from the most dominant harmonic coefficients. In particular, the contribution from the triangular flow, v 3 , is removed from the proper correlations following the procedure implemented by the STAR collaboration. The resultant structure observed in the correlations was sometimes attributed to the mini-jet dynamics, but the present calculations show that a pure hydrodynamic model gives a reasonable agreement with the main feature of the published data. A brief discussion on the physical content of the present findings is presented.

In this work, we study the two-particle correlations regarding a peripheral tube model. From our perspective, the main characteristics of the observed two-particle correlations are attributed to the multiplicity fluctuations and the locally disturbed one-particle distribution associated with hydrodynamic response to the geometric fluctuations in the initial conditions. We investigate the properties of the initial conditions and collective flow concerning the proposed model. It is shown that the experimental data can be reproduced by hydrodynamical simulations using appropriately constructed initial conditions. Besides, instead of numerical calibration, we extract the model parameters according to their respective physical interpretations and show that the obtained numerical values are indeed qualitatively in agreement with the observed data. Possible implications of the present approach are discussed. 2